Statistical optimization of microchannel heat sink (MCHS) geometry cooled by different nanofluids using RSM analysis

  • M. Rahimi-Gorji
  • O. Pourmehran
  • M. Hatami
  • D. D. Ganji
Regular Article


In this work, an analytical investigation of the heat transfer for the microchannel heat sink (MCHS) cooled by different nanofluids (Cu, Al2O3, Ag, TiO2 in water and ethylene glycol as base fluids) is studied by the porous media approach and the Galerkin method and results are compared with numerical procedure. Response surface methodology (RSM) is applied to obtain the desirability of the optimum design of the channel geometry. The effective thermal conductivity and viscosity of the nanofluid are calculated by the Patel et al. and Khanafer et al. model, respectively, and MCHS is considered as a porous medium, as proposed by Kim and Kim. In addition, to deal with nanofluid heat transfer, a model based on the Brownian motion of nanoparticles is used. The effects of the nanoparticles volume fraction, nanoparticle type and size, base fluid type, etc., on the temperature distribution, velocity and Nusselt number are considered. Results show that, by increasing the nanoparticles volume fraction, the Brownian movement of the particles, which carries the heat and distributes it to the surroundings, increases and, consequently, the difference between coolant and wall temperature becomes less.


Heat Transfer Nusselt Number Response Surface Methodology Galerkin Method Friction Factor 
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.



Porosity ratio


Thermal conductivity ratio


Particle area ratio


Wetted area per volume


correction factor


Specific heat in constant pressure

\(\dot Q\)

Volume flow rate of heat sink (m3/s)


Constants in trial function


Darcy number


Nanoparticles diameter


Friction factor


Convection heat transfer coefficient




Thermal conductivity


Boltzmann constant



\(\tilde u\)

