Research Papers: Electronic Cooling

Optimal Time-Varying Heat Transfer in Multilayered Packages With Arbitrary Heat Generations and Contact Resistance

[+] Author and Article Information
M. Fakoor-Pakdaman

Laboratory for Alternative Energy
Conversion (LAEC),
Mechatronic Systems Engineering,
Simon Fraser University,
Surrey, BC V3T 0A3, Canada
e-mail: mfakoorp@sfu.ca

Mehran Ahmadi

Laboratory for Alternative Energy
Conversion (LAEC),
Mechatronic Systems Engineering,
Simon Fraser University,
Surrey, BC V3T 0A3, Canada
e-mail: mahmadi@sfu.ca

Farshid Bagheri

Laboratory for Alternative Energy
Conversion (LAEC),
Mechatronic Systems Engineering,
Simon Fraser University,
Surrey, BC V3T 0A3, Canada
e-mail: fbagheri@sfu.ca

Majid Bahrami

Laboratory for Alternative Energy
Conversion (LAEC),
Mechatronic Systems Engineering,
Simon Fraser University,
Surrey, BC V3T 0A3, Canada
e-mail: mbahrami@sfu.ca

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 5, 2013; final manuscript received July 25, 2014; published online April 21, 2015. Assoc. Editor: Jim A. Liburdy.

J. Heat Transfer 137(8), 081401 (Aug 01, 2015) (10 pages) Paper No: HT-13-1570; doi: 10.1115/1.4028243 History: Received November 05, 2013; Revised July 25, 2014; Online April 21, 2015

Integrating the cooling systems of power electronics and electric machines (PEEMs) with other existing vehicle thermal management systems is an innovative technology for the next-generation hybrid electric vehicles (HEVs). As such, the reliability of PEEM must be assured under different dynamic duty cycles. Accumulation of excessive heat within the multilayered packages of PEEMs, due to the thermal contact resistance between the layers and variable temperature of the coolant, is the main challenge that needs to be addressed over a transient thermal duty cycle. Accordingly, a new analytical model is developed to predict transient heat diffusion inside multilayered composite packages. It is assumed that the composite exchanges heat via convection and radiation mechanisms with the surrounding fluid whose temperature varies arbitrarily over time (thermal duty cycle). As such, a time-dependent conjugate convection and radiation heat transfer is considered for the outer-surface. Moreover, arbitrary heat generation inside the layers and thermal contact resistances between the layers are taken into account. New closed-form relationships are developed to calculate the temperature distribution inside multilayered media. The present model is used to find an optimum value for the angular frequency of the surrounding fluid temperature to maximize the interfacial heat flux of composite media; up to 10% higher interfacial heat dissipation rate compared to constant fluid-temperature case. An independent numerical simulation is also performed using Comsol Multiphysics; the maximum relative difference between the obtained numerical data and the analytical model is less than 6%.

