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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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Figures

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. 1

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

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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