Cholik Chan

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• Li, P. W., & Chan, C. L. (2017). Thermal Energy Storage Analyses and Designs. Elsevier Inc..
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  Thermal Energy Storage Analyses and Designs considers the significance of thermal energy storage systems over other systems designed to handle large quantities of energy, comparing storage technologies and emphasizing the importance, advantages, practicalities, and operation of thermal energy storage for large quantities of energy production. Including chapters on thermal storage system configuration, operation, and delivery processes, in particular the flow distribution, flow arrangement, and control for the thermal charge and discharge processes for single or multiple thermal storage containers, the book is a useful reference for engineers who design, install, or maintain storage systems. Includes computer code for thermal storage analysis, including code flow charts. Contains a database of material properties relevant to storage. Provides example cases of input and output data for the code.

Journals/Publications

• Chan, C. L. (2023).

  Simple model for the laser powder interaction during direct metal deposition

  . Journal of Laser Applications, 35(1). doi:10.2351/7.0000907
• Chan, C. (2018). Cell transport and suspension in high conductivity electrothermal flow with negative dielectrophoresis by immersed boundary-lattice Boltzmann method. International Journal of Heat and Mass Transfer, 128, 1229-1244.
• Ren, Q., Meng, F., & Chan, C. (2019). Cell transport and suspension in high conductivity electrothermal flow with negative dielectrophoresis by immersed boundary-lattice Boltzmann method. International Journal of Heat and Mass Transfer, 128(Issue). doi:10.1016/j.ijheatmasstransfer.2018.09.062
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  The cell transport and suspension using AC electrokinetics is essential for cell patterning and other biomedical applications in microfluidics. To avoid the undue cellular stress and irreversible damage to cells caused by low conductivity media, direct manipulations of cells in physiological solution of high electrical conductivity without dilution becomes significant. The driving mechanism of alternating current electrothermal (ACET) flow makes it attractive for pumping the physiological conductivity solution and transporting cells through the electrohydrodynamic (EHD) force. In addition, negative dielectrophoresis (nDEP) force is induced on a cell when its electrical conductivity is lower than that of solution media. In this paper, the effectiveness of ACET flow and negative DEP force in high conductivity solution is novelly used simultaneously to achieve a successful long-range cell transport and suspension in the microfluidic chamber. An immersed boundary-lattice Boltzmann method (IB-LBM) is developed to investigate the cell transport and suspension mechanism with respect to AC voltage magnitude, electrical conductivities of cell and solution, cell initial position, and cell size. It is found that a sufficient DEP force is indispensable for stabilizing the cell transport process and anchoring cells by overcoming the cell-cell interaction. Based on this, the design of a lab-on-a-chip device to generate a large DEP force is essential for future research to realize an efficient AC electrokinetic-based cell transport and suspension in physiological fluids.
• Ren, Q., Wang, Y., Lin, X., & Chan, C. L. (2019). AC electrokinetic induced non-Newtonian electrothermal blood flow in 3D microfluidic biosensor with ring electrodes for point-of-care diagnostics. JOURNAL OF APPLIED PHYSICS, 126(8).
• Ren, Q., Wang, Y., Lin, X., Chan, C. L., Ren, Q., Wang, Y., Lin, X., & Chan, C. L. (2019). AC electrokinetic induced non-Newtonian electrothermal blood flow in 3D microfluidic biosensor with ring electrodes for point-of-care diagnostics. Journal of Applied Physics, 126(Issue 8). doi:10.1063/1.5099272
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  Efficient pumping of whole blood is an essential task in biomedical engineering, especially for point-of-care diagnostics using lab-on-a-chip devices. Alternating current (AC) electrokinetics have been widely used for several different applications among which pumping fluids using the precisely controlled electric field without any moving mechanical parts is significant. Due to its high conductive characteristic, it is difficult to drive the blood flow using the AC electroosmosis phenomenon because the electric double layer is highly compressed. Fortunately, the AC electrothermal (ACET) phenomenon occurs due to the variation of temperature-dependent permittivity and conductivity caused by Joule heating effects or other heat sources making it powerful for driving high electrical conductivity physiological fluids in biomedical devices. Compared with Newtonian fluids like saline solutions or urine, the non-Newtonian rheological nature and AC frequency-dependent dielectric property of blood make its ACET driving mechanism more complicated and attractive. In this paper, ACET induced blood flow in the 3D microfluidic channel is modeled by the lattice Boltzmann method accelerated using graphics processor units. The Carreau-Yasuda model is applied to simulate the shear-thinning behavior of blood flow, and its electrothermal pumping efficiency is investigated with respect to the AC electrode configuration, AC voltage magnitude, and AC signal frequency by comparing it with the ACET pumping of Newtonian fluids using scaling law analysis. The results demonstrate that the ACET phenomenon is effective for pumping non-Newtonian whole blood flow in microfluidic devices with ring electrodes which will contribute to the point-of-care diagnostic of bacterial bloodstream infections or rapid detection of circulating tumor cells.
• Ren, Q., He, Y., Su, K., & Chan, C. (2017). Investigation of the effect of metal foam characteristics on the PCM melting performance in a latent heat thermal energy storage unit by pore-scale lattice Boltzmann modeling. Numerical Heat Transfer; Part A: Applications, 72(10). doi:10.1080/10407782.2017.1412224
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  Latent heat thermal energy storage (LHTES) has many advantages such as high energy density and phase change at a nearly constant temperature compared with sensible thermal energy storage or chemical energy storage techniques. However, one of its major drawbacks is the low thermal conductivity of phase change materials (PCMs) which impedes the heat transfer efficiency. High thermal conductivity metal foams could be added into the LHTES to enhance the heat transfer speed. Under this case, the investigation of the effects of metal foam porosity and pore size on the melting process is essential for improving the heat storage capability of LHTES. In this article, a pore-scale modeling of melting process in a LHTES unit filled with metal foams is carried out by enthalpy-based multiple-relaxation-time lattice Boltzmann method. The quartet structure generation set is used to generate the morphology of metal foams. In addition, a Compute Unified Device Architecture (CUDA) Fortran code is developed in this work for executing highly parallel computation through graphics processing units. The melting process in the PCMs is investigated in terms of porosity, pore size, nonuniform metal foam, hot wall temperature, and initial subcooled temperature to optimize the design of LHTES filled with metal foams.
• Li, P., Van Lew, J., Chan, C., Karaki, W., Stephens, J., & O'Brien, J. (2016). Erratum: Corrigendum to “Similarity and generalized analysis of efficiencies of thermal energy storage systems” (Renew. Energy (2012) (39) (388–402)). Renewable Energy, 97(Issue). doi:10.1016/j.renene.2016.06.031
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  The paper, Similarity and generalized analysis of efficiencies of thermal energy storage systems, in Renewable Energy, 39 (2012), 388–402, presented a work in which the authors considered that the two fluid-solid configurations in thermal storage systems, as shown in Fig. 2 (in the paper) denoted as (a) and (b), have similarity. The authors considered that a thermal storage system that has heat transfer fluid tubes imbedded through a packed solid (or liquid), also shown clearly in Fig. 8 (in the paper), can be viewed as a case that fluid passing through a porous material as that of the configuration (a), if similarity analysis is made. Because of this similarity, the authors developed methods to introduce and find several equivalent parameters in the paper to describe the energy storage process in case (b) in the similar manner so that our method of generalized charts for analysis of energy storage effectiveness for case (a) in a previous work can be used. These equivalent parameters include equivalent porosity, equivalent heat transfer area per unit length, and effective heat transfer coefficient, as were presented in the paper. The idea of introducing the similarity parameters and analyzing a much complicate fluid-solid configuration (b) in a similar and simple method as applied to case (a) is very valuable due to the less effort needed for analysis while with no sacrifice of the accuracy. Fig. 2 (from the paper) Thermal storage tanks with the use of thermal storage medium and heat transfer fluid (HTF). (a) Filler material, such as rocks, fully submerged in flowing HTF; (b) HTF pipes passing through filler materials, such as soil, concrete, sands, or molten salts.[figure presented] Fig. 8 (from the paper) Heat transfer fluid tubes and the surrounding thermal storage material (Deq is an equivalent diameter based on the area that the cross section area of the container is divided by the number of HTF tubes.)[figure presented] The authors would like to point out here that our method of generalized charts for analysis of energy storage effectiveness for case (a) was published in a previous paper, Generalized charts of energy storage effectiveness for thermocline heat storage tank design and calibration, in Solar Energy, 85 (2011), 2130–2143, by the same group with most of the same authors. Furthermore, in order to lay the foundation for the new findings presented in Renewable Energy, 39 (2012), 388–402, text and graphics from our previous work in Solar Energy, 85 (2011), 2130–2143, were repeated without reference. Specifically, Figures 5, 6, 7, 11, 12, 13, 14 from Solar Energy, 85 (2011), 2130–2143, were duplicated in Renewable Energy, 39 (2012), 388–402. The authors regret that Solar Energy, 85 (2011), 2130–2143 was not cited in Renewable Energy, 39 (2012), 388–402 as the original source. With this corrigendum the authors wish to add the missing reference: Solar Energy, 85 (2011), 2130–2143.The authors apologize to readers this was not done prior to publication and for any inconvenience caused.
• Lu, Y., Ren, Q., Liu, T., Leung, S. L., Gau, V., Liao, J. C., Chan, C. L., & Wong, P. K. (2016). Long-range electrothermal fluid motion in microfluidic systems. International Journal of Heat and Mass Transfer, 98(Issue). doi:10.1016/j.ijheatmasstransfer.2016.03.034
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  AC electrothermal flow (ACEF) is the fluid motion created as a result of Joule heating induced temperature gradients. ACEF is capable of performing major microfluidic operations, such as pumping, mixing, concentration, separation and assay enhancement, and is effective in biological samples with a wide range of electrical conductivity. Here, we report long-range fluid motion induced by ACEF, which creates centimeter-scale vortices. The long-range fluid motion displays a strong voltage dependence and is suppressed in microchannels with a characteristic length below ∼300 μm. An extended computational model of ACEF, which considers the effects of the density gradient and temperature-dependent parameters, is developed and compared experimentally by particle image velocimetry. The model captures the essence of ACEF in a wide range of channel dimensions and operating conditions. The combined experimental and computational study reveals the essential roles of buoyancy, temperature rise, and associated changes in material properties in the formation of the long-range fluid motion. Our results provide critical information for the design and modeling of ACEF based microfluidic systems toward various bioanalytical applications.
• Ren, Q., & Chan, C. (2016). GPU accelerated numerical study of PCM melting process in an enclosure with internal fins using lattice Boltzmann method. International Journal of Heat and Mass Transfer, 100(Issue). doi:10.1016/j.ijheatmasstransfer.2016.04.059
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  Latent heat thermal energy storage (LHTES) has many applications in engineering fields such as electronic cooling, thermal storage of solar energy, heating and cooling in buildings, waste heat utilization and so on. The advantages of LHTES over sensible thermal energy storage or chemical energy storage techniques are high energy density and phase change at nearly constant temperature. Unfortunately, the low thermal conductivity of PCMs increases the thermal gradient in the energy storage system and impedes the heat transfer efficiency. However, high thermal conductivity fins could be used to promote the melting process in PCM enclosures. As a powerful numerical method developed during the past two decades, lattice Boltzmann method (LBM) was used to simulate the conjugate heat transfer in the solid walls, fins and PCM region. By changing the velocity field and diffusivities, only one distribution function was needed to simulate the melting with natural convection in PCMs and conduction in fins and enclosure surfaces. As a result, the thermal boundary conditions on the interfaces of PCMs, fins and solid walls were satisfied automatically. By using enthalpy-based multiple-relaxation-time (MRT) LBM model, the iteration steps for the latent-heat source term were avoided. Under this case, the conjugate convective heat transfer with phase change is modeled efficiently. The graphics processing units (GPU) computing becomes attractive since the advent of CUDA which includes both hardware and programming environment in 2007. Consequently, the developed MRT LBM code is further implemented to run on GPU. High computation speed was achieved. The melting process in PCMs was investigated for different materials of fins and walls, number of fins, fin configurations, hot wall temperature, thermal boundary conditions, and inclination angle of the PCM cavity. Lattice Boltzmann method implemented on GPU was demonstrated as an efficient approach to study the PCM melting process with internal fins.
• Ren, Q., & Chan, C. (2016). Numerical simulation of a 2D electrothermal pump by lattice Boltzmann method on GPU. Numerical Heat Transfer; Part A: Applications, 69(7). doi:10.1080/10407782.2015.1090826
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  Electrothermal flow in a microfluidic system is a fast-developing technology because of the advancement in micro-electro-mechanical systems. The motion is driven by the electrothermal force generated by the AC electric field and non-uniform temperature distribution inside the system. Electrothermal force can be explored for pumps in microfluidic systems. In this paper, the lattice Boltzmann method (LBM) is used to simulate a 2D electrothermal pump. As an alternative numerical method for fluid dynamics, LBM has many advantages compared with traditional CFD methods, such as its suitability for parallel computation. With its parallel characteristic, LBM is well fitted to the parallel hardware in graphic processor units (GPU). To save computational time in parametric studies, a CUDA code was developed for executing parallel computation. The comparison of computational time between CPU and GPU is presented to demonstrate the advantage of using GPU. The effects of the frequency, thermal boundary conditions, electrode size, and gap between electrodes on volumetric flow rate were investigated in this study. It was shown that LBM is an effective approach to studying 2D electrothermal pumps on a CUDA platform.
• Ren, Q., & Chan, C. L. (2016). Natural convection with an array of solid obstacles in an enclosure by lattice Boltzmann method on a CUDA computation platform. INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 93, 273-285.