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O'Keefe, M., and Bennion, K., 2007, “A Comparison of Hybrid Electric Vehicle Power Electronics Cooling Options,” IEEE Vehicle Power and Propulsion Conference, Arlington, TX, Sept. 9–12, pp. 116–123.
Bennion, K., and Thornton, M., 2010, “Integrated Vehicle Thermal Management for Advanced Vehicle Propulsion Technologies,” SAE Paper No. 2010-01-0836.
Bennion, K., and Kelly, K., 2009, “Rapid Modeling of Power Electronics Thermal Management Technologies,” Vehicle Power and Propulsion Conference, Dearborn, MI, Sept. 7–10, pp. 622–629.
Bennion, K., and Thornton, M., 2010, “Integrated Vehicle Thermal Management for Advanced Vehicle Propulsion Technologies,” SAE Paper No. NREL/CP-540-47416.
Panão, M. R. O., Correia, A. M., and Moreira, A. L. N., 2012, “High-Power Electronics Thermal Management With Intermittent Multijet Sprays,” Appl. Therm. Eng., 37, pp. 293–301. [CrossRef]
Ghalambor, S., Agonafer, D., and Haji-Sheikh, A., 2013, “Analytical Thermal Solution to a Nonuniformly Powered Stack Package With Contact Resistance,” ASME J. Heat Transfer, 135(11), p. 111015. [CrossRef]
McGlen, R. J., Jachuck, R., and Lin, S., 2004, “Integrated Thermal Management Techniques for High Power Electronic Devices,” Appl. Therm. Eng., 24(8–9), pp. 1143–1156. [CrossRef]
Brooks, D., and Martonosi, M., 2001, “Dynamic Thermal Management for High-Performance Microprocessors,” 7th International Symposium on High-Performance Computer Architucture (HPCA-7), Monterey, CA, Jan. 19–24, pp. 171–182.
Yuan, T.-D., Hong, B. Z., Chen, H. H., and Wang, L.-K., 2001, “Thermal Management for High Performance Integrated Circuits With Non-Uniform Chip Power Considerations,” 17th Annual IEEE Semiconductor Thermal Measurement and Management Symposium (Cat. No.01CH37189), San Jose, CA, pp. 95–101.
Choobineh, L., and Jain, A., 2013, “Determination of Temperature Distribution in Three-Dimensional Integrated Circuits (3D ICs) With Unequally-Sized Die,” Appl. Therm. Eng., 56(1–2), pp. 176–184. [CrossRef]
Gurrum, S., and Suman, S., 2004, “Thermal Issues in Next-Generation Integrated Circuits,” IEEE Trans. Device Mater. Reliab., 4(4), pp. 709–714. [CrossRef]
Kelly, K., Abraham, T., and Bennion, K., 2007, “Assessment of Thermal Control Technologies for Cooling Electric Vehicle Power Electronics,” 23rd International Electric Vehicle Symposium (EVS-23), Anaheim, CA, Dec. 2–5, Paper No. NREL/CP-540-42267.
De Monte, F., 2000, “Transient Heat Conduction in One-Dimensional Composite Slab, A “Natural” Analytic Approach,” Int. J. Heat Mass Transfer, 43(19), pp. 3607–3619. [CrossRef]
Carslaw, H. S., and Jaeger, J. C., 1959, Conduction of Heat in Solids, Oxford University, London.
Feng, Z. G., and Michaelides, E. E., 1997, “The Use of Modified Green's Functions in Unsteady Heat Transfer,” Int. J. Heat Mass Transfer, 40(12), pp. 2997–3002. [CrossRef]
Yener, Y., and Ozisik, M. N., 1974, “On the Solution of Unsteady Heat Conduction in Multi-Region Finite Media With Time-Dependent Heat Transfer Coefficient,” 5th International Heat Transfer Conference, Tokyo. [CrossRef]
Mayer, E., 1952, “Heat Flow in Composite Slabs,” ARS J., 22(3), pp. 150–158. [CrossRef]
Tittle, C. W., 1965, “Boundary Value Problems in Composite Media: Quasi-Orthogonal Functions,” Appl. Phys., 36(4), pp. 1487–1488. [CrossRef]
Yeh, H. C., 1976, “Solving Boundary Value Problems in Composite Media by Seperation of Variables and Transient Temperature of a Reactor Vessel,” Nucl. Eng. Des., 36(2), pp. 139–157. [CrossRef]
Olek, S., Elias, E., Wacholder, E., and Kaizerman, S., 1991, “Unsteady Conjugated Heat Transfer in Laminar Pipe Flow,” Int. J. Heat Mass Transfer, 34(6), pp. 1443–1450. [CrossRef]
