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Heat and Mass Transfer

, Volume 49, Issue 11, pp 1613–1624 | Cite as

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

  • Afzal Husain
  • Sun-Min Kim
  • Kwang-Yong KimEmail author
Original

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.

Keywords

Design Variable Heat Sink Nozzle Diameter Stagnation Heat Transfer Increase Coolant Flow Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

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

Greek symbols

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

Subscripts

f

Fluid

i

Inlet

j

Jet

max

Maximum value

mean

Mean value

o

Outlet

s

Substrate

Notes

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringInha UniversityIncheonRepublic of Korea
  2. 2.Department of Mechanical and Industrial EngineeringSultan Qaboos UniversityMuscatSultanate of Oman

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