• Ren, Q., & Chan, C. L. (2016). Natural convection with an array of solid obstacles in an enclosure by lattice Boltzmann method on a CUDA computation platform. International Journal of Heat and Mass Transfer, 93(Issue). doi:10.1016/j.ijheatmasstransfer.2015.09.059
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  Lattice Boltzmann method is implemented for conjugate heat transfer of a square cavity with solid obstacles. Natural convection is considered in the fluid region while conduction is assumed in the solid obstacles. By adjusting the velocity field and thermal diffusivities, only one single temperature distribution function is needed to simulate the convection in the fluid region and the heat conduction in the solid obstacles region. As a result, matching boundary conditions at the interface are automatically satisfied. The conjugate heat transfer in a rectangular enclosure of natural convection with solid obstacles is considered next. Streamlines, temperature distributions are presented for different Rayleigh numbers, thermal diffusivity ratios and number of solid blocks. The parallel characteristic of LBM is well fitted to the parallel hardware of graphic processor units (GPU) using a CUDA platform. Implementation of conjugate heat transfer LBM algorithm on GPU is presented next. It is found that GPU can accelerate the computation by a factor up to 20 as compared to the non-parallel CPU code. It is demonstrated that lattice Boltzmann method is an effective approach to simulate conjugate heat transfer with solid obstacles.
• Ren, Q., & Chan, C. L. (2016). Numerical study of double-diffusive convection in a vertical cavity with Soret and Dufour effects by lattice Boltzmann method on GPU. INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 93, 538-553.
• Ren, Q., & Chan, C. (2015). Analytical evaluation of the BEM singular integrals for 3D Laplace and Stokes flow equations using coordinate transformation. Engineering Analysis with Boundary Elements, 53(Issue). doi:10.1016/j.enganabound.2014.11.018
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  It is well-known that singular integrals arise when the source point and field point are in the same element in boundary element method. To improve the accuracy, analytical evaluation of the singular integral should be carried out whenever possible. However, the analytical formulas for the BEM singular integrals are always quite complicated in 3D problems. In this paper, by applying a coordinate transformation, the analytical formulas of the singular integrals for 3D Laplace's and Stokes flow equations are obtained for arbitrary triangular boundary elements with constant elements approximation. In addition, numerical examples will be presented to demonstrate the improvement on accuracy.
• Ren, Q., Chan, C. L., & Arvayo, A. L. (2015). A numerical study of 2D electrothermal flow using boundary element method. APPLIED MATHEMATICAL MODELLING, 39(9), 2777-2795.
• Ren, Q., Chan, C. L., & Arvayo, A. L. (2015). A numerical study of 2D electrothermal flow using boundary element method. Applied Mathematical Modelling, 39(Issue 9). doi:10.1016/j.apm.2014.11.013
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  The electrothermal flow phenomena can be applied to many microfluidic devices such as lab-on-a-chip. As a result of the small length scale in these devices, the fluid flow is characterized by a low Reynolds number thus allowing the governing equations to become linear. In this paper, a 2D numerical modeling of the electrothermal flow using boundary element method (BEM) is presented. BEM is an advantageous option for simulating the electrothermal flow. In an electrothermal flow, the volumetric body force depends on the electric field and temperature gradient. The physics is mathematically modeled by (i) Laplace's equation for the electrical potential, (ii) Poisson's equation for the heat conduction with Joule heating, and (iii) continuity and Stokes equations for the low Reynolds number flow. When using BEM to solve the equations, it is well known that a singular integral arises when the source point approaches the field point. Accurate evaluation of the singular integral is important to obtain an accurate simulation. To this end, all the singular and non-singular integrals are evaluated analytically. Consequently, an accurate algorithm is obtained. The formulation and implementation of BEM to model the electrothermal flow and the resulting electrical potential, temperature field, Joule heating and velocity field are presented in this paper.
• Xu, B., Li, P., & Chan, C. (2015). Application of phase change materials for thermal energy storage in concentrated solar thermal power plants: A review to recent developments. APPLIED ENERGY, 160, 286-307.
• Xu, B., Li, P., & Chan, C. L. (2015). Energy Storage Start-up Strategies for Concentrated Solar Power Plants With a Dual-Media Thermal Storage System. JOURNAL OF SOLAR ENERGY ENGINEERING-TRANSACTIONS OF THE ASME, 137(5).
• Xu, B., Li, P., & Chan, C. L. (2015). Energy Storage Start-up Strategies for Concentrated Solar Power Plants With a Dual-Media Thermal Storage System. Journal of Solar Energy Engineering, Transactions of the ASME, 137(Issue 5). doi:10.1115/1.4030851
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  A concentrated solar power (CSP) plant typically has thermal energy storage (TES), which offers advantages of extended operation and power dispatch. Using dual-media, TES can be cost-effective because of the reduced use of heat transfer fluid (HTF), usually an expensive material. The focus of this paper is on the effect of a start-up period thermal storage strategy to the cumulative electrical energy output of a CSP plant. Two strategies - starting with a cold storage tank (referred to as "cold start") and starting with a fully charged storage tank (referred to as "hot start") - were investigated with regards to their effects on electrical energy production in the same period of operation. An enthalpy-based 1D transient model for energy storage and temperature variation in solid filler material and HTF was applied for both the sensible heat storage system (SHSS) and the latent heat storage system (LHSS). The analysis was conducted for a CSP plant with an electrical power output of 60 MWe. It was found that the cold start is beneficial for both the SHSS and LHSS systems due to the overall larger electrical energy output over the same number of days compared to that of the hot start. The results are expected to be helpful for planning the start-up operation of a CSP plant with a dual-media thermal storage system.
• Xu, B., Li, P., Chan, C., & Tumilowicz, E. (2015). General volume sizing strategy for thermal storage system using phase change material for concentrated solar thermal power plant. APPLIED ENERGY, 140, 256-268.
• Xu, B., Li, P., Chan, C., & Tumilowicz, E. (2015). General volume sizing strategy for thermal storage system using phase change material for concentrated solar thermal power plant. Applied Energy, 140(Issue). doi:10.1016/j.apenergy.2014.11.046
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  With an auxiliary large capacity thermal storage using phase change material (PCM), Concentrated Solar Power (CSP) is a promising technology for high efficiency solar energy utilization. In a thermal storage system, a dual-media thermal storage tank is typically adopted in industry for the purpose of reducing the use of the heat transfer fluid (HTF) which is usually expensive. While the sensible heat storage system (SHSS) has been well studied, a dual-media latent heat storage system (LHSS) still needs more attention and study. The volume sizing of the thermal storage tank, considering daily cyclic operations, is of particular significance. In this paper, a general volume sizing strategy for LHSS is proposed, based on an enthalpy-based 1D transient model. One example was presented to demonstrate how to apply this strategy to obtain an actual storage tank volume. With this volume, a LHSS can supply heat to a thermal power plant with the HTF at temperatures above a cutoff point during a desired 6. h of operation. This general volume sizing strategy is believed to be of particular interest for the solar thermal power industry.
• Tumilowicz, E., Chan, C. L., Li, P., & Xu, B. (2014). An enthalpy formulation for thermocline with encapsulated PCM thermal storage and benchmark solution using the method of characteristics. INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 79, 362-377.
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  An enthalpy-based model of thermocline operation applicable to both single phase and encapsulated phase change filler materials was developed. Numerical simulation of the model was created using MAT-LAB. The method of characteristics was applied in space and time, mapping fluid temperature and filler enthalpy to a numerical grid, and in the case of a melting filler, allowed accurate tracking of PCM filler phase state interfaces to fractional positions of the grid. Careful consideration of various possible heat transfer conditions along with placement of PCM filler phase state interfaces in the numerical grid allowed for great versatility and accuracy in model application. Input of fluid and filler properties, tank size, time of operation, and initial and boundary conditions to the program returned a full representation to any desired amount of charge/discharge processes or cycles. The paper covers mathematical formulation, certain intricacies of numerical implementation, model verification, and the beginnings of application to prove proper operation and generality. (C) 2014 Elsevier Ltd. All rights reserved.
• Tumilowicz, E., Chan, C. L., Li, P., & Xu, B. (2014). An enthalpy formulation for thermocline with encapsulated PCM thermal storage and benchmark solution using the method of characteristics. International Journal of Heat and Mass Transfer, 79(Issue). doi:10.1016/j.ijheatmasstransfer.2014.08.017
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  An enthalpy-based model of thermocline operation applicable to both single phase and encapsulated phase change filler materials was developed. Numerical simulation of the model was created using MATLAB. The method of characteristics was applied in space and time, mapping fluid temperature and filler enthalpy to a numerical grid, and in the case of a melting filler, allowed accurate tracking of PCM filler phase state interfaces to fractional positions of the grid. Careful consideration of various possible heat transfer conditions along with placement of PCM filler phase state interfaces in the numerical grid allowed for great versatility and accuracy in model application. Input of fluid and filler properties, tank size, time of operation, and initial and boundary conditions to the program returned a full representation to any desired amount of charge/discharge processes or cycles. The paper covers mathematical formulation, certain intricacies of numerical implementation, model verification, and the beginnings of application to prove proper operation and generality. © 2014 Elsevier Ltd. All rights reserved.
• Xu, B., Li, P., & Chan, C. (2014). Fluid Charge and Discharge Strategies of Dual-media Thermal Storage Systems in the Starting-up Process of Daily Cyclic Operations. PROCEEDINGS OF THE ASME 8TH INTERNATIONAL CONFERENCE ON ENERGY SUSTAINABILITY, 2014, VOL 1.
• Xu, B., Li, P., & Chan, C. (2014). Volume Sizing for Thermal Storage with Phase Change Material for Concentrated Solar Power Plant. PROCEEDINGS OF THE ASME 8TH INTERNATIONAL CONFERENCE ON ENERGY SUSTAINABILITY, 2014, VOL 1.
• Karaki, W., Li, P., Van, L. J., Valmiki, M. M., Chan, C., & Stephens, J. (2012). Experimental Investigation of Thermal Storage Processes in a Thermocline Storage Tank. PROCEEDINGS OF THE ASME 5TH INTERNATIONAL CONFERENCE ON ENERGY SUSTAINABILITY 2011, PTS A-C, 1389-1396.
• Li, P., Van Lew, J., Chan, C., Karaki, W., Stephens, J., & O'Brien, J. E. (2012). Similarity and generalized analysis of efficiencies of thermal energy storage systems. Renewable Energy, 39(Issue 1). doi:10.1016/j.renene.2011.08.032
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  This paper examined the features of three typical thermal storage systems including: 1) direct storage of heat transfer fluid in containers, 2) storage of thermal energy in a packed bed of solid filler material, with energy being carried in/out by a flowing heat transfer fluid which directly contacts the packed bed, and 3) a system in which heat transfer fluid flows through tubes that are imbedded into a thermal storage material which may be solid, liquid, or a mixture of the two. The similarity of the three types of thermal storage systems was discussed, and generalized energy storage governing equations were introduced in both dimensional and dimensionless forms. The temperatures of the heat transfer fluid during energy charge and discharge processes and the overall energy storage efficiencies were studied through solution of the energy storage governing equations. Finally, provided in the paper are a series of generalized charts bearing curves for energy storage effectiveness against four dimensionless parameters grouped up from many of the thermal storage system properties including dimensions, fluid and thermal storage material properties, as well as the operational conditions including mass flow rate of the fluid, and the ratio of energy charge and discharge time periods. Engineers can conveniently look up the charts to design and calibrate the size of thermal storage tanks and operational conditions without doing complicated individual modeling and computations. It is expected that the charts will serve as standard tools for thermal storage system design and calibration. © 2011 Elsevier Ltd.
• Li, P., Van, L. J., Chan, C., Karaki, W., Stephens, J., & O'Brien, J. E. (2012). Similarity and generalized analysis of efficiencies of thermal energy storage systems. RENEWABLE ENERGY, 39(1), 388-402.
• Valmiki, M. M., Karaki, W., Li, P., Lew, J. V., Chan, C., & Stephens, J. (2012). Experimental investigation of thermal storage processes in a thermocline tank. Journal of Solar Energy Engineering, Transactions of the ASME, 134(Issue 4). doi:10.1115/1.4006962
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  This paper presents an experimental study of the energy charge and discharge processes in a packed bed thermocline thermal storage tank for application in concentrated solar power plants. A mathematical analysis was provided for better understanding and planning of the experimental tests. The mathematical analysis indicated that the energy storage effectiveness is related to fluid and solid material properties, tank dimensions, packing schemes of the solid filler material, and the durations of the charge and discharge times. Dimensional analysis of the governing equations was applied to consolidate many parameters into a few dimensionless parameters, allowing scaling from a laboratory system to an actual industrial application. Experiences on the system design, packing of solid filler material, system operation, and data analysis in a laboratory-scale system have been obtained in this work. These data are used to validate a recently published numerical solution method. The study will benefit the application of thermocline thermal storage systems in the large scale concentrated solar thermal power plants in industry. © 2012 American Society of Mechanical Engineers.
• Valmiki, M. M., Karaki, W., Li, P., Van, L. J., Chan, C., & Stephens, J. (2012). Experimental Investigation of Thermal Storage Processes in a Thermocline Tank. JOURNAL OF SOLAR ENERGY ENGINEERING-TRANSACTIONS OF THE ASME, 134(4).
• Valmiki, M. M., Li, P., & Chan, C. (2012). PARAMETRIC STUDY SIMULATING THE DAILY OPERATION OF A THERMOCLINE THERMAL STORAGE SYSTEM. PROCEEDINGS OF THE ASME 6TH INTERNATIONAL CONFERENCE ON ENERGY SUSTAINABILITY - 2012, PTS A AND B, 1033-1040.
• Xu, B., Li, P. W., & Chan, C. L. (2012). Extending the validity of lumped capacitance method for large Biot number in thermal storage application. Solar Energy, 86(Issue 6). doi:10.1016/j.solener.2012.03.016
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  In a typical thermal energy storage system, a heat transfer fluid is usually used to deposit/extract heat when it flows through a packed bed of solid thermal storage material. A one-dimensional model of the heat transfer and energy storage/extraction for a packed-bed thermal storage system has been developed previously by the authors. The model treats the transient heat conduction in the thermal storage material by using the lumped capacitance method, which is not valid when the Biot number is large. The current work presents an effective heat transfer coefficient between the solid and fluid for large Biot numbers. With the corrected heat transfer coefficient, the lumped capacitance method can be applied to model the thermal storage in a wide range of Biot numbers. Four typical structures for the solid thermal storage material are considered. Formulas for the effective heat transfer coefficient (and effective Biot number) are presented. To verify the prediction by the lumped capacitance method using the effective heat transfer coefficient, we compare the results to the corresponding analytical solutions. The results are in very good agreement. The effective heat transfer coefficient extended the validity of the lumped capacitance method to large Biot numbers, which is of significance to the analysis of thermal energy storage systems. © 2012 Elsevier Ltd.