Olek, S., 1998, “Heat Transfer in Duct Flow of Non-Newtonian Fluid With Axial Conduction,” Int. Commun. Heat Mass Transfer, 25(7), pp. 929–938. [CrossRef]
Olek, S., 1999, “Multiregion Conjugate Heat Transfer,” Hybrid Methods Eng., 1, pp. 119–137. [CrossRef]
Fakoor-Pakdaman, M., Ahmadi, M., Bagheri, F., and Bahrami, M., 2014 “Dynamic Heat Transfer Inside Multilayered Packages with Arbitrary Heat Generations,” Journal of Thermo. and Heat Trans., 28(4), pp. 687–699. [CrossRef]
Antonopoulos, K. A., and Tzivanidis, C., 1996, “Analytical Solution of Boundary Value Problems of Heat Conduction in Composite Regions With Arbitrary Convection Boundary Conditions,” Acta Mech., 118(1–4), pp. 65–78. [CrossRef]
De Monte, F., 2004, “Transverse Eigenproblem of Steady-State Heat Conduction for Multi-Dimensional Two-Layered Slabs With Automatic Computation of Eigenvalues,” Int. J. Heat Mass Transfer, 47(2), pp. 191–201. [CrossRef]
Jain, P. K., and Singh, S., 2010, “An Exact Analytical Solution for Two-Dimensional, Unsteady, Multilayer Heat Conduction in Spherical Coordinates,” Int. J. Heat Mass Transfer, 53(9–10), pp. 2133–2142. [CrossRef]
Jain, P. K., and Singh, S., 2009, “Analytical Solution to Transient Asymmetric Heat Conduction in a Multilayer Annulus,” ASME J. Heat Transfer, 131(1), p. 011304. [CrossRef]
Miller, J. R., and Weaver, P. M., 2003, “Temperature Profiles in Composite Plates Subject to Time-Dependent Complex Boundary Conditions,” Compos. Struct., 59(2), pp. 267–278. [CrossRef]
Lu, X., Tervola, P., and Viljanen, M., 2006, “Transient Analytical Solution to Heat Conduction in Composite Circular Cylinder,” Int. J. Heat Mass Transfer, 49(1–2), pp. 341–348. [CrossRef]
Kreyszig, E., Kreyzig, H., and Norminton, E. J., 2012, Advanced Engineering Mathematics, Wiley, New York.
Chapman, A. J., 1960, Heat Transfer, Macmillan, New York.
Jakob, M., 1949, Heat Transfer, Wiley, New York.
Zerkle, R. D., and Sunderland, J. E., 1965, “The Transint Temperature Distribution in a Slab Subject to Thermal Radiation,” ASME J.Heat Transfer, 87(1), pp. 117–132. [CrossRef]
Narumanchi, S., Mihalic, M., and Kelly, K., 2008, “Thermal Interface Materials for Power Electronics Applications,” Itherm’08, Orlando, FL, May 28–31, Paper No. NREL/CP–540–42972.
Iyengar, M., and Schmidt, R., 2006, “Analytical Modeling for Prediction of Hot Spot Chip Junction Temperature for Electronics Cooling Applications,” ITHERM’06, San Diego, CA, May 30–Jun. 2, pp. 87–95.
Mudawar, I., Bharathan, D., Kelly, K., and Narumanchi, S., 2009, “Two-Phase Spray Cooling of Hybrid Vehicle Electronics,” IEEE Trans. Compon. Packag. Technol., 32(2), pp. 501–512. [CrossRef]
Incropera, F. P., Dewitt, D. P., Bergman, T. L., and Lavine, A. S., 2007, Introduction to Heat Transfer, Wiley, New York.


Grahic Jump Location
Fig. 1

Schematic of multilayered composites in (a) Cartesian, (b) cylindrical, and (c) spherical coordinate systems

Grahic Jump Location
Fig. 2

Schematic of a two-die stack, and TIM subjected to time-dependent conjugate convection–radiation with a surrounding fluid

Grahic Jump Location
Fig. 3

Variations of the dimensionless temperature of the insulated axis θη=0, Eq. (9), against the Fourier number for different values of the dimensionless conductance between the layers, Λ1

Grahic Jump Location
Fig. 4

Variations of the maximum interfacial heat flux, Eq. (A12), versus the angular frequency for different values of the thickness ratios

Grahic Jump Location
Fig. 5

Variations of the insulated axis temperature Tx0, Eq. (9), versus time for an arbitrary time-dependent conjugate convective–radiative boundary condition, Eq. (15)



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