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Performance analysis and design optimization of micro-jet impingement heat sink

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Abstract

This study evaluated a silicon-based micro-jet impingement heat sink for electronic cooling applications. First, the pressure-drop and thermal characteristics were investigated for steady incompressible and laminar flow by solving three-dimensional Navier–Stokes equations, and the performance enhancement was carried out through parametric and optimization studies. Several parallel and staggered micro-jet configurations consisting of a maximum of 16 jet impingements were tested. The effectiveness of the micro-jet configurations, i.e. inline 2 × 2, 3 × 3 and 4 × 4 jets, and staggered 5-jet and 13-jet arrays with nozzle diameters 50, 76, and 100 μm, were analyzed at various flow rates for the maximum temperature-rise and pressure-drop characteristics. A design with a staggered 13-jet array showed the best performance among the various configurations investigated in the present study. The design optimization based on three-dimensional numerical analysis, surrogate modeling and a multi-objective evolutionary algorithm were carried out to understand the thermal resistance and pumping power correlation of the micro-jet impingement heat sink. Two design variables, the ratio of height of the channel and nozzle diameter, and the ratio of nozzle diameter and interjet spacing, were chosen for design optimization. The global Pareto-optimal front was achieved for overall thermal resistance and required pumping power of the heat sink. The Pareto-optimal front revealed existing correlation between pumping power and thermal resistance of the heat sink. Of the range of Pareto-optimal designs available, some representative designs were selected and their functional relationships among the objective functions and design variables were examined to understand the Pareto-optimal sensitivity and optimal design space. A minimum of 66 °C of maximum-temperature-rise was obtained for a heat flux of 100 W/cm2 at a pressure drop of about 24 kPa.

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Abbreviations

A>s :

Surface area of the substrate base, m2

A>j :

Area of the nozzle cross-section, m2

C>p :

Specific heat at constant pressure, J kg−1K−1

COP :

Coefficient of performance

d>n :

Diameter of the nozzle, m

H>c :

Height of the channel, m

h :

Heat transfer coefficient, W m−2 K−1

k :

Thermal conductivity, W m−1 K−1

l>n :

Length of the nozzle, m

l>x , l>y , l>z :

Length, width and height of the heat sink, respectively, m

n :

Number of jets

p, Δp :

Pressure and pressure drop, respectively, Pa

P :

Pumping power, W

\(P^{\prime\prime}\) :

Pumping power flux, W m−2

q :

Heat flux, W m−2

R>th :

Thermal resistance, K W−1

S4, S9, S16, S5, S13 :

Interjet spacings of inline 2 × 2, 3 × 3 and 4 × 4 jet and staggered 5-jet and 13-jet arrays, respectively, m

T, ΔT :

Temperature and temperature-rise, respectively, K

v :

Fluid velocity, m s−1

\(\dot{V}\) :

Volume flow rate, m3 s−1

x, y, z :

Orthogonal coordinate system

α :

Design variable, H>c /d>n

α* :

Normalized α

β :

Design variable, d>n /S>n

β* :

Normalized β

μ :

Dynamic viscosity, kg s−1 m−1

ρ :

Density, kg m−3

σ :

Standard deviation, K

τ>ij :

Stress tensor, N m−2

f :

Fluid

i :

Inlet

j :

Jet

max :

Maximum value

mean :

Mean value

o :

Outlet

s :

Substrate

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Acknowledgments

This research was supported by the National Research Foundation of Korea (NRF) Grant No. 20090083510 funded by government (MSIP) through Multi-phenomena CFD Engineering Research Center. Authors also acknowledge the support of Sultan Qaboos University for conducting this research.

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  1. Afzal Husain

    Present address: Department of Mechanical and Industrial Engineering, Sultan Qaboos University, PO Box 33, Muscat, PC 123, Sultanate of Oman

Authors and Affiliations

  1. Department of Mechanical Engineering, Inha University, 253 Yonghyun-Dong, Nam-Gu, Incheon, 402-751, Republic of Korea

    Afzal Husain, Sun-Min Kim & Kwang-Yong Kim

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  1. Afzal Husain
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Correspondence to Kwang-Yong Kim.

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Husain, A., Kim, SM. & Kim, KY. Performance analysis and design optimization of micro-jet impingement heat sink. Heat Mass Transfer 49, 1613–1624 (2013). https://doi.org/10.1007/s00231-013-1202-3

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