• Xu, B., Li, P., & Chan, C. L. (2012). Extending the validity of lumped capacitance method for large Biot number in thermal storage application. SOLAR ENERGY, 86(6), 1709-1724.
• Li, P., Van Lew, J., Karaki, W., Chan, C., Stephens, J., & Wang, Q. (2011). Generalized charts of energy storage effectiveness for thermocline heat storage tank design and calibration. Solar Energy, 85(Issue 9). doi:10.1016/j.solener.2011.05.022
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  Solar thermal energy storage is important to the daily extended operation and cost reduction of a concentrated solar thermal power plant. To provide industrial engineers with an effective tool for sizing a thermocline heat storage tank, this paper used dimensionless heat transfer governing equations for fluid and solid filler material and studied all scenarios of energy charge and discharge processes. It has been found that what can be provided through the analysis is a series of well-configured general charts bearing curves of energy storage effectiveness against four dimensionless parameters grouped up from the storage tank dimensions, properties of the fluid and filler material, and operational conditions (such as mass flow rate of fluid and energy charge and discharge periods). As the curves in the charts are generalized, they are applicable to general thermocline heat storage systems. Engineers can conveniently look up the charts to design and calibrate the dimensions of thermocline solar thermal storage tanks and operational conditions, without doing complicated modeling and computations. It is of great significance that the generalized charts will serve as tools for thermal energy storage system design and calibration in energy industry. © 2011 Elsevier Ltd.
• Li, P., Van, L. J., Karaki, W., Chan, C., Stephens, J., & Wang, Q. (2011). Generalized charts of energy storage effectiveness for thermocline heat storage tank design and calibration. SOLAR ENERGY, 85(9), 2130-2143.
• Van Lew, J. T., Li, P., Chan, C. L., Karaki, W., & Stephens, J. (2011). Analysis of heat storage and delivery of a thermocline tank having solid filler material. Journal of Solar Energy Engineering, Transactions of the ASME, 133(Issue 2). doi:10.1115/1.4003685
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  Thermal storage has been considered as an important measure to extend the operation of a concentrated solar power plant by providing more electricity and meeting the peak demand of power in the time period from dusk to late night everyday, or even providing power on cloudy days. Discussed in this paper is thermal energy storage in a thermocline tank having a solid filler material. To provide more knowledge for designing and operating of such a thermocline storage system, this paper firstly presents the application of method of characteristics for numerically predicting the heat charging and discharging process in a packed bed thermocline storage tank. Nondimensional analysis of governing equations and numerical solution schemes using the method of characteristics were presented. The numerical method proved to be very efficient, accurate; required minimal computations; and proved versatile in simulating various operational conditions for which analytical methods cannot always provide solutions. Available analytical solutions under simple boundary and initial conditions were used to validate the numerical modeling and computation. A validation of the modeling by comparing the simulation results to experimental test data from literature also confirmed the effectiveness of the model and the related numerical solution method. Finally, design procedures using the numerical modeling tool were discussed and other issues related to operation of a thermocline storage system were also studied. © 2011 American Society of Mechanical Engineers.
• Van, L., Li, P., Chan, C. L., Karaki, W., & Stephens, J. (2011). Analysis of Heat Storage and Delivery of a Thermocline Tank Having Solid Filler Material. JOURNAL OF SOLAR ENERGY ENGINEERING-TRANSACTIONS OF THE ASME, 133(2).
• Chan, C. L., & Chen, C. F. (2010). Effect of gravity on the stability of thermocapillary convection in a horizontal fluid layer. JOURNAL OF FLUID MECHANICS, 647, 91-103.
• Chan, C. L., & Chen, C. F. (2010). Effect of gravity on the stability of thermocapillary convection in a horizontal fluid layer. Journal of Fluid Mechanics, 647(Issue). doi:10.1017/s0022112009994046
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  Smith & Davis (J. Fluid Mech., vol. 132, 1983, pp. 119-144) considered the stability of thermocapillary convection in a horizontal fluid layer with an upper free surface generated by a horizontal temperature gradient. They showed that for a return-flow velocity profile, the convection will become unstable in the hydrothermal mode with waves propagating upstream obliquely. Their findings provided a theoretical explanation for the defects often found in crystals grown by the floating-zone technique and in thin-film coating processes. Their predictions were verified experimentally by Riley & Neitzel (J. Fluid Mech., vol. 359, 1998, pp. 143-164) in an experiment with 0.75 mm thick layer of silicone oil. Their results with 1 and 1.25 mm thick layers show that as the thickness of the layer is increased, the angle of propagation, the frequency of oscillation and the phase speed of the hydrothermal wave instability decrease, while the wavelength stays nearly constant. We have extended the linear stability analysis of the problem with the effect of gravity included. It is found that when the Grashof number Gr is increased from zero, the angle of propagation first increases slightly, reaches a maximum and then decreases steadily to zero at Gr = 18. The phase speed, the frequency of oscillation and the wavelength of the instability waves all decrease with increasing Grashof number. For Gr larger than 18, there is the onset of the instability into travelling transverse waves. We have also carried out energy analysis at the time of the instability onset. It is found that the major contribution to the energy of the disturbances is from the surface-tension effect. As the gravitational effect is increased, there is a reduction in the kinetic energy supply to sustain the motion of the disturbances. We also found that it requires more kinetic energy to sustain the hydrothermal mode of instability than that required for the travelling transverse mode of instability. As a result, with increasing Grashof number, the kinetic energy available for the disturbances decreases, causing the angle of propagation to gradually decrease until finally reaching zero at Gr = 18. © 2010 Cambridge University Press.
• Chen, C. F., & Chan, C. L. (2010). Stability of buoyancy and surface tension driven convection in a horizontal double-diffusive fluid layer. INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 53(7-8), 1563-1569.
• Chen, C. F., & Chan, C. L. (2010). Stability of buoyancy and surface tension driven convection in a horizontal double-diffusive fluid layer. International Journal of Heat and Mass Transfer, 53(Issue 7-8). doi:10.1016/j.ijheatmasstransfer.2009.11.022
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  Linear stability analysis has been applied to examine the stability of convection in a horizontal double-diffusive fluid layer driven by the combined effects of buoyancy and surface tension. Such a convective flow may serve as an idealized model of the horizontal Bridgman process for crystallization or solidification of liquid melts. Results show that salt-finger instability is excited over a wide range of thermal and solutal Grashof numbers. Travelling wave instabilities caused by surface tension effects are excited when the effective Marangoni number becomes large. © 2009 Elsevier Ltd. All rights reserved.
• DeSilva, S. J., & Chan, C. L. (2008). Coupled boundary element method and finite difference method for the heat conduction in laser processing. APPLIED MATHEMATICAL MODELLING, 32(11), 2429-2458.
• DeSilva, S. J., & Chan, C. L. (2008). Coupled boundary element method and finite difference method for the heat conduction in laser processing. Applied Mathematical Modelling, 32(Issue 11). doi:10.1016/j.apm.2007.09.034
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  This paper is presented as a way to model transient heat conduction in a 3-D axisymmetric case where large rates of heat fluxes are applied on the surfaces as done in the case of laser processing. This would result in large temperature gradients in a small area irradiated by the laser on the incident surface that could also reach melting and subsequent vaporization. BEM can handle large fluxes very easily and it also can be formulated if needed to incorporate the moving boundary problem in a unique manner while on the other hand FDM is a fast and efficient method. For these reasons a coupled BEM-FDM method is formulated to simulate the heat conduction process. In the BEM method linear elements for the boundary and quadratic elements for the domain were used. The integrals in BEM were integrated in time using the asymptotic expansion for the modified Bessel functions in the Green's function. To further improve the accuracy, special techniques were employed in the spatial integration. As for the FDM formulation, a flux conservation scheme with a 4th order formula for the fluxes was used. The FDM and BEM were coupled at the interface by the temperature from the FDM formulation being imposed on the BEM and the flux from the BEM being utilized by the FDM elements near to the interface. To advance in time, the Crank-Nicholson scheme was used on the FDM directly and due to coupling indirectly on the BEM. The relative errors for the simulation of constant and variable flux cases demonstrate the successful nature of the numerical model. © 2007 Elsevier Inc. All rights reserved.
• Yu, Y., Chan, C. L., & Chen, C. F. (2007). Effect of gravity modulation on the stability of a horizontal double-diffusive layer. JOURNAL OF FLUID MECHANICS, 589, 183-213.
• Yu, Y., Chan, C. L., & Chen, C. F. (2007). Effect of gravity modulation on the stability of a horizontal double-diffusive layer. Journal of Fluid Mechanics, 589(Issue). doi:10.1017/s0022112007007690
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  The instability characteristics of a horizontal stably stratified fluid layer being heated from below, including its subsequent nonlinear evolution under steady and modulated gravity, have been investigated by experiments and two-dimensional numerical simulations. The critical condition at instability onset is also checked using linear stability analysis. The fluid is contained in a horizontal test tank with an initial stable solute gradient and a constant-temperature gradient imposed by heating from below. Because of the non-diffusive boundaries, the vertical solute gradient slowly decreases and, eventually, the layer becomes unstable. From the time of the onset of instability, the critical solute Rayleigh number is determined. For the experiments with modulated gravity, the tank is fixed onto a platform that oscillates vertically at 1 Hz with an amplitude of 10 cm. The experiment is designed such that no internal wave mode of instability can be excited. The experimental results show that gravity modulation destabilizes the system slightly by increasing the solute Rayleigh number at onset by 8.4% and causes the oscillation frequency at onset to increase by 32.6%. Linear stability analysis and two-dimensional numerical simulations for the steady gravity case yield results that are in good agreement with the experiment. For the gravity modulation case, linear stability results do not show any effect of gravity modulation at the frequency of 1 Hz. Numerical simulation results do show increases in both the onset solute Rayleigh number and the oscillation frequency; however, their values are smaller than those obtained in the experiment. The characteristics of the internal wave mode of instability are explored by numerical simulations of a stably stratified solute fluid layer under gravity modulation. The interference effects between the internal wave mode and double-diffusive mode of instabilities are studied by imposing an adverse temperature gradient on the stratified layer. © 2007 Cambridge University Press.
• Chan, C., Yu, Y., & Chen, C. (2004). Instability of convection of an ethanol-water solution in a vertical tank. Journal of Fluid Mechanics, 510(Issue). doi:10.1017/S002211200400953X
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  An experimental and numerical investigation has been carried out into the instability characteristics of natural convection of an ethanol-water solution in a vertical tank with aspect ratio (height/width) of 15. The solution contains 39 wt% ethanol with Prandtl number Pr=26. The density anomaly due to the Soret effect may be safely ignored in the present test configuration. Onset of instability, in the form of multicellular convection located in the mid-height of the tank, occurs at Grashof number Gr ≅ 13 500. These convection cells are unsteady even at low supercritical states, similar to earlier observations for higher Pr fluids. The cause of such unsteadiness of the flow has been determined by studying the streak images constructed by superposing individual frames of a digital movie sequence. New cells are generated in the upper and lower portions of the tank and then migrate toward the centre, causing the convection cells in the mid-section to merge. At higher Gr, even the tertiary cells, which rotate in the opposite direction of the secondary cells, participate in the merging process. Numerical simulations of the two-dimensional natural convection of a Boussinesq fluid with constant thermophysical properties, carried out at low supercritical Gr equivalent to the experimental value, show the same process of cell generation and merging as that observed in the experiments. By analysing the substantial time rate of change of the kinetic energy of the fluid using the mechanical energy equation, it is determined that the energy needed for the cell generation process is supplied by the work of the dynamic pressure. The subsequent migration of the cells toward the middle is caused by the pressure gradient in the tank. The total kinetic energy of the fluid attains a relative maximum right after a merging process due to the reduction of dissipation associated with the region of strong shear between the cells. © 2004 Cambridge University Press.
• Chan, C., Chen, W., & Chen, C. (2002). Secondary motion in convection layers generated by lateral heating of a solute gradient. Journal of Fluid Mechanics, 455(Issue). doi:10.1017/S0022112001007297
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  The three-dimensional motion observed by Chen & Chen (1997) in the convection cells generated by sideways heating of a solute gradient is further examined by experiments and linear stability analysis. In the experiments, we obtained visualizations and PIV measurements of the velocity of the fluid motion in the longitudinal plane perpendicular to the imposed temperature gradient. The flow consists of a horizontal row of counter-rotating vortices within each convection cell. The magnitude of this secondary motion is approximately one-half that of the primary convection cell. Results of a linear stability analysis of a parallel double-diffusive flow model of the actual flow show that the instability is in the salt-finger mode under the experimental conditions. The perturbation streamlines in the longitudinal plane at onset consist of a horizontal row of counter-rotating vortices similar to those observed in the experiments.
• Chan, C., & Chen, C. (1999). Salt-finger convection generated by thermal and solutal capillary motion in a stratified fluid. International Journal of Heat and Mass Transfer, 42(12). doi:10.1016/S0017-9310(98)00329-9
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  Experiments and numerical simulations were performed to study the onset of finger convection in a stratified fluid layer caused by thermal and solutal capillary motion. Experiments were performed in a stratified ethanol-water solution contained in a shallow tank. Capillary motion was generated by a 2°C temperature difference maintained between the sidewalls. It caused the onset of finger convection by bringing relatively warm and solute-rich fluid on top of relatively cooler solute-poor fluid. A two-dimensional numerical simulation at early times prior to the onset of finger convection was carried out. The results clearly show the interactive effects of thermal and solutal capillary motion. Experiments and numerical simulations were performed to study the onset of finger convection in a stratified fluid layer caused by thermal and solutal capillary motion. Experiments were performed in a stratified ethanol-water solution contained in a shallow tank. Capillary motion was generated by a 2 °C temperature difference maintained between the sidewalls. It caused the onset of finger convection by bringing relatively warm and solute-rich fluid on top of relatively cooler solute-poor fluid. A two-dimensional numerical simulation at early times prior to the onset of finger convection was carried out. The results clearly show the interactive effects of thermal and solutal capillary motion.
