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


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.


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


Surface area of the substrate base, m2


Area of the nozzle cross-section, m2


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


Coefficient of performance


Diameter of the nozzle, m


Height of the channel, m


Heat transfer coefficient, W m−2 K−1


Thermal conductivity, W m−1 K−1


Length of the nozzle, m

l>x, l>y, l>z

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


Number of jets

p, Δp

Pressure and pressure drop, respectively, Pa


Pumping power, W


Pumping power flux, W m−2


Heat flux, W m−2


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


Temperature and temperature-rise, respectively, K


Fluid velocity, m s−1


Volume flow rate, m3 s−1

x, y, z

Orthogonal coordinate system

Greek symbols


Design variable, H>c/d>n


Normalized α


Design variable, d>n/S>n


Normalized β


Dynamic viscosity, kg s−1 m−1


Density, kg m−3


Standard deviation, K


Stress tensor, N m−2









Maximum value


Mean value







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.


  1. 1.
    Tuckerman DB, Pease RFW (1981) High-performance heat sinking for VLSI. IEEE Electron Device Lett EDL-2(5)126–129CrossRefGoogle Scholar
  2. 2.
    Kawano K, Minakami K, Iwasaki H, Ishizuka M (1998) Development of micro channels heat exchanging. In: Nelson Jr RA, Swanson LW, Bianchi MVA, Camci C (eds) Application of heat transfer in equipment systems, and education. ASME, New York, HTD-361-3/PID-3:173–180Google Scholar
  3. 3.
    Knight RW, Hall DJ, Goodling JS, Jaeger RC (1992) Heat sink optimization with application to microchannels. IEEE Trans Compon Hybrids Manufact Technol 15(5):832–842CrossRefGoogle Scholar
  4. 4.
    Qu W, Mudawar I (2002) Experimental and numerical study of pressure drop and heat transfer in a single-phase micro-channel heat sink. Int J Heat Mass Transf 45:2549–2565CrossRefGoogle Scholar
  5. 5.
    Toh KC, Chen XY, Chai JC (2002) Numerical computation of fluid flow and heat transfer in microchannels. Int J Heat Mass Transf 45:5133–5141CrossRefGoogle Scholar
  6. 6.
    Liu D, Garimella SV (2005) Analysis and optimization of the thermal performance of microchannel heat sinks. Int J Num Meth Heat Fluid flow 15(1):7–26CrossRefGoogle Scholar
  7. 7.
    Wu S, Mai J, Tai YC, Ho CM (1999) Micro heat exchanger by using MEMS impinging jets. In: Proceedings of the 12th IEEE international conference on micro electro mechanical systems (MEMS), Orlando, FL, pp 171–176Google Scholar
  8. 8.
    Lee DY, Vafai K (1999) Comparative analysis of jet impingement and microchannel cooling for high heat flux applications. Int J Heat Mass Transf 42:1555–1568CrossRefGoogle Scholar
  9. 9.
    Jackson MJ (2006) Microfabrication and nanofabrication. CRC Press, Boca RatonGoogle Scholar
  10. 10.
    Wang EN, Zhang L, Jiang L, Koo J-M, Maveety JG, Sanchez EA, Goodson KE, Kenny TW (2004) Micromachined jets for liquid impingement cooling of VLSI chips. J Microelectromechanical Syst 13(5):833–842CrossRefGoogle Scholar
  11. 11.
    Fabbri M, Dhir VK (2005) Optimized heat transfer for high power electronic cooling using array of microjets. J Heat Transf 127:760–769CrossRefGoogle Scholar
  12. 12.
    Sung MK, Mudawar I (2006) Experimental and numerical investigation of single-phase heat transfer using hybrid jet impingement/micro-channel cooling scheme. Int J Heat Mass Transf 49:682–694CrossRefGoogle Scholar
  13. 13.
    Paz MLD, Jubran BA (2011) Numerical modeling of multi micro jet impingement cooling of a three dimensional turbine vane. Heat Mass Transf 47:1561–1579CrossRefGoogle Scholar
  14. 14.
    Michna GJ, Browne EA, Peles Y, Jensen MK (2009) Single–phase microscale jet stagnation point heat transfer. J Heat Transf 131:100402-1–100402-8CrossRefGoogle Scholar
  15. 15.
    Michna GJ, Browne EA, Peles Y, Jensen MK (2009) The effect of area ratio on microjet array heat transfer. Int J Heat Mass Transf 54:1782–1790CrossRefGoogle Scholar
  16. 16.
