Abstract

A study on the prospect of designing high power electronic packages with phase change cooling is presented, with special emphasis on minimising the rising of junction temperatures due to thermal transient effects. The one-dimensional thermal model consists of a finite slab suddenly exposed to a uniform heat flux at the top surface and cooled by convective air at the bottom. The phase change problem is divided into sub-problems and solved progressively. Before the slab starts to melt, both exact and approximate solutions are presented for the distribution of temperature in the slab as functions of time and Biot number Bi. The necessity of partitioning the time domain into two regimes, separated by the time t₀ needed for the thermal front to traverse across the whole slab, is emphasised. After the slab melts, quasi-steady state solutions are obtained both for the melt depth and the evolution of surface temperature as functions of time and Biot number when t_m>t₀, with t_m denoting the time needed for melting to commence at the top surface of the slab. The quasi-steady state solutions are compared with those obtained by using the method of finite elements. Approximate but simple analytical solutions are also constructed for the t_m<t₀ case which, again, are compared with the finite element results. Finally, these solutions are analysed to guide the design of advanced packages with optimised phase change cooling strategies.

Author Keywords: Phase change cooling; Power electronics; Thermal management; Finite elements; Materials selection

Nomenclature

Bi

Biot number

c_s, c_l

solid and melt specific heat

h

local heat transfer coefficient

H

phase change layer thickness

I₁, I₂

material indices

k_s, k_l

Solid and melt thermal conductivities

L

latent heat

Q

heat flux

t

time

t_c

time for complete melting

t₀

thermal penetration time

t_m

melting time

T₀

initial and environmental temperature

T_m, T_v

melting and boiling temperatures

T_s, T_l

solid and melt temperatures

x

coordinate

X

melt front position

ΔT

≡T_m−T₀

κ_s, κ_l

solid and melt thermal diffusivities

ρ

density

l

liquid

s

solid

Article Outline

Nomenclature

1. Introduction

2. Specifications of the problem

3. Solutions before melting

3.1. Temperature profiles

3.2. Temperature regimes I and II

4. Solutions for low power densities (t_m>t₀)

4.1. Quasi-steady state solutions

4.2. Range of validity

5. Solutions for high power densities (t_m<t₀)

5.1. Approximate solutions

5.2. Finite element solutions

6. Design implications

Acknowledgements

Appendix. Effective coefficient of heat transfer

References