• DeSilva, S., Lik Chan, C., Chandra, A., & Lim, J. (1998). Boundary element method analysis for the transient conduction - convection in 2-D with spatially variable convective velocity. Applied Mathematical Modelling, 22(1-2). doi:10.1016/S0307-904X(98)00010-9
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  A boundary element method (BEM) formulation for the solution of transient conduction-convection problems with spatially variable convective velocities is developed in this paper. A time-dependent fundamental solution for a moving heat source with constant velocity is utilized for this purpose. Such a formulation is expected to be accurate and stable at high Peclet numbers. Numerical examples are included to establish the validity of the approach. It is observed that the BEM scheme avoids considerable false diffusion, and the numerical results for sample problems compare very well to analytical results.
• Kabir, H., Ortega, A., & Chan, C. (1995). A Boundary Element Formulation of the Conjugate Heat Transfer from a Convectively Cooled Discrete Heat Source Mounted on a Conductive Substrate. IEEE Transactions on Components Packaging and Manufacturing Technology Part A, 18(1). doi:10.1109/95.370743
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  A novel formulation is presented for solving the conjugate heat transfer problem that arises due to a thin flush heat source mounted on a conductive substrate. The geometry is a paradigm for direct air cooling of components on conducting boards. PCB thermal algorithms based on this approach are being developed for rapid estimation of the thermal field in a direct air-cooled board. The algorithms are part of a suite of tools for integrated electronic packaging design being developed at the Center for Electronic Packaging Research (CEPR). This paper presents the formulation of the approach and demonstrates its utilization for parametric studies of board level thermal management, in particular for studying the effects of board conductivity. The unique formulation allows one to couple a wide variety of flow models to the solid conduction. The solid side is modeled with a Boundary Element Method (BEM). The temperature field in the fluid side is not explicitly solved, rather, analytical “step temperature” solutions, relevant to the particular flow model, are used to express convective heat flux as a function of interface temperatures. A noniterative solution for the conjugate problem is found by matching the temperatures and fluxes at the solid-fluid interface. Results of a parametric study of the effects of board conduction on component thermal performance are presented. © 1995 IEEE
• Lim, J., & Chan, C. (1995). Modelling deep penetration laser welding using a BEM sensitivity scheme. Engineering Analysis with Boundary Elements, 16(2). doi:10.1016/0955-7997(95)00048-8
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  The process of deep penetration welding is modelled by dividing the problem into three sub-regions: solid, liquid and vapor. Each of these sub-regions are analyzed individually by the most suitable method. By matching these three solutions with appropriate boundary conditions, a complete model is obtained. The boundary element method (BEM) is used to simulate the heat transfer within the solid region. Lubrication theory is applied to model the heat transfer within the liquid. The non-equilibrium vaporization and subsequent gas dynamics are modelled by a one-dimensional model. This paper presents a BEM formulation for three-dimensional steady-state convection-conduction problems and a BEM sensitivity formulation for the determination of sensitivities of temperature and heat flux due to a boundary shape parameter. The BEM sensitivity formulation is based on the direct differentiation approach (DDA). These formulations are applied to simulate deep penetration welding. It is found that the BEM and the sensitivity formulation are very efficient and robust in the determination of the solid-liquid interface in a workpiece. © 1995.
• Chan, C. L., Huang, H. W., & Roemer, R. B. (1994). Analytical Solutions of Pennes Bio-Heat Transfer Equation With a Blood Vessel. Journal of Biomechanical Engineering, 116(2), 208-212. doi:10.1115/1.2895721
• Chandra, A., & Chan, C. (1994). Thermal aspects of machining: A BEM approach. International Journal of Solids and Structures, 31(12-13). doi:10.1016/0020-7683(94)90213-5
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  Elevated temperatures generated in machining operations significantly influence the chip formation mechanics, the process efficiency and the surface quality of the machined part. A BEM approach is used here to analyse the thermal aspects of machining processes. Particular attention is given to modeling of the tool-chip, chip-workpiece, and tool-workpiece interfaces. An exact expression for matching the boundary conditions across these interfaces is developed to avoid any iterations. A direct differentiation approach (DDA) is used to determine the sensitivities of temperature and flux distributions with respect to various design parameters. The numerical results obtained by the BEM are first verified against existing analytical and FEM results.s The temperature and flux fields for various machining conditions, along with their sensitivities, are presented next. The situations of progressive flank and crater wear of the tool with continued machining are also considered, and their effects on thermal fields are investigated. The BEM is found to be very robust and efficient for this class of steady-state conduction-convection problems. The application of DDA with BEM allows efficient determination of design sensitivities and avoids strongly singular kernels. This approach also provides a new avenue toward efficient optimization of the thermal aspects of machining processes. © 1994.
• Gupta, A., Chan, C., & Chandra, A. (1994). BEM formulation for steady-state conduction-convection problems with variable velocities. Numerical Heat Transfer, Part B: Fundamentals, 25(4). doi:10.1080/10407799408955928
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  Development of a boundary-element method (BEM) for steady-state conduction-convection problems with an arbitrary velocity field is the principal focus of this article. The steady-state fundamental solution for a moving heat source is used in the present approach. An arbitrary velocity field is decomposed into a constant part and a variable part. In addition to the boundary integrals for the constant-velocity case, variable velocity requires a domain integral in the BEM formulation. Both iterative and noniterative schemes have been used to solve the BEM equation including the domain integral term. Numerical results obtained from the proposed formulation are first validated against analytical results. Other example problems are then investigated and a detailed parametric study is conducted to understand the effects of the decomposition level and mesh refinement. The proposed BEM formulation is found to produce stable and accurate solutions under a variety of conditions for steady-state conduction-convection problems with arbitrary velocity fields. © 1994 Taylor & Francis Group, LLC.
• Lim, J., Chan, C., & Chandra, A. (1994). A bem analysis for transient conduction-convection problems. International Journal of Numerical Methods for Heat & Fluid Flow, 4(1). doi:10.1108/EUM0000000004029
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  A boundary element method (BEM) formulation for the solution of transient conduction-convection problems is developed in this paper. A time-dependent fundamental solution for moving heat source problems is utilized for this purpose. This reduces the governing parabolic partial differential equations to a boundary-only form and obviates the need for any internal discretization. Such a formulation is also expected to be stable at high Peclet numbers. Numerical examples are included to establish the validity of the approach and to demonstrate the salient features of the BEM algorithm. © 1994, MCB UP Limited. All rights reserved.
• Chan, C. (1993). A local iteration scheme for nonlinear two-dimensional steady-state heat conduction: a BEM approach. Applied Mathematical Modelling, 17(12). doi:10.1016/0307-904X(93)90075-R
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  An efficient algorithm is proposed to solve the steady-state nonlinear heat conduction equation using the boundary element method (BEM). Nonlinearity of the heat conduction equation arises from nonlinear boundary conditions and temperature dependence of thermal conductivity. Using Kirchhoff's transformation, the case of temperature dependence of thermal conductivity can be transformed to the nonlinear boundary conditions case. Applying the BEM technique, the resulting matrix equation becomes nonlinear. The nonlinearity, however, only involves the boundary nodes that have nonlinearboundary conditions. The proposed local iterative scheme reduces the entire BEM matrix equation to a smaller matrix equation whose rank is the same as the number of boundary nodes with nonlinear boundary conditions. The Newton-Raphson iteration scheme is used to solve the reduced nonlinear matrix equation. The local iterative scheme is first applied to two one-dimensional problems (analytical solutions are possible) with different nonlinear boundary conditions. It is then applied to a two-region problem. Finally, the local iterative scheme is applied to two cavity problems in which radiation plays a role in the heat transfer. © 1993.
• Chan, C. (1992). Boundary element method analysis for the bioheat transfer equation. Journal of Biomechanical Engineering, 113(4). doi:10.1115/1.2891396
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  In this paper, the boundary element method (BEM) approach is applied to solve the Pennes (1948) bioheat equation. The objective is to develop the BEM formulation and demonstrate its feasibility. The basic BEM formulations for the transient and steady-state cases are first presented. To demonstrate the usefulness of the BEM approach, numerical solutions for 2-D steady-state problems are obtained and compared to analytical solutions. Further, the BEM formulation is applied to model a conjugate problem for an artery imbedded in a perfused heated tissue. Analytical solution is possible when the conduction in the x-direction is negligible. The BEM and analytical results have very good agreement. © 1992 by ASME.
• Chandra, A., & Chan, C. (1992). A boundary element method formulation for design sensitivities in steady-state conduction-convection problems. Journal of Applied Mechanics, Transactions ASME, 59(1). doi:10.1115/1.2899426
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  A Boundary Element Method (BEM) formulation for the determination of design sensitivities of temperature distributions to various shape and process parameters in steady-state convection-diffusion problems is presented in this paper. The present formulation is valid for constant or piecewise-constant convective velocities. This approach is based on direct differentiation (DDA) of the relevant BEM formulation of the problem. It retains the advantages of the BEM regarding accuracy and efficiency while avoiding strongly singular kernels. The BEM formulation is also observed to avoid any false diffusion. This approach provides a new avenue toward efficient optimization of steady-state convection-diffusion problems and may be easily adapted to investigate the thermal aspects of various machining processes. © 1992 by ASME.
• Ganesan, S., Chan, C., & Poirier, D. (1992). Permeability for flow parallel to primary dendrite arms. Materials Science and Engineering A, 151(1). doi:10.1016/0921-5093(92)90186-5
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  The permeability for the flow of interdendritic liquid parallel to primary dendrite arms in columnar structures was calculated using the boundary element method for fully developed flow. The permeability was calculated because when the volume fraction of liquid (gL)exceeds approximately 0.60 -0.65, experiments fail. The calculated results, based on the microstructures of directionally solidified alloys, agreed with analytical results for flow parallel to circular cylinders arranged in square and triangular arrays. It appears that there is a transition in the behavior of the permeability at gL ≈ 0.65. © 1992.
• Kar, A., Chan, C., & Mazumder, J. (1992). Comparative studies on nonlinear hyperbolic and parabolic heat conduction for various boundary conditions: Analytic and numerical solutions. Journal of Heat Transfer, 114(1). doi:10.1115/1.2911240
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  With the advent of lasers with very short pulse durations and their use in materials processing, the effect of thermal wave propagation velocity becomes important. Also, localized heating in laser-aided materials processing causes significant variations in the material properties. To account for these two effects, hyperbolic heat conduction is studied in this paper by considering all the thermophysical properties, except the thermal diffusivity, to be temperature dependent. The resulting nonlinear hyperbolic equations are linearized by using Kirchhoff transformation. Both analytical and numerical solutions are obtained for finite domains. Results are presented and compared with parabolic conduction results. © 1992 by ASME.
• Chan, C., & Chandra, A. (1991). A BEM approach to thermal aspects of machining processes and their design sensitivities. Topics in Catalysis, 15(11-12). doi:10.1016/S0307-904X(09)81002-0
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  Elevated temperatures generated in machining operations influence the process efficiency, surface quality, and chip formation mechanics. This paper presents a boundary element method (BEM) formulation for the determination of design sensitivities of temperature and flux distributions for several shape and process parameters in machining operations. This approach is based on direct differentiation (DDA) of the relevant BEM formulation of the problem. The heat transfer and its sensitivities within the tool, the chip, and the workpiece are first calculated separately. A complete model for steady-state machining is then obtained by matching the boundary conditions across the tool-chip, chip-workpiece, and tool-workpiece interfaces. An exact expression for matching is developed to avoid any iterations. The temperature fields and their sensitivities within the workpiece, the chip, and the tool are obtained for various processing conditions. The situation of progressive flank wear and progressive crater wear with continued machining is considered, and its effects on the temperature and flux fields are investigated. The BEM is found to be very robust and efficient for this class of steady-state conduction-convection problems. The application of DDA in conjunction with BEM allows efficient determination of design sensitivities and avoids strongly singular kernels. This approach provides a new avenue toward efficient optimization of the thermal aspects of machining processes. © 1991, Butterworth-Heinemann, a division of Reed Publishing (USA) Inc.. All rights reserved.
• Chan, C., & Chandra, A. (1991). An algorithm for handling corners in the boundary element method: Application to conduction-convection equations. Applied Mathematical Modelling, 15(5). doi:10.1016/0307-904X(91)90002-7
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  Accurate and efficient determination of temperatures and fluxes along with their design sensitivities in conduction-convection problems involving geometric or generalized corners is the primary objective of this paper. A boundary element method (BEM) approach is used for this purpose, and the design sensitivities are obtained through direct differentiation of the governing integral equations. Conforming elements are used, and corners are treated through constraint equations. Several numerical results are presented, and a few of them are compared with existing analytical results to establish the validity of this approach. © 1991.
• Chan, C., & Chandra, A. (1991). Boundary element method analysis of the thermal aspects of metal cutting processes. Journal of engineering for industry, 113(3). doi:10.1115/1.2899702
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  In this paper, the boundary element method (BEM) approach is used to analyze the thermal aspects of steady state metal cutting processes. Particular attention is paid to modeling of the boundary conditions at the tool-chip and the chip-workpiece interfaces. Since the velocities in each of the regions are different, the heat transfer within the tool, the chip, and the workpiece are first calculated separately. A complete model for heat transfer during steady state turning is then obtained by matching the boundary conditions across the primary and the secondary shear zones. An exact expression for matching is developed to avoid any iterations. The temperature fields within the workpiece, the chip, and the tool for various processing conditions are obtained and presented. The numerical results obtained by the BEM are also compared to Jaeger solutions and existing FEM results reported in the literature. The BEM is found to be efficient and robust for this class of steady state conduction-convection problems.