Trial function




Mean fluid velocity


Weighted function


Horizontal axes coordinate


Vertical axes coordinate


Brownian velocity


Dimensionless vertical coordinate


Fluid particle diameter

Greek symbols


channel aspect ratio








Brownian Reynolds number


Number of channel


Nusselt number




Power law index


Prandtl number


Heat flux


Reynolds number


Residual function




Dimensionless velocity




Nanoparticles volume fraction


Dimensionless temperature


Kinematic viscosity













heat sink






  1. 1.
    D.B. Tuckerman, F.R. Pease, Digest of Technical Papers, in Symposium on VLSI Tech, Maui, HI (1983) pp. 60--61.Google Scholar
  2. 2.
    M. Mahalingam, Proc. IEEE 73, 1396 (1985).ADSCrossRefGoogle Scholar
  3. 3.
    T. Kishimoto, T. Ohsaki, in Proceedings of the 25th Electrics Components Conference (1986) pp. 595--601.Google Scholar
  4. 4.
    R.J. Philips, in Microchannel Heat Sinks, edited by A. Bar-Cohen, A.D. Kraus, Vol. 2 (ASME, New York, 1990) chapt. 3.Google Scholar
  5. 5.
    J.C.Y. Koh, R. Colony, Int. Commun. Heat Mass Transfer 13, 89 (1986).CrossRefGoogle Scholar
  6. 6.
    S.J. Kim, D. Kim, D.Y. Lee, Int. J. Heat Mass Transfer 43, 1735 (2000).CrossRefzbMATHGoogle Scholar
  7. 7.
    C.Y. Zhao, T.J. Lu, Int. J. Heat Mass Transfer 45, 4857 (2002).CrossRefzbMATHGoogle Scholar
  8. 8.
    S. Kim, Heat Transfer Eng. 25, 37 (2004).ADSCrossRefGoogle Scholar
  9. 9.
    K. Vafai, L. Zhu, Int. J. Heat Mass Transfer 42, 2287 (1999).CrossRefGoogle Scholar
  10. 10.
    K. Vafai, P.C. Huang, ASME J. Heat Transfer 116, 604 (1994).CrossRefGoogle Scholar
  11. 11.
    Tu-Chieh Hung, Yu-Xian Huang, Wei-Mon Yan, Int. J. Heat Mass Transfer 66, 235 (2013).CrossRefGoogle Scholar
  12. 12.
    P.C. Huang, K. Vafai, AIAA J. Thermophys. Heat Transfer 8, 563 (1994).CrossRefGoogle Scholar
  13. 13.
    A. Hadim, ASME J. Heat Transfer 116, 465 (1994).ADSCrossRefGoogle Scholar
  14. 14.
    M.B. Bowers, I. Mudawar, ASME J. Electr. Packaging 116, 290 (1994).CrossRefGoogle Scholar
  15. 15.
    M. Ghazvini, H. Shokouhmand, Energy Convers. Manag. 50, 2373 (2009).CrossRefGoogle Scholar
  16. 16.
    X. Wang, A.S. Mujumdar, Int. J. Therm. Sci. 46, 1 (2007).CrossRefzbMATHGoogle Scholar
  17. 17.
    E. Farsad, S.P. Abbasi, M.S. Zabihi, J. Sabbaghzadeh, Heat Mass Transfer 47, 479 (2011).ADSCrossRefGoogle Scholar
  18. 18.
    C. Okhio, D. Hodges, J. Black, Cyber J. Multidisciplinary J. Sci. Technol. 12, 1 (2010).Google Scholar
  19. 19.
    Benjamin Rimbault, Cong Tam Nguyen, Nicolas Galanis, Int. J. Therm. Sci. 84, 275 (2014).CrossRefGoogle Scholar
  20. 20.
    S. Kakac, A. Pramuanjaroenkijb, Int. J. Heat Mass Transfer 52, 3187 (2009).CrossRefzbMATHGoogle Scholar
  21. 21.
    Yong H. Kim, Woo Chong Chun, Jin Taek Kim, Bock Choon Pak, Byoung Joon Baek, KSME Int. J. 12, 709 (1998).Google Scholar
  22. 22.
    G. Huminic, A. Huminic, Renew. Sustain. Energy Rev. 16, 5625 (2012).CrossRefGoogle Scholar
  23. 23.
    E. Mat Tokit, H.A. Mohammed, M.Z. Yusoff, Int. Commun. Heat Mass Transfer 39, 1595 (2012).CrossRefGoogle Scholar
  24. 24.
    M. Mital, Appl. Therm. Eng. 52, 321 (2013).CrossRefGoogle Scholar
  25. 25.
    C.J. Ho, L.C. Wei, Z.W. Li, Appl. Therm. Eng. 30, 96 (2010).CrossRefGoogle Scholar
  26. 26.
    M. Kalteh, A. Abbassi, M. Saffar-Avval, A. Frijns, A. Darhuber, J. Harting, Appl. Therm. Eng. 36, 260 (2012).CrossRefGoogle Scholar
  27. 27.
    X.D. Wang, B. An, J.L. Xu, Energy Convers. Manag. 65, 528 (2013).CrossRefGoogle Scholar
  28. 28.
    O. Pourmehran, M. Rahimi-Gorji, M. Gorji-Bandpy, D.D. Ganji, Alex. Eng. J. DOI:10.1016/j.aej.2014.11.002 (2014).
  29. 29.
    S.M. Aminossadati, A. Raisi, B. Ghasemi, Int. J. Non-Linear Mech. 46, 1373 (2011).ADSCrossRefGoogle Scholar
  30. 30.
    M. Sheikholeslami, M. Hatami, G. Domairry, J. Taiwan Inst. Chem. Eng. 46, 43 (2015).CrossRefGoogle Scholar
  31. 31.
    M. Hatami, R. Nouri, D.D. Ganji, J. Mol. Liq. 187, 294 (2013).CrossRefGoogle Scholar
  32. 32.
    P. Nitiapiruk, M. Sheikholeslami, D.D. Ganji, J. Mol. Liq. 195, 230 (2014).CrossRefGoogle Scholar
  33. 33.
    M. Rahimi-Gorji, O. Pourmehran, D.D. Ganji, Ain Shams Enj. J. DOI:10.1016/j.asej.2014.10.016 (2014).
  34. 34.
    S.P. Jang, S.U.S. Choi, Appl. Therm. Eng. 26, 2457 (2006).CrossRefGoogle Scholar
  35. 35.
    Mohsen Sheikholeslami, Davood Domiri Ganji, Comput. Methods Appl. Mech. Eng. 283, 651 (2015).ADSCrossRefGoogle Scholar