    Luo X, Chen W, Sun R, Liu S (2008) Experimental and numerical investigation of a microjet-based cooling system for high power LEDs. Heat Transf Eng 19(9):774–781CrossRefGoogle Scholar
  17. 17.
    Husain A, Kim S-M, Kim J-H, Kim K-Y (2013) Thermal performance analysis and optimization of multiple micro-jet impingements cooling of high power LEDs. J Thermophys Heat Transf 27(2):235–245CrossRefGoogle Scholar
  18. 18.
    Webb BW, Ma C-F (1995) Single-phase liquid jet impingement heat transfer. Adv Heat Transf 26:105–217CrossRefGoogle Scholar
  19. 19.
    Womac DJ, Ramadhdhyani S, Incropera FP (1993) Correlating equations for impingement cooling of small heat sources with single circular liquid jets. ASME J Heat Transf 115(1):106–116CrossRefGoogle Scholar
  20. 20.
    Womac DJ, Incropera FP, Ramadhdhyani S (1994) Correlating equations for impingement cooling of small heat sources with multiple circular liquid jets. ASME J Heat Transf 116(2):482–486CrossRefGoogle Scholar
  21. 21.
    Garimella SV, Rice RA (1995) Confined and submerged liquid jet impingement heat transfer. ASME J Heat Transf 117(4):871–877CrossRefGoogle Scholar
  22. 22.
    Heo M-W, Lee K-D, Kim K-W (2011) Optimization of an inclined elliptic impinging jet with cross flow for enhancing heat transfer. Heat Mass Transf 47:731–742CrossRefGoogle Scholar
  23. 23.
    Husain A, Kim K-Y (2011) Thermal transport and performance analysis of pressure- and electroosmotically-driven liquid flow microchannel heat sink with wavy wall. Heat Mass Transf 47:93–105CrossRefGoogle Scholar
  24. 24.
    Foli K, Okabe T, Olhofer M, Jin Y, Sendhoff B (2006) Optimization of micro heat exchanger: CFD, analytical approach and multi-objective evolutionary algorithms. Int J Heat Mass Transf 49:1090–1099CrossRefGoogle Scholar
  25. 25.
    Husain A, Kim K-Y (2008) Shape optimization of micro-channel heat sink for micro-electronic cooling. IEEE Trans Comp Pack Tech 31(2):322–330CrossRefGoogle Scholar
  26. 26.
    Husain A, Kim K-Y (2010) Enhanced multi-objective optimization of a microchannel heat sink through evolutionary algorithm coupled with multiple surrogate models. Appl Thermal Eng 30:1683–1691CrossRefGoogle Scholar
  27. 27.
    Samad A, Lee K-D, Kim K-Y (2008) Multi-objective optimization of a dimpled channel for heat transfer augmentation. Heat Mass Transf 45:207–217CrossRefGoogle Scholar
  28. 28.
    Martin JD, Simpson TW (2005) Use of Kriging models to approximate deterministic computer models. AIAA J 43(4):853–863CrossRefGoogle Scholar
  29. 29.
    Goel T, Vaidyanathan R, Haftka RT, Shyy W, Queipo NV, Tucker K (2007) Response surface approximation of Pareto optimal front in multi-objective optimization. Comput Methods Appl Mech Eng 196:879–893CrossRefGoogle Scholar
  30. 30.
    CFX-11.0 (2006) Solver theory. ANSYS Europe LtdGoogle Scholar
  31. 31.
    Raw MJ (1996) Robustness of coupled algebraic multigrid for the Navier-Stokes equations. In: 34th aerospace and sciences meeting & exhibit, January 15–18, AIAA 96-0297, Reno NVGoogle Scholar
  32. 32.
    Incropera FP, DeWitt DP (2002) Fundamentals of heat and mass transfer. Wiley, New YorkGoogle Scholar
  33. 33.
    Herwig H, Mahulikar SP (2006) Variable property effects in single-phase incompressible flows through microchannels. Int J Therm Sci 45:977–981CrossRefGoogle Scholar
  34. 34.
    Queipo NV, Haftka RT, Shyy W, Goel T, Vaidyanathan R, Tucker PK (2005) Surrogate-based analysis and optimization. Prog Aerosp Sci 41:1–28CrossRefGoogle Scholar
  35. 35.
    JMP® 5.1 (2004) SAS Institute, IncGoogle Scholar
  36. 36.
    Zuckerman N, Lior N (2006) Jet impingement heat transfer: physics, correlations, and numerical modeling. Adv Heat Transf 39:565–631CrossRefGoogle Scholar
  37. 37.
    Martin H (1997) Heat and mass transfer between impinging jets and solid surfaces. Adv Heat Transf 13:1–60Google Scholar
  38. 38.
    Lophaven SN, Nielsen HB, Sondergaard J (2002) DACE-A MATLAB Kriging toolbox. Technical Report IMM-TR2002-12, Technical University of DenmarkGoogle Scholar

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

Personalised recommendations