• Chan, C. L., & Mazumder, J. (1988).

  The effect of radiative heat lost on laser material damage

  . Journal of Applied Physics, 63(12), 5890-5892. doi:10.1063/1.340284
• Chan, C., & Mazumder, J. (1988). Erratum: "One-dimensional steady-state model for damage by vaporization and liquid expulsion due to laser-material interaction" (Journal of Applied Physics (1987) 62 (4579)). Journal of Applied Physics, 63(9). doi:10.1063/1.341183
• Chan, C., Chen, M., & Mazumder, J. (1988). Asymptotic solution for thermocapillary flow at high and low prandtl numbers due to concentrated surface heating. Journal of Heat Transfer, 110(1). doi:10.1115/1.3250444
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  Thermocapillary convection due to nonuniform surface heating is the dominant form of fluid motion in many materials processing operations. The velocity and temperature distributions for the region adjacent to the area of peak surface heating are analyzed for the limiting cases of large and small Prandtl numbers. For a melt pool whose depth and width are large relative to the thermal and viscous boundary layers, it is shown that the most important parameter is the curvature (i.e., ∇2q) of the surface heat flux distribution. The solutions of the temperature and stream functions are presented, some of which are in closed form. Simple, explicit expressions for the velocity and maximum temperature are presented. These results are found to be quite accurate for realistic Prandtl number ranges, in comparison with exact solutions for finite Prandtl numbers. Besides being more concise than exact results, the asymptotic results also display the Prandtl number dependence more clearly in the respective ranges. © 1988 by ASME.
• Chan, C., Mazumder, J., & Chen, M. (1988). Effect of surface tension gradient driven convection in a laser melt pool: Three-dimensional perturbation model. Journal of Applied Physics, 64(11). doi:10.1063/1.342121
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  A three-dimensional model of the thermocapillary flow within the molten region during laser surface heating is developed. This physically corresponds to the process of a stationary laser beam irradiating on the surface of a moving workpiece. The recirculating flow due to the surface tension gradient is much faster than the scanning motion. This allows a perturbation solution. The basic solution corresponds to the stationary axisymmetric case, and the perturbation is based on a small scanning velocity. The advantage of seeking a perturbation solution is that the three-dimensional flow is modeled by two sets of two-dimensional equations which are presumably much more tractable than the original three-dimensional equations. Numerical solutions are obtained. The solid-liquid interface is determined by an iterative scheme. In the presence of the recirculating flow, the heat transfer becomes convection dominated. The absorbed laser energy is convected sideways so that a wider and shallower molten region is obtained. The molten pool shape is obtained and presented. The effect of various operation parameters (such as laser power, beam radius) on the pool shape are obtained and discussed. The cooling rate of resolidifying materials is also determined. Trajectory of a fluid particle is presented. This provides the most realistic scenario of mixing in a laser melted pool obtained to date. This also gives a semiquantitative understanding of the mechanism of solute redistribution. The effect of alloying elements, which may change the temperature dependence to an increasing function, is also considered. A reverse recirculating vortex is obtained and its effect on pool shape is presented and discussed.
• Chan, C., & Mazumder, J. (1987). One-dimensional steady-state model for damage by vaporization and liquid expulsion due to laser-material interaction. Journal of Applied Physics, 62(11). doi:10.1063/1.339053
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  A one-dimensional steady-state model describing the damage caused by materials removal by vaporization and liquid expulsion due to laser-material interaction is developed and presented. When vaporization occurs, there exists a discontinuity across the Knudsen layer of a few molecular mean free paths. This discontinuity is modeled by a Mott-Smith-type solution. The vaporization process creates a recoil pressure that pushes the vapor away from the target and expels the liquid. The materials are, therefore, removed in both vapor and liquid phases. The materials-removal rates are incorporated in the moving boundary immobilization transformation. The vapor phase is assumed to be optically thin so that its absorption of the high-energy beam is negligible. Closed-form analytical solutions are obtained and presented. The effect of heat-source power on removal rates, vaporization rate, liquid-expulsion rate, surface temperature, and Mach number are presented and discussed. Results are obtained for three different materials: aluminum, superalloy, and titanium.
• Chan, C., Mazumder, J., & Chen, M. (1987). Three-dimensional axisymmetric model for convection in laser-melted pools. Materials Science and Technology (United Kingdom), 3(4). doi:10.1179/mst.1987.3.4.306
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  A three-dimensional axisymmetric model of the fluid flow and heat transfer in a laser-melted pool is developed. The model corresponds to the limiting case when the scanning velocity is small compared with the recirculating velocity. This model is also valid for spot welding. Non-dimensional forms of the governing equations are derived, from which four dimensionless parameters are obtained: the Marangoni number, the Prandtl number, the dimensionless melting temperature, and the radiation factor. Their effects and significance are discussed, and numerical solutions are obtained. The position and shape of the solid/liquid interface are obtained by an iterative scheme. The quantitative effects of the dimensionless parameters on pool shape are presented. In the presence of the flow field, the heat transfer becomes convection dominated. The effect of convection on isotherms within the molten pool is discussed, and experimental results are presented. © 1987 The Institute of Metals.
• Chan, C., Mazumder, J., & Chen, M. (1983). TWO-DIMENSIONAL TRANSIENT MODEL FOR CONVECTION IN LASER MELTED POOL.. Metallurgical transactions. A, Physical metallurgy and materials science, 15(12). doi:10.1007/bf02647100
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  A two-dimensional transient model for convective heat transfer and surface tension driven fluid flow is developed. The model describes the transient behavior of the heat transfer process of a stationary band source. Semi-quantitative understanding of scanning is obtained by a coordinate transformation. The non-dimensional forms of the equations are derived and four dimensionless parameters are identified, namely, Peclet number (Pe), Prandtl number (Pr), surface tension number (S), and dimensionless melting temperature (T//m*). Their governing characteristics and their effects on pool shape, cooling rate, velocity field, and solute redistribution are discussed. A numerical solution is obtained and presented. Quantitative effects of Prandtl number and surface tension number on surface velocity, surface temperature, pool shape, and cooling rate are presented graphically.

Proceedings Publications

• Ramadani, D., Akbar, M., Angelica, P., Saptaji, K., Chan, C., & Triawan, F. (2023, April). A quick-release hanging hook design and 3D printing. In AIP Conference Proceedings, Volume 2646, Issue 1, April 27, 2023, 2646.
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  Innovative and efficient are the goal of all products made by humans. In addition to innovative designs, the ease with which users can use the product is an essential aspect of a product design. This paper reports the work of a group of undergraduate student project in additive manufacturing course. The aim of the project is to produce a hook prototype that can be used on a pegboard located at the ceiling. The hook is expected can be installed and removed easily from the bottom of the pegboard with hole diameter of 12.7 mm and thickness of 6.35 mm and able to carry a 7 kg load. In this paper, the hook is designed and simulated using SolidWorks software, printed using the FDM 3D printing machine, and tested with a 7 kg hanging load. The finite element simulation shows the proposed design is able to hold the required 7 kg load. The ease installation and removal of the 3D printed hanging hook is also can be fulfilled. The finite element simulation is also validated by applying 7 kg load onto the hanging hook. Hence the proposed design can accomplish the requirements of the project.
• Saptaji, K., Prayogo, M., Fauzah, H., Nugroho, L., Chan, C., & Triawan, F. (2022, September). Optimization of Quick Release Hanging Hook Design and Fabrication Using 3D Printing. In Innovative Manufacturing, Mechatronics and Materials Forum, 347-357.
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  3D printing technology has been widely applied for academic research and industries. The 3D printing can be used for reverse engineering purpose such as to produce an existing object, components, or products. It can also be used to modify product development, such as improving simple or complex designs with higher endurance for its function. In this study, a quick release hanging hook design was developed and a prototype was fabricated using 3D printing with a thermoplastic material such as PLA. The quick release hanging hook needs to fulfill some requirements such as ease to be inserted and released from the bottom side of the pegboard, fit into 12.7 mm diameter of the hole and 3.81 mm pegboard thickness, and being able to carry and hold a minimum of 7 kg load. The 3D design was built and simulated to determine the strength. The simulation result by ANSYS software shows the maximum stress was not exceeded the yield strength of the PLA material and has a safety factor of 1.7. The proposed design was 3D printed using the FDM process and successfully achieved the 7 kg minimum load.
• Diaz-Flores, A., Pedersen, C., Xu, Y., Williams, L., Chan, C., & Thangavelautham, J. (2021). Lunar Pits and Lava Tubes for a Modern Ark. In 2021 IEEE Aerospace Conference, AERO 2021, 2021-.
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  There have been several hundred pits found on the lunar surface. These lunar pits are hypothesized to be remnant lava tubes. Considering the Moon is not geologically active, these lava tubes could be an excellent shelter. Not only could these lava tubes be a shelter for human habitat, but they could also be an ideal location to shelter seeds, sperms, eggs, and DNA of endangered animal and plant species of Earth in a modern Ark. Lunar lava tubes are excellent locations that are sheltered from radiation, temperature swings, and small meteorite impact. Earth is undergoing significant changes resulting in loss of whole ecosystems, extinction of many thousands of species, and endangering a critical food chain that could threaten human survival. Earth faces dire threats of nuclear war, accelerated climate change, environmental poisoning, and natural disasters such as super-volcanic eruptions, earthquakes, tsunamis, and asteroid impact. These lunar pits are nearly 80 m deep and 80-100 m in diameter. The temperature is expected to be a balmy - 25 °C compared to surface temperatures reaching 130 °C during the daytime and up to -150 °C in the night-time. To store seeds, sperms, eggs, and DNA would require cryogenic temperatures below -180 °C. It is possible to store grains, eggs, sperms safely, and DNA at these cryogenic temperatures without risk of decomposition over many decades, if not centuries. This paper extends our earlier concept of building a human base inside a lava tube network to develop a modern-day robotic Ark containing seeds, eggs, sperms, and DNA. Here we present a modular, expandable design of a modern-day Ark that will preserve bio-material. The Ark will be powered using photovoltaics located on the lunar surface. Power will be generated during the lunar day sufficient to keep the Ark refrigerated both during the lunar day and night. These biomaterials will be stored in cassette storage units packaged into rotating shelves. In turn, the shelves will be placed in a modular cylindrical storage room that is 25 m in length and have a diameter of 10 m. Access to these cylindrical storage rooms will be possible using vertical shafts containing elevators constructed into the lunar pits. The vertical shafts will also include laboratories to verify the stored bio-material integrity and prepare for transport back to Earth. A series of mobile robots equipped with 7-DOF robot arms will be used to retrieve and deposit a cassette containing the cryo-preserved biomaterial. In this paper, we analyze the concept's principal feasibility, examining the Ark's structures, thermal design, and power needs.
• Ren, Q., Meng, F., & Chan, C. (2018). Numerical simulation of long-range cell manipulation with AC electrokinetics by immersed boundary-lattice Boltzmann method. In 16th International Heat Transfer Conference, IHTC 2018, 2018-.
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  Alternating current (AC) electrokinetics have been widely used to manipulate bioparticles such as mammalian cell, bacteria, DNA, and protein among which the efficient cell patterning is essential for several biomedical and tissue engineering applications. Dielectrophoresis (DEP) is a well-known phenomenon that a force acts on the polarized particle in the non-uniform electric field, and it has been demonstrated as an effective, noninvasive, and non-destructive technique for cell trapping and separation. However, DEP force reduces dramatically with the decrease of electric field gradients which makes it ineffective for controlling the motion of cell in the region far away from the electrode edges. Fortunately, AC electrothermal (ACET) flow occurs when there exists electric field and temperature gradient caused by Joule heating or other external heat sources. The driving mechanism of ACET flow makes it important for pumping the physiological media of high conductivity under which circumstance the AC electroosmosis flow is weak. The drag force induced by ACET flow on the cell could transport it into the region near the electrode where the negative DEP force is significant. By balancing the DEP force, the drag force, and the gravitational force, the cell could be successfully suspended in the solution which is useful for cell patterning or other biomedical operations. In the current work, the immersed boundary-lattice Boltzmann method (IB-LBM) with GPU acceleration on a CUDA computational platform is used to accurately simulate the motion of cell under hybrid AC electrokinetic phenomena. The results indicate that a single cell could be successfully suspended at an equilibrium position due to the balanced ACET electrohydrodynamic force, negative DEP force, and gravitational force. However, the double cells confront a periodic motion around each other when the DEP force is not sufficient to overcome the effects of ACET flow and cell-cell interaction.
• Ren, Q., & Chan, C. L. (2017). Three dimensional simulation of AC electrothermal pumping by lattice boltzmann method with non-uniform meshes using GPU. In 2nd Thermal and Fluid Engineering Summer Conference, TFESC 2017 and 4th International Workshop on Heat Transfer, IWHT 2017, 2017-.
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  Alternating current (AC) electrothermal flow induced by electric field and temperature gradient due to Joule heating or thermal boundary conditions in an aqueous solution have been widely used to manipulate the fluid flow in microfluidic systems. Due to the importance of pumping of electrolytes in microfluidics, AC electrothermal pumping has become an attractive research topic. As numerical modeling of AC electrothermal flow can be used to design and direct the experiments, there are a few efforts focusing on the simulations of electrothermal flow by different methods or commercial software. However, most of the simulations are limited in two dimensions because of the huge computational load in three dimensional cases. Due to the low cost, GPU makes high performance computing possible on personal computers since the advent of CUDA by NVIDIA in 2007. With thousands of cores, GPU can be used to accelerate the computational speed. As a mesoscale numerical method, lattice Boltzmann method (LBM) has been developed as a powerful numerical approach for heat transfer and fluid flow problems during the past two decades. LBM is very well suited for GPU computing. In the current work, LBM is applied to simulate 3D electrothermal pumping using GPU. To further save the memory of GPU and improve the computational efficiency, non-uniform LBM meshes are used. AC electrothermal pumping is presented in terms of electric field, Joule heating, temperature field, electrothermal forces, and fluid velocities.
