Flow and thermal modeling of liquid metal in expanded microchannel heat sink

Abstract

Liquid metal-based microchannel heat sinks (MCHSs) suffer from the low heat capacity of coolant, resulting in an excessive temperature rise of coolant and heat sink when dealing with high-power heat dissipation. In this paper, it was found that expanded space at the top of fins could distribute the heat inside microchannels, reducing the temperature rise of coolant and heat sink. The orthogonal experiments revealed that expanding the top space of channels yielded similar temperature reductions to changing the channel width. The flow and thermal modeling of expanded microchannel heat sink (E-MCHS) were analyzed by both using the 3-dimensional (3D) numerical simulation and the 1-dimensional (1D) thermal resistance model. The fin efficiency of E-MCHS was derived to improve the accuracy of the 1D thermal resistance model. The heat conduction of liquid metal in Z direction and the heat convection between the top surface of fins and the liquid metal could reduce the total thermal resistance (R_t). The above process was effective for microchannels with low channel aspect ratio, low mean velocity (U_m) or long heat sink length. The maximum thermal resistance reduction in the example of this paper reached 36.0%. The expanded space endowed the heat sink with lower pressure, which might further reduce the pumping power (P). This rule was feasible both when fins were truncated (h₂ < 0, h₂ is the height of expanded channel for E-MCHS) and when over plate was raised (h₂ > 0).

Graphical abstract

Keywords

liquid metal cooling / heat sink / expanded microchannel / flow and thermal modeling

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Acknowledgements

Thanks to Jing LIU, Zhongshan DENG and Yixin ZHOU for their guidance and suggestions on this work.

Notations

A	Area of heat sink
B	Intermediate variable/(-\sqrt{h{A}_{\text{c}}/k_{\text{s}}P})
Cp	Specific heat capacity/(J·kg−1·K−1)
Dh	Hydrodynamic diameter/(2WcH/(Wc + H))
H	Distance from the bottom of the fins to the cover plate
h	Height of fins for the MCHS or initial high of fins for E-MCHS
h1	Height of fins for E-MCHS
h2	Height of expanded channel for E-MCHS
hc	Heat transfer coefficient
k	Thermal conductivity
L	Heat sink length
m	Intermediate variable/(-\sqrt{hP/k_{\text{s}}{W}_{\text{w}}})
Nu	Nusselt number
n	Channel number
P	Pumping power
Pr	Prandtl number
q	Heat flux
qm	Mass flow
Rt	Total thermal resistance
Rcal	Thermal resistance of heat capacity
Rcov	Thermal resistance of convection
Rcond	Thermal resistance of heat conduction
Re	Reynolds number
T	Temperature
t	Heat sink base thickness
Um	Mean velocity
W	Heat sink width
Ww	Fin width
Wc	Channel width
x, y, z	Rectangular coordinates
Greek letters
α	Ww/Wc, width ratio of the fin to channel
β	H/Wc, channel aspect ratio
δ	h2/H
η	Fin efficiency
θ	T−T∞
μ	Dynamic viscosity
ρ	Mass density
Subscripts
b	Heat sink base
c	Channel
cal	Capacity
conv	Convection
cond	Conduction
f	Fluid

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