  36. 36.
    J. Koo, C. Kleinstreuer, Int. J. Heat Mass Transfer 48, 2652 (2005).CrossRefzbMATHGoogle Scholar
  37. 37.
    S.P. Jang, S.U.S. Choi, Appl. Therm. Eng. 26, 2457 (2006).CrossRefGoogle Scholar
  38. 38.
    M. Hatami, M. Sheikholeslami, M. Hosseini, D.D. Ganji, J. Mol. Liq. 194, 251 (2014).CrossRefGoogle Scholar
  39. 39.
    R. Chein, J. Chuang, Int. J. Therm. Sci. 46, 57 (2007).CrossRefGoogle Scholar
  40. 40.
    J. Lee, I. Mudawar, Int. J. Heat Mass Transfer 50, 452 (2007).CrossRefGoogle Scholar
  41. 41.
    M.N. Ozisik, Heat Conduction, 2nd edition (John Wiley & Sons Inc, USA, 1993).Google Scholar
  42. 42.
    S. Kiwan, Int. J. Therm. Sci. 46, 1046 (2007).CrossRefGoogle Scholar
  43. 43.
    M. Sheikholeslami, D.D. Ganji, Powder Technol. 235, 873 (2013).CrossRefGoogle Scholar
  44. 44.
    M. Sheikholeslami, D.D. Ganji, Comput. Methods Appl. Mech. Eng. 283, 651 (2015).ADSCrossRefMathSciNetGoogle Scholar
  45. 45.
    S. Kiwan, Trans Porous Media 67, 17 (2007).CrossRefGoogle Scholar
  46. 46.
    M. Hatami, D.D. Ganji, Particuology 16, 206 (2014).CrossRefGoogle Scholar
  47. 47.
    B. Vaferi, V. Salimi, D. Dehghan Baniani, A. Jahanmiri, S. Khedri, J. Petrol. Sci. Eng. 98, 156 (2012).CrossRefGoogle Scholar
  48. 48.
    M. Hatami, A. Hasanpour, D.D. Ganji, Energy Convers. Manag. 74, 9 (2013).CrossRefGoogle Scholar
  49. 49.
    M. Sheikholeslami, M. Hatami, D.D. Ganji, Powder Technol. 246, 327 (2013).CrossRefGoogle Scholar
  50. 50.
    M.N. Bouaziz, A. Aziz, Energy Convers. Manag. 51, 76 (2010).CrossRefGoogle Scholar
  51. 51.
    A. Aziz, M.N. Bouaziz, Energy Convers. Manag. 52, 2876 (2011).CrossRefGoogle Scholar
  52. 52.
    F.A. Hendi, A.M. Albugami, J. King Saud. Uni-Sci. 22, 37 (2010).CrossRefGoogle Scholar
  53. 53.
    F. Mohammadi, M.M. Hosseini, S.T. Mohyud-Din, Int. J. Syst. Sci. 42, 579 (2011).CrossRefzbMATHMathSciNetGoogle Scholar
  54. 54.
    R. Nouri, D.D. Ganji, M. Hatami, Prop. Pow. Res. 3, 96 (2014).CrossRefGoogle Scholar
  55. 55.
    M. Hatami, D.D. Ganji, Energy Convers. Manag. 78, 347 (2014).CrossRefGoogle Scholar
  56. 56.
    S.J. Kim, D. Kim, J. Heat Transfer 121, 639 (1999).CrossRefGoogle Scholar
  57. 57.
    R.W. Knight, D.J. Hall, J.S. Goodling, R.C. Jaeger, IEEE Trans. Compon. Hybrid. Manuf. Technol. 15, 832 (1992).CrossRefGoogle Scholar
  58. 58.
    D.B. Tuckerman, R.F. Pease, IEEE Elect. Dev. Lett. 2, 126 (1981).ADSCrossRefGoogle Scholar
  59. 59.
    K. Vafai, C.L. Tien, Int. J. Heat Mass Transfer 24, 195 (1981).CrossRefzbMATHGoogle Scholar
  60. 60.
    K. Khanafer, K. Vafai, M. Lightstone, Int. J. Heat Mass Transfer 446, 3639 (2003).CrossRefGoogle Scholar
  61. 61.
    N. Masoumi, N. Sohrabi, A. Behzadmehr, J. Phys. D 42, 055501 (2009).ADSCrossRefGoogle Scholar
  62. 62.
    L. Miettinen, P. Kekäläinen, J. Merikoski, J. Timonen, Int. J. Thermophys. 30, 1902 (2009).ADSCrossRefGoogle Scholar
  63. 63.
    B.K. Reddy, C. Balaji, Int. J. Heat Mass Transfer 55, 3686 (2012).CrossRefGoogle Scholar
  64. 64.
    A. Aziz, M. Torabi, K. Zhang, Energy Convers. Manag. 74, 366 (2013).CrossRefGoogle Scholar
  65. 65.
    M. Torabi, Q.B. Zhang, Energy Convers. Manag. 66, 199 (2013).CrossRefGoogle Scholar
  66. 66.
    M. Torabi, A. Aziz, K. Zhang, Energy 51, 243 (2013).CrossRefGoogle Scholar
  67. 67.
    J.H. Lee, S.H. Lee, Ch.J. Choi, S.P. Jang, S.U.S. Choi, Int. J. Micro-Nano Scale Transport 1, 269 (2010).CrossRefGoogle Scholar
  68. 68.
    H.E. Patel, T. Sundarrajan, T. Pradeep, A. Dasgupta, N. Dasgupta, S.K. Das, Pramana J. Phys. 65, 863 (2005).ADSCrossRefGoogle Scholar
  69. 69.
    J. Buongiorno, ASME J. Heat Transfer 128, 240 (2006).CrossRefGoogle Scholar
  70. 70.
    R. Prasher, E.P. Phelan, ASME J. Heat Transfer 128, 58 (2006).Google Scholar
  71. 71.
    H.F. Oztop, E. Abu-Nada, Int. J. Heat Fluid Flow 29, 1326 (2008).CrossRefGoogle Scholar
  72. 72.
    Jelena Sekulić, Johan E. ten Elshof, Dave H.A. Blank, Langmuir 21, 508 (2005).CrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • M. Rahimi-Gorji
    • 1
  • O. Pourmehran
    • 1
  • M. Hatami
    • 2
  • D. D. Ganji
    • 1
  1. 1.Mechanical Engineering DepartmentBabol University of TechnologyBabol, MazandaranIran
  2. 2.Mechanical Engineering DepartmentEsfarayen University of TechnologyEsfarayen, North KhorasanIran

Personalised recommendations