• Ren, Q., & Chan, C. L. (2017, April). THREE DIMENSIONAL SIMULATION OF AC ELECTROTHERMAL PUMPING BY LATTICE BOLTZMANN METHOD WITH NON-UNIFORM MESHES USING GPU. In 2nd Thermal and Fluid Engineering Conference.
• Ren, Q., & Chan, C. (2015). Transient double-diffusive convection in a vertical cavity with Soret and Dufour effects by lattice Boltzmann method on CUDA platform. In ASME 2015 International Mechanical Engineering Congress and Exposition, IMECE 2015, 8.
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  Double diffusive flow in a cavity has attracted lots of attention due to its importance in many engineering fields such as ocean circulation, crystal growth, pollution transportation in air, metal manufacturing process and so on. When heat and mass transfer occur simultaneously in the double diffusive flow, the fluid flow is not only driven by the temperature gradient but also by the concentration gradient as well. In some cases, the Dufour and Soret effects will play a significant role in the double diffusive flow process. The energy flux created by the concentration gradient is called Dufour effect and the temperature gradient can cause the mass flux which is Soret effect. When taking the Soret and Dufour effects into account, the temperature and concentration equations become coupled with each other. However, the coupling diffusivities matrix can be diagonalized. The coupled system can then be transformed to two uncoupled diffusion-advection equations of two independent species. The temperature and concentration can be obtained by the inverse transformation of these two independent species. As a numerical method developed in the past two decades, lattice Boltzmann method (LBM) is powerful in simulating complex heat transfer and fluid mechanics problems. In the current study, a lattice Boltzmann model was developed and implemented for the double-diffusive convection with Soret and Dufour effects. Three distribution functions were used to compute the fluid velocity, specie 1, and specie 2, respectively. Specifically, a rectangular enclosure with horizontal temperature and concentration gradients was investigated. On the other hand, the graphics processing units (GPU) computing becomes popular since the advent of the NVIDIA's CUDA platform, which includes both hardware components and software programming environment. The developed LBM code was adapted on the CUDA platform to accelerate the computation for parametric studies. The GPU is responsible for the parallel tasks while CPU tackles the sequential steps in the computation. To verify the improvement on computation ability by using GPU, the ratio of the computational time between CPU code and CUDA code is presented by simulating the classical natural convection process in a cavity. The computational speed can be accelerated by more than 20 times when large number of nodes is used. The fluid flow, temperature field and concentration field are presented for different Rayleigh numbers, buoyancy ratios, Prandtl numbers, Lewis numbers, aspect ratios, as well as Soret and Dufour coefficients. In addition, the results of Nusselt and Sherwood numbers are shown for different parametric conditions. As a result, lattice Boltzmann method was demonstrated as a good option to study the complex double-diffusive convection with Soret and Dufour effects in a vertical cavity.
• Ren, Q., & Chan, C. (2014, June 16-20). Lattice Boltzmann Simulation of 2D AC Electrothermal Pump. In AIAA Aviation and Aeronautics Forum and Exposition.
• Xu, B., Li, P., & Chan, C. (2014). Fluid charge and discharge strategies of dual-media thermal storage systems in the starting-up process of daily cyclic operations. In ASME 2014 8th International Conference on Energy Sustainability, ES 2014 Collocated with the ASME 2014 12th International Conference on Fuel Cell Science, Engineering and Technology, 1.
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  Because of the capability of large capacity thermal storage and extended operation during night and cloudy days, concentrated solar thermal power generation is getting more and more attention in the recent years. Dual-media thermal energy storage system is typically adopted in industry for reducing the use of the heat transfer fluid, which is usually expensive. In such a dual-media system, the solid filler material can be a phase change material relying on latent heat or a regular solid material using sensible heat for energy storage. Two strategies of startingup fluid charge and discharge are considered for the operation of a concentrated solar thermal power plant incorporated with a dual-media thermal storage system. These two strategies include: 1) starting daily cyclic charge and discharge operation with an initially cold tank; 2) to fully charge the thermal storage system before operation of the cyclic discharge/charge for the power plant. The energy storage efficiency and the effects to the power plant operation due to the application of these two strategies are studied in the current work based on an enthalpy-based 1-D model, and significant difference is found in starting-up process of the daily cyclic operations, which will help us decide the best strategy of operating a thermal energy storage system with more electrical energy output.
• Xu, B., Li, P., & Chan, C. (2014, June 29-July 2). Volume Sizing for Thermal Storage with Phase Change Material for Concentrated Solar Power Plant. In ASME 8th International Conference on Energy Sustainability.
• Ren, Q., Chan, C., & Arvayo, A. (2013). Numerical simulation of 2D electrothermal flow using boundary element method. In ASME 2013 4th International Conference on Micro/Nanoscale Heat and Mass Transfer, MNHMT 2013.
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  Microfluidics and its applications to Lab-on-a-Chip have attracted a lot of attention. Because of the small length scale, the flow is characterized by a low Re number. The governing equations become linear. Boundary element method (BEM) is a very good option for simulating the fluid flow with high accuracy. In this paper, we present a 2D numerical modeling of the electrothermal flow using BEM. In electrothermal flow the volumetric force is caused by electric field and temperature gradient. The physics is mathematically modeled by (i) Laplace equation for the electrical potential, (ii) Poisson equation for the heat conduction caused by Joule heating, (iii) continuity and Stokes equation for the low Reynolds number flow. We begin by solving the electrical potential and electric field. The heat conduction is caused by the Joule heating as the heat generation term. Superposition principle is used to solve for the temperature field. The Coulomb and dielectric forces are generated by the electrical field and temperature gradient of the system. We analyze the Stokes flow problem by superposition of fundamental solution for free-space velocity caused by body force and BEM for the corresponding homogeneous Stokes equation. It is well known that a singularity integral arises when the source point approaches the field point. To overcome this problem, we solve the free-space velocity analytically. For the BEM part, we also calculate all the integral terms analytically. With this effort, our solution is more accurate. In addition, we improve the robustness of the matrix system by combining the velocity integral equation with the traction integral equation. Our purpose is to design a pump for the microfluidics system. Since the system is a long channel, the flow is fully developed in the area far away from the electrodes. With this assumption, the velocity profile is parabolic at the inlet and outlet of the channel. So we can get appropriate boundary conditions for the BEM part of Stokes equation. Consequently, we can simulate the electrothermal flow in an open channel. In this paper, we will present the formulation and implementation of BEM to model electrothermal flow. Results of electrical potential, temperature field, Joule heating, electrothermal force, and velocity field will be presented. Copyright © 2013 by ASME.
• Tumilowicz, E., Chan, C., Xu, B., & Li, P. (2013). An enthalpy formulation for thermocline with encapsulated PCM thermal storage and benchmark solution using the method of characteristics. In ASME 2013 Heat Transfer Summer Conference, HT 2013 Collocated with the ASME 2013 7th International Conference on Energy Sustainability and the ASME 2013 11th International Conference on Fuel Cell Science, Engineering and Technology, 1.
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  An enthalpy-based model of thermocline operation general to both single phase and encapsulated phase change filler materials was created in MATLAB. The method of characteristics is applied in space and time, mapping fluid temperature and filler enthalpy to a numerical grid, and in the case of a melting filler, allowing accurate tracking of phase state interfaces to fractional positions of the grid. Careful consideration of various possible heat transfer conditions along with placement of phase state interfaces in the numerical grid allows for extreme versatility and accuracy in model application. Input of specific fluid and filler properties, tank size, time of operation, and initial and boundary conditions returns a full representation to any desired amount of charge/discharge processes or cycles. The paper covers mathematical formulation, certain intricacies of numerical implementation, model verification, and the beginnings of application to prove proper operation and generality. Copyright © 2013 by ASME.
• Valmiki, M., Li, P., & Chan, C. (2012). Parametric study simulating the daily operation of a thermocline thermal storage system. In ASME 2012 6th International Conference on Energy Sustainability, ES 2012, Collocated with the ASME 2012 10th International Conference on Fuel Cell Science, Engineering and Technology.
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  This work considers a packed-bed thermocline for use as an energy storage device in solar thermal power generation. A preliminary sizing procedure of a thermocline system for a 50 MWe plant is demonstrated along with predicted transient performance under various conditions. The inlet fluid temperatures are modeled as constant or time-dependent. The time-varying inlet conditions represent solar insolation variations throughout the day which roughly take a periodic form. Sinusoidal and periodic functions based on recorded data supply this inlet condition. A constant inlet temperature can be produced by circulating the heat transfer fluid in the collection field. Both possibilities are explored and the performance is compared for various charging time allotments. The study uses an efficient, accurate numerical scheme which has been developed to model the transient behavior of a porous thermocline tank. The model can be a useful tool for thermocline heat storage sizing. This can help take guess work out of the early stages of the design process as many simulations can be run efficiently and accurately. Copyright © 2012 by ASME.
• Chan, C., Li, P., Karaki, W., Van Lew, J., Valmiki, M. M., & Stephens, J. (2011, August 7-11). Experimental Investigation of Thermal Storage Processes in a Thermocline Storage Tank. In ASME 2011 5th International Conference on Energy Sustainability.
• Karaki, W., Van Lew, J., Li, P., Chan, C., & Stephens, J. (2010). Heat transfer in thermocline storage system with filler materials: Analytical model. In ASME 2010 4th International Conference on Energy Sustainability, ES 2010, 2.
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  Parabolic trough power systems utilizing concentrated solar energy have proven their worth as a means for generating electricity. However, one major aspect preventing the technologies widespread acceptance is the deliverability of energy beyond a narrow window during peak hours of the sun. Thermal storage is a viable option to enhance the dispatchability of the solar energy and an economically feasible option is a thermocline storage system with a low-cost filler material. Utilization of thermocline storage facilities have been studied in the past and this paper hopes to expand upon that knowledge. The heat transfer between the heat transfer fluid and filler materials are governed by two conservation of energy equations, often referred as Schumann [1] equations. We solve these two coupled partial differential equations using Laplace transformation. The initial temperature distribution can be constant, linear or exponential. This flexibility allows us to apply the model to simulate unlimited charging and discharging cycles, similar to a day-today operation. The analytical model is used to investigate charging and discharging processes, and energy storage capacity. In an earlier paper [2], the authors presented numerical solution of the Schumann equations using method of characteristics. Comparison between analytical and numerical results shows that they are in very good agreement. © 2010 by ASME.
• Van Lew, J., Li, P., Chan, C., Karaki, W., & Stephens, J. (2010). Transient heat delivery and storage process in a thermocline heat storage system. In 2009 ASME International Mechanical Engineering Congress and Exposition, IMECE2009, 6.
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  Parabolic trough power systems utilizing concentrated solar energy have proven their worth as a means for generating electricity. However, one major aspect preventing the technologies widespread acceptance is the deliverability of energy beyond a narrow window during peak hours of the sun. Thermal storage is a viable option to enhance the dispatchability of the solar energy and an economically feasible option is a thermocline storage system with a low-cost filler material. Utilization of thermocline storage facilities have been studied in the past and this paper hopes to expand upon that knowledge. The current study aimed to effectively model the heat transfer of a working fluid interacting with filler material. An effective numerical method and efficient computation schemes were developed and verified. A thermocline storage system was modeled under specific conditions and results of great significance to heat storage design and operation were obtained. Copyright © 2010 by ASME.
• Li, P., Chan, C., & Chen, C. (2007). Buoyancy-driven circulation flow of an electrically conductive liquid in a rectangular annulus. In 2007 ASME/JSME Thermal Engineering Summer Heat Transfer Conference, HT 2007, 1.
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  A study on the characteristics of a buoyancy-driven flow in a rectangular circulation channel in a solar-energy-harvesting device is presented in this paper. The solar-energy-harvesting device is projected to convert solar radiation into electrical energy. As a first step of the energy conversion in the device, a flow is generated by an imbalance of buoyancy forces in the heating and cooling sections for a liquid in the circulation channel. Whereas solar energy is collected to provide the heat, free convection of ambient air provides the cooling in the device. The fluid used in the circulation channel is electrically conductive and has high thermal expansion coefficient. The present investigation focuses on the effects of channel dimensions on the buoyancy-driven flow field and uniformities of velocities. Both analytical and numerical approaches are applied in the study. Analytical closed-form solution is obtained by assuming uni-direction flow. Steady-state two-dimensional laminar solutions are obtained by numerical computation using QUICK scheme and SIMPLE algorithm. Copyright © 2007 by ASME.
• Squires, M., & Cho, L. (2006). Modeling of ultrafast laser ablation into vacuum. In ICALEO 2006 - 25th International Congress on Applications of Laser and Electro-Optics.
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  Laser-matter interaction is a very complicated phenomenon. There exist three principal regimes for laser pulses, namely long, short, and ultrashort pulse lasers. In the ultrashort regime, the target material is ionized more rapidly than the thermal relaxation time, and the material is ablated without signi.cant transfer of heat to the surrounding lattice. The absence of heat transfer to the surrounding lattice provides important advantages to micromachining: reducing both the material property change due to heating and slag deposition. To further understand the ablation process, a solver using the Space-Time Conservation Element Solution Element (CE/SE) Method is used to describe the material removal based on a gas dynamics model. The model uses a coordinate transformation with an immobilized boundary, .xing the size of the computational domain in time. The expanding computational domain facilitates the use of vacuum boundary conditions. The immobilized boundary is used to explore the expansion the ionized gas into a vacuum. In addition, exploration of the equation of state highlights some shortfalls and errors that require future attention.
• Viegas, R., & Chan, C. (2005). Effect of recombination on ultrashort pulse laser material removal by coulomb explosion. In 24th International Congress on Applications of Lasers and Electro-Optics, ICALEO 2005.
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  The femtosecond laser material interaction takes place on a very short time scale. The transfer of energy from the pulse to the material cannot be described using thermal concepts as these are based on a time scale which is much longer than that during femtosecond pulse interaction. Therefore the femtosecond pulse may be considered as an intense electromagnetic wave. When a ultra short laser pulse impinges a semiconductor, the atoms are ionized by two processes mainly multiphoton ionization and impact ionization. These processes are responsible for exciting the electrons from the valence band to the conduction band. We also study how collisional absorption of photons affects the ionization rate and bring out its significance. As the atoms are ionized the cohesive energy which binds them together becomes very small, the intermolecular bonds between nuclei are weakened and the positively charged nuclei repel each other. As the substrate is ionized by each laser pulse, the cohesive energy decreases and the material ablation results due to Coulomb explosion which is the hypothesis for this study. As they are repelled, the electrons that were excited from the valence band to the conduction band show a tendency to recombine with the holes created in the valence band. This process is called recombination. For very high carrier densities generated by ultra short pulses the primary recombination mechanism is called Auger recombination. The recombination mechanism causes the repulsion between atoms to reduce and our purpose is to try and understand how much of an effect the recombination mechanism has on the ablation rate and hence the expansion of the ablation zone. In this paper we present a model for the ionization processes and hence solve for the ionization rate at the end of the pulse. As the material expands the electrons are assumed to move with it and hence this process can be aptly described by the 1-D convection equation with recombination. This convection equation is solved along with the Euler equations and the ionization rate is used as the initial condition to predict expansion velocity, pressure and the temperature in the ablation zone.
• Tao, G., Sridhar, K., & Chan, C. (2004). Study of carbon dioxide electrolysis at electrode/electrolyte interface: Part I. Pt/YSZ interface. In Solid State Ionics, 175, 615-619.
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  CO2 electrolysis to produce O2 has been investigated at the Pt/YSZ interface by means of the solid oxide electrolysis in preparation for future human exploration of Mars. With the aid of the current interruption method, the activation overpotentials, which are free of ohmic losses, were measured in the temperature range from 1023 to 1123 K. Both the CO2 electrolysis performance curve and the activation overpotential curve show three distinct regions. Only impurity O2 is electrolyzed in regions I and II, which occur at an applied cell voltage well below the threshold value of the open circuit voltage for CO2 electrolysis, and the reaction is controlled by O2 gas diffusion on the cathode side. Active electrolysis of CO2 to form CO and oxygen anion occurs in the third region, where both the magnitudes of the anode and cathode activation overpotentials increase with the current density, and CO2 electrolysis is controlled kinetically. The large magnitudes of the anode and cathode activation overpotentials indicate that significant room exists for improvement of the cell's performance. © 2004 Elsevier B.V. All rights reserved.
• Tao, G., Sridhar, K., & Chan, C. (2004). Study of carbon dioxide electrolysis at electrode/electrolyte interface: Part II. Pt-YSZ cermet/YSZ interface. In Solid State Ionics, 175.
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  CO2 electrolysis to produce O2 has been investigated by means of solid oxide electrolysis (SOE) in preparation for future human exploration of Mars. In order to increase the cell efficiency, a new cermet electrode mixture of Pt and YSZ was studied. SOE cells constructed from the Pt-YSZ cermet electrodes have been tested in a temperature range from 1023 to 1123 K. Comparisons of CO2 electrolysis performances have been conducted between cells using Pt-YSZ cermet electrodes and Pt electrodes. Characteristics investigated include current-voltage performance, ohmic resistances and activation overpotentials. The results demonstrate that the current density is nearly tripled and the performance improvement made by Pt-YSZ cermet electrodes is more significant at low temperature. Both the ohmic resistance and activation overpotential at the anode decrease significantly for the Pt-YSZ cermet electrodes. It suggests that the contact resistance and the electrode delamination are greatly reduced. However, change to the Pt-YSZ cermet electrodes does not have a profound influence on the cathode. © 2004 Elsevier B.V. All rights reserved.
• Jun, H. P., & Cho, L. C. (2003). Ultrashort pulse laser material removal by coulomb explosion. In ICALEO 2003 - 22nd International Congress on Applications of Laser and Electro-Optics.
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  In the ultrashort regime laser material interaction can no longer be described by thermal concepts. The femtosecond laser should be considered as an intense electromagnetic wave. In the case of semiconductors, when the electromagnetic wave interacts with the electrons, the electrons are excited from the valence band to the conduction band through multi-photon and impact. These highly energized electrons are now free carriers similar to those in metals and rapidly equilibrate with themselves, on the order of femtoseconds. The excited electrons collide with the lattice and may also recombine with the holes that were created when the electrons were lifted to the conduction band. When the electrons collide with the lattice energy is transferred to the lattice. At this time the electrons and the lattice are not in thermal equilibrium. Since the electrons that are providing the cohesive energy have been lifted to the conduction band, the intermolecular bonds between the nuclei are weakened and the positively charged nuclei repel each other. Consequently, the repulsive force between nuclei causes the material to expand. As the substrate is ionized by each laser pulse, the cohesive force decreases and ultimately leads to Coulomb explosion. It is hypothesized in this paper that the Coulomb explosion is the mechanism responsible for material ablation. We have developed a model for the multi-photon ionization and impact ionization. This model can predict the ionization at the end of the femtosecond laser pulse. The ionization at the end of the pulse is the initial condition for the modeling of the Coulomb explosion. Predictions of ionization rate and expansion velocities will be presented and discussed.
• Chan, C., Campbell, D., & Paul, A. (2002). The effect of temporal pulse shape on drilling efficiency. In ICALEO 2002 - 21st International Congress on Applications of Laser and Electro-Optics.
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  A previously developed 1-D transient laser uniting model with variable properties is used to investigate effect of temporal pulse shape on drilling efficiency during laser uniting. The model contains three different physical domains, solid, liquid and vapor. The material properties such as absorptivity, thermal conductivity, and heat capacity can be functions of temperature. The governing equations in each domain are solved numerically using the boundary irnmobilization transformation. The final solution is obtained by an iterative scheme to satisfy the energy balance along the solid-liquid and liquid-vapor interfaces. An Energy balance is implemented by calculating the energy reflected, Er, the energy loss due to convection and radiation at the boundaries, Eloss the energy storage, Eg, energy removal by vaporization, Ev, and energy removal by liquid expulsion, E l at each time step. These energies sum up to the total incident energy from the laser with less than 0.1% error. Using this drilling model, we perform a study of the effect of different pulse shape on drilling efficiency as defined by mass removal per unit laser energy per pulse. Simulations are done using mild steel properties. Results for top hat and ramp temporal laser pulse shapes are presented and discussed. Energy partition and threshold are calculated. It was found that the ramp temporal laser pulse shape is more efficient in material removal.
• Dang, E., & Chan, C. (2002). Ultrashort pulse laser material removal. In ICALEO 2002 - 21st International Congress on Applications of Laser and Electro-Optics.
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  Laser material interaction is a very complicated problem. Depending on the pulse length, the mechanism could be thermal or electronic. There are three regimes of pulse length: long (> ns), short (> ps and < ns), and ultrashort (< ps) pulses. In the long pulse regime, the laser energy in most cases can be modeled as a surface heat source. The deposited energy melts and vaporizes the substrate. The material is removed in the form of vapor and liquid. Depending in the material, if the pulse length is short enough, the laser energy first absorbed by the electrons does not have enough time to equilibrate with the lattice. In this case, the electron and lattice temperatures are different. Consequently, the ususal local thermal equilibrium does not apply. Two-temperature models have been used by a number of researchers to model the interaction. In the ultrashort regime, the laser material interaction is through electron excitation, such as avalanche, impact, multiphoton, and strong optical field ionizations. These hot electrons equilibrate with themselves very rapidly, in the order of femtoseconds. As the electrons are excited from their ground states, the bonding between the nuclei are weakened. The Coulomb force causes the material to expand. In this paper, we postulate that the material removal is due to Coulomb explosion. A simple model is developed to model the Coulomb explosion. The model can then be used to predict the material removal rate.
• Guven, I., Madenci, E., & Chan, C. (2002). Transient two-dimensional heat conduction analysis of electronic packages by coupled boundary and finite element methods. In 48th Electronic Components and Technology Conference, 25.
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  Electronic packages experience large temperature excursions during their fabrication and under operational conditions. Inherent to electronic packages are the presence of geometric and material discontinuities. The regions where adhesive bond lines intersect with convective heat-loss surfaces are the most critical locations for failure initiation due to heat flux singularities and extreme thermo-mechanical stresses. Thus, accurate calculation of the flux field, as well as the temperature field, is essential in transient thermo-mechanical stress analysis. Although the finite element method (FEM) is highly efficient and commonly used, its application with conventional elements suffers from poor accuracy in the prediction of the flux field in these regions. The accuracy of the results from the boundary element method (BEM) formulation, which requires computationally intensive time-integratian schemes, is much higher than that of the FEM. However, in this study, a novel boundary element-finite element coupling algorithm is developed to investigate transient thermal responses of electronic packages consisting of dissimilar materials. The new algorithm combines the advantages of both methods while not requiring any iterations along the interfaces between BEM and FEM domains. This type of coupled formulation avoids the fine discretization required by FEM to achieve accurate results in regions with small length scales and geometric and material discontinuities. The capabilities of this new approach are demonstrated by considering two typical electronic packages. One is composed of a chip attached to a substrate with an adhesive and the other is representative of BGA technology. Both are subjected to buoyancy-induced cooling from a uniform temperature.
• Guven, I., Madenci, E., & Chan, C. (1998). Transient heat conduction analysis of electronic packages by coupled boundary and finite element methods. In 48th Electronic Components and Technology Conference, ECTC 1998, 133492.
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  Electronic packages experience large temperature excursions during their fabrication and under operational conditions. Inherent to electronic packages are the presence of geometric and material discontinuities. The regions where adhesive bond lines intersect with convective heat loss surfaces are the most critical locations for failure initiation due to heat flux singuhuities and extreme thermo-mechanical stresses. Thus, accurate calculation of the flux field, as well as the temperature field, is essential in transient thennomechanical stress anillysis. Although the finite element method (FEM) is highly efficient and commonly used, its application with conventional elements suffers fiom poor accuracy in the predicrion of the flux field in these regions. The accuracy of the results fiom the boundary element method (BEM) formulation, which requires computationally intensive time-integrabon schemes, is much higher than that of the FEM. However, in this study, a novel boundary element-finite element coupling algorithm is developed to investigate transient thermal response of electronic packages consisting of dissimilar materials. The new algorithm combines the advantages of both methods while not requiring any iterations along the interfaces between BEM and FEM domains. The BEM pafi of the solution captures the singular nature of the flux field arising from geometric and material discontinuities and also provides accurate solutions in a region described by smaller length scales, such as the dieattach or the solder ball, than those of the other components. This type of coupled formulation avoids the fine discretization required by FEM to achieve accurate results in regions with small length scales and geometric and material discontinuities. The capabilities of this new approach are demonstrated by considering two typical electronic packages. One is composed of (3 chip attached to a substrate with an adhesive and the other is representative of BGA technology. Both are subjected to natural cooling from a uniform temperature. The boundary conditions along the interfaces between BEM and FBM domains are matched by satisfying temperature continuity and energy balance. The present algorithm combines the efficiency of FEM and accuracy of BEM and provides a robust method for the solution of timedependent heat conduction problems involving dissimilar materials.
• Chan, C. (1997). Diffusion controlled and convection dominated vaporization. In Proceedings of the 1997 Laser Materials Processing Conference, ICALEO'97. Part 1 (of 2), 83.
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  The material removal by an intense power source is modeled. The vaporization rate is governed by the heat transfer within the substrate. Both convection dominated and diffusion controlled vapor removal are examined. Langmuir's model for vapor removal rate is also studied. The vaporizing temperatures and material removal rates subject to an intense power are obtained. It is found that the material removal rates are about the same regardless of the vapor removal models used. The diffusion controlled model, however, predicted a considerable higher vaporizing temperature. It is found that for most material removal process, the bulk flow motion driven by the pressure difference (convection dominated) is the predominant mechanism of vapor removal. Langmuir's model predicts the highest material removal but not much higher than that predicted by the convection dominated model.
• Chen, C. F., & Chan, C. L. (1997, November 16-21/Microscale Energy Transport). Double Diffusive Convection in a Stratified Fluid Layer Induced by Thermal and Solutal Capillary Motion. In ASME 1997 International Mechanical Engineering Congress and Exposition.
• Guven, I., Chan, C. L., & Madenci, E. (1997). Transient thermal analysis of electronic packages by the boundary element method. In Proceedings of the 1997 47th IEEE Electronic Components & Technology Conference.
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  The fabrication of electronic packages involves heating and then cooling from high processing temperatures. Because these devices consist of bonded materials with different thermal and mechanical properties, high thermo-mechanical stresses develop due to thermal and stiffness mismatches of bonded materials at regions with geometric and/or material discontinuities. These high stresses may result in crack initiations, leading to delaminations. Therefore, accurate temperature and flux distributions are critical when computing thermo-mechanical stresses, knowledge of which is essential for reliable designs. This study presents an analysis method based on the Boundary Element Method (BEM) to investigate the transient thermal response of electronic packages consisting of dissimilar materials while subjected to general boundary conditions. In order to demonstrate its capability, a chip on a substrate configuration subject to natural cooling is considered. The boundary conditions across the interfaces between the chip and the adhesive and adhesive and substrate are matched through exact expressions. The results capture the singular flux field arising from the mismatch in the thermal conduction coefficients and geometric discontinuity. The comparison of the results with those obtained from finite element analysis shows that BEM is rather robust and efficient for this class of transient conduction analyses.
• Chen, C. F., & Chan, C. L. (1996). Salt-finger convection in a stratified fluid layer induced by thermal and solutal capillary motion. In Proceedings of the 1996 3rd Microgravity Fluid Physics Conference.
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  Salt-finger convection in a double-diffusive system is a motion driven by the release of gravitational potential due to differential diffusion rates. The normal expectation is that, when the gravitational field is reduced, salt-finger convection together with other convective motions driven by buoyancy forces will be rapidly suppressed. However, because the destabilizing effect of the concentration gradient is amplified by the Lewis number, with values varying from 102 for aqueous salt solutions to 104 for liquid metals, salt-finger convection may be generated at much reduced gravity levels. In the microgravity environment, the surface tension gradient assumes a dominant role in causing fluid motion. In this paper, we report some experimental results showing the generation of salt-finger convection due to capillary motion on the surface of a stratified fluid layer. A numerical simulation is presented to show the cause of salt-finger convection.
• Kabir, H., Ortega, A., Chan, C. L., & Prince, J. L. (1994). Boundary element formulation of the conjugate heat transfer from a convectively cooled discrete heat source mounted on a substrate. In Proceedings of the 1994 IEEE 44th Electronic Components & Technology Conference.
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  A novel formulation is presented for solving the conjugate heat transfer problem that arises due to a thin flush heat source mounted on a conductive substrate. The geometry is a paradigm for direct air cooling of components on conducting boards. PCB thermal algorithms based on this approach are being developed for rapid estimation of the thermal field in a direct air cooled board. The algorithms are part of a suite of tools for integrated electronic packaging design being developed at the Center for Electronic Packaging Research (CEPR). This paper presents the formulation of the approach and demonstrates its utilization for parametric studies of board level thermal management, in particular for studying the effects of board conductivity. The unique formulation allows one to couple a wide variety of flow models to the solid conduction. The solid side is modelled with a Boundary Element Method (BEM). The temperature field in the fluid side is not explicitly solved, rather, analytical 'step temperature' solutions, relevant to the particular flow model, are used to express convective heat flux as a function of interface temperatures. A non-iterative solution for the conjugate problem is found by matching the temperatures and fluxes at the solid-fluid interface. Results of a parametric study of the effects of board conduction on component thermal performance are presented.
• Kabir, H., Ramanathan, S., Ortega, A., & Chan, C. L. (1994). Numerical solution of conjugate heat transfer in convective cooling of electronics using the boundary element method. In Proceedings of the 1994 International Mechanical Engineering Congress and Exposition, 299.
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  A formulation of the conjugate heat transfer in convective cooling of electronics is presented using the boundary element method. A general formulation for combining the fluid convection region and the solid conduction region is presented. The effects of upstream conduction on the component heat transfer, and the effects of substrate conductivity on the downstream thermal wake are presented. The fundamental issue of matching different equation types, elliptic in the solid, and parabolic in the fluid, is also briefly discussed.
• Lim, J., & Chan, C. L. (1993). Analysis of deep penetration laser welding using BEM sensitivity scheme. In Proceedings of the 1st International Conference on Inverse Problems in Engineering: Theory and Practice.
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  This paper presents a Boundary Element Method (BEM) formulation for the three-dimensional steady-state convection-conduction problems and a BEM sensitivity formulation for the determination of sensitivities of temperature and heat flux to a boundary shape parameter. The BEM sensitivity formulation is based on the direct differentiation approach (ADD). These formulations are applied to simulate deep penetration laser welding. It is found that the BEM and sensitivity formulations are very efficient and robust in the determination of the solid-liquid interface in a workpiece.
• Chan, C. L. (1992). Radiation effect in sintering process. In Winter Annual Meeting of the American Society of Mechanical Engineers, 233.
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  The radiation effect during sintering is investigated in this study. The heat conduction with in the solid and radiation within the void is modeled for a unit cell. The heat conduction model is two-dimensional, steady state and constant properties. The radiation is assumed to be grey and diffuse with uniform radiosity. The resulting nonlinear problem is solved by boundary element method (BEM). Local iterative scheme is developed. The algorithm is found to be very efficient. Temperature distributions for different processing conditions (e.g. radius of powder and sintering temperature) are presented. The equivalent thermal conductivity is determined numerically and presented.
• Chandra, A., & Chan, C. L. (1990). Thermal aspects of machining processes and their design sensitivities. A BEM approach. In Winter Annual Meeting of the American Society of Mechanical Engineers, 115.
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  Elevated temperatures generated in machining operations influence the process efficiency, surface quality, and the chip formation mechanics. A BEM formulation for the determination of design sensitivities of temperature and flux distributions to several shape and process parameters in machining operations is presented in this paper. This approach is based on direct differentiation (DDA) of the relevant BEM formulation of the problem. The heat transfer and its sensitivities within the tool, the chip, and the workpiece are first calculated separately. A complete model for steady-state machining is then obtained by matching the boundary conditions across the tool-chip, the chip-workpiece, and the tool-workpiece interfaces. An exact expression for matching is developed to avoid any iterations. The temperature fields and their sensitivities within the workpiece, the chip, and the tool are obtained for various processing conditions. The situation of progressive flank wear with continued machining is considered, and its effect on the temperature field is investigated. The BEM is found to be very robust and efficient for this class of steady-state conduction-convection problems. The application of DDA in conjunction with BEM allows efficient determination of design sensitivities and avoids strongly singular kernels. This approach provides a new avenue toward efficient optimization of the thermal aspects of machining processes.
• Chan, C. L., & Chandra, A. (1989). Boundary element method for the heat transfer in metal cutting. In National Heat Transfer Conference 1989, 113.
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  In this paper, the boundary element method (BEM) approach is used to analyze the thermal aspects of steady state metal cutting processes. Particular attention is paid to modelling of the boundary conditions at the tool-chip and the chip-workpiece interfaces. Since the velocities in each of the regions are different, the heat transfer within the tool, the chip, and the workpiece are first calculated separately. A complete model for heat transfer during steady state turning is then obtained by matching the boundary conditions across the primary and the secondary shear zones. An exact expression for matching is developed to avoid any iterations. The temperature fields within the workpiece, the chip and the tool for various processing conditions are obtained and presented. The BEM is found to be very efficient and robust for this class of steady state conduction-convection problems.
• Chan, C., & Mazumder, J. (1987). MATERIALS REMOVAL BY VAPORIZATION AND LIQUID EXPULSION USING A CONCENTRATED HEAT SOURCE.. In Proceedings of the 1987 ASME-JSME Thermal Engineering Joint Conference., 3.
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  One-dimensional transient and steady-state models describing the process of material removal by vaporization and liquid expulsion using a concentrated heat source are developed and presented. Before melting occurs, the conduction has a known analytical similarity solution. This provides the initial temperature field for the melting problem. Before vaporization occurs, the heat transfer in liquid and solid phases is solved by moving boundary immobilization transformation so that the liquid and solid regions become fixed domains. When vaporization commences, there exists a discontinuity across the Knudsen layer of a few molecular mean free paths. This discontinuity is modeled by a Mott-Smith type solution. The vaporization process creates a recoil pressure which pushes the vapor away from the target and expels the liquid. The materials are, therefore, removed in both vapor and liquid phases. The materials removal rates are incorporated in the moving boundary immobilization transformation. The vapor phase is assumed to be optically thin so that its absorption of the high energy beam is negligible. Finite difference solution is obtained for the transient model. Closed form analytical solutions are obtained for the steady-state.
• Kar, A., Chan, C. L., & Mazumder, J. (1987). SOLUTIONS OF HYPERBOLIC HEAT CONDUCTION EQUATIONS WITH VARIABLE PROPERTIES.. In Fundamentals of Conduction and Recent Developments in Contact Resistance. Presented at the 24th National Heat Transfer Conference and Exhibition., 69.
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  This paper examines the effects of the temperature-dependent thermophysical properties and the propagation velocity of heat on temperature field. The hyperbolic heat conduction equation has been solved for variable material properties. Three types of boundary conditions have been considered and the numerical solution as well as analytical expressions for the temperature distribution for each of these conditions have been presented.
• Chan, C. L., Mazumder, J., & Chen, M. M. (1986). PERTURBATION MODEL FOR THREE-DIMENSIONAL THERMOCAPILLARY CONVECTION IN LASER MELT POOL.. In Selection de Communications au Symposium AIRH: L'Approche Stochastique des Ecoulements Souterrains..
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  A three-dimensional model of the thermocapillary flow during laser surface heating is developed. This physically corresponds to the process of a stationary laser beam irradiating on the surface of a moving work-piece. A molten pool is formed by the laser heating. Due to the high temperature gradient on the surface, a surface tension gradient is created. Being a decreasing function of temperature for most metal, the surface tension therefore pulls the liquid metal from the hot central region to the cold outer region. Return flow is set up because of the existence of the solid-liquid interface. This recirculating flow, as it turns out, is much faster than the scanning motion. This allows a perturbation solution. The basic solution corresponds to the stationary axisymmetric case, and the perturbation is based on a small scanning velocity. The advantage of seeking a perturbation solution is that the three-dimensional flow is modeled by two sets of two-dimensional equations which are presumably much more tractable than the original three-dimensional equations. Numerical solutions are obtained.
• Chan, C. L., Zehr, R., Mazumder, J., & Chen, M. M. (1986). THREE-DIMENSIONAL MODEL FOR CONVECTION IN LASER WELD POOL.. In Modeling and Control of Casting and Welding Processes, Proceedings of the Third Conference..
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  Two three-dimensional models of a surface tension gradient driven flow during laser surface heating are developed. The first model is based on a perturbation solution. The basic solution corresponds to the stationary axisymmetric case, and perturbation is based on a small scanning velocity. The advantage of seeking a perturbation solution, as it turns out, is that the three-dimensional flow is modeled by two sets of two-dimensional equations which are presumably much more tractable than the original three-dimensional equations. Numerical solutions are obtained and discussed. The second model is a full three-dimensional numerical solution of the Navier-Stokes equations, using a point-by-point partially vectorized iteration scheme. Surface shape is also determined in a self-consistent manner. The effect of the presence of convection on pool geometry, cooling rate, and solute redistribution is presented and discussed.
• Chan, C. L., Chen, M. M., & Mazumder, J. (1985). THERMOCAPILLARY CONVECTION IN THE CENTRAL REGION OF A DEEP MELT POOL DUE TO INTENSE, NON-UNIFORM SURFACE HEATING.. In 1985 ASME National Heat Transfer Conference..
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  A generalized theory for thermocapillary flow and heat transfer in the stagnation region of a deep liquid layer under intense, non-uniform surface heating is developed for both plane two-dimensional and axisymmetric geometries. The theory approximates the surface heat flux distribution near the center by a parabola, and invokes the boundary layer approximation for the energy equation, but not for the momentum equation. The governing partial differential equations are transferred to a set of decoupled ordinary differential equations. Analytical solutions are found for some conditions. For other conditions numerical results are presented. The nature of the flow and heat transfer characteristics are presented and discussed. The results provide the basic scaling laws for thermocapillary convection in the deep fluid layer due to concentrated heating.
• Chan, C., Mazumder, J., & Chen, M. M. (1985). AXIS-SYMMETRY MODEL FOR CONVECTION IN A LASER MELTED POOL.. In Laser Processing of Materials. Proceedings of a Symposium Held at the 113th AIME Annual Meeting..
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  An axis-symmetry model of the fluid flow and heat transfer of laser melted pool is developed. The model corresponds physically to a stationary laser source. Non-dimensional form of the governing equations are derived. Four dimensionless parameters arise from the non-dimensionalization, namely, Peclet number, Prandtl number, Dimensionless melting temperature, and Radiation factor. Their effects and significances are discussed. Numerical solutions for some low melting point metals are obtained. The solid liquid interface, which is not known a priori, is solved. Quantitative effects of the dimensionless parameters on pool shape are obtained. In order to understand the process in a more physical sense, the effects on pool shape due to process parameters, total power and beam radius, are also presented. In the presence of the flow field, the heat transfer becomes convection dominated. Its effect on isotherms within the molten pool is discussed.
• Chan, C., Mazumder, J., & Chen, M. M. (1985). THREE-DIMENSIONAL MODEL FOR CONVECTION IN LASER MELTED POOL.. In Proceedings of the Medicine & Biology Symposium, ICALEO '84., 43-48.
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  A three-dimensional axis-symmetry model of the fluid flow and heat transfer of laser melted pool is developed. The model corresponds physically to a stationary laser source. Non-dimensional forms of the governing equations are derived. Four dimensionless parameters arise from the non-dimensionalization, namely, Marangoni number, Prandtl number, Dimensionless melting temperature, and Radiation factor. Their effects and significances are discussed. Numerical solutions are obtained. The solid liquid interface, which is not known a priori, is solved. Quantitative effects of the dimensionless parameters on pool shape are obtained. In the presence of the flow field, the heat transfer becomes convection dominated. Its effect on isotherms within the molten pool is discussed. Experimental results are presented.
• Chan, C., Mazumder, J., & Chen, M. M. (1984). FLUID FLOW IN LASER MELTED POOL.. In Modeling of Casting and Welding Processes II..
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  A two-dimensional transient model for convective heat transfer and surface tension driven fluid flow is developed. The model describes the transient behavior of the heat transfer process of a stationary band source. Some semi-quantitative understanding of scanning is obtained by a co-ordinate transformation. The non-dimensional form of the the equations are derived and four dimensionless parameters are identified, namely, Peclet number (Pe), Prandtl number (Pr), Surface tension number (S), and dimensionless melting temperature. Their governing characteristics and their effect on pool shape, cooling rate, velocity field and solute redistribution is discussed. Numerical solution is obtained and presented.
• Chan, C., Mazumder, J., & Chen, M. M. (1983). MODEL FOR SURFACE TENSION DRIVEN FLUID FLOW IN LASER SURFACE ALLOYING.. In Lasers in Materials Processing, Conference Proceedings - American Society for Metals..
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  A model of the fluid flow and heat transfer of laser surface alloying is presented. The general three-dimensional governing equations are first considered. Their non-dimensional form is derived. A limiting case is considered - line source parallel to scanning direction. Governing parameters are derived and their significance is discussed. A numerical solution for a line source parallel to scanning direction is obtained. The flowfield within the molten pool and the shape of the molten pool thus obtained are presented. The predicted heat affected zone is shown. Characteristics of the process in the presence of the flowfield are discussed.