Optimization of thermal and hydraulic performance of nanofluids in a rectangular miniature-channel with various fins using response surface methodology

  • Zahra Sarbazi
  • Faramarz Hormozi


In the present work, optimization of the thermal and hydraulic performances of various nanofluids inside a rectangular miniature-channel heat sink with different longitudinal fins was studied. Response surface methodology was used to obtain optimal condition of miniature-channel. The selected cross sections for fins were semi-circular, quadrant (bi-directional) and rectangular. Gamma alumina–water and silicon oxide–water nanofluids were utilized as working fluids. The thermal conductivity, viscosity, convective heat transfer coefficient and pressure drop of working fluids are measured. The test facility provided experimental conditions to measure the heat transfer coefficient and pressure drop at different Reynolds numbers ranged between 400 and 1200. KD2 pro property analyzer for thermal conductivity and Brookfield DV3T rheometer for viscosity of nanofluids were applied. Experimental results showed that the efficiency of miniature-channel increases when nanofluid and extended surface are both employed. The highest and lowest values for the heat transfer enhancement belonged to the case of silicon oxide–water and for a miniature-channel with a rectangular fin. The highest thermal–hydraulic performance belonged to the miniature-channel with quadrant-2, rectangular, quadrant-1 and semi-circular fin with silicon oxide/water nanofluid, which was 1.27, 1.26, 1.16 and 1.11, respectively. According to statistical analysis, new correlations are also proposed to predict the Nusselt number and friction factor of various finned miniature-channel. The results of the proposed models are in good agreement with experimental data.


Optimization Process intensification Miniature-channel Fin cross section Nanofluid Heat transfer 

List of symbols


Contact surface area (m2)


Total heat transfer area (m2)


Curvature angle (°)


Analysis of variance


Specific heat capacity (J kg−1 K−1)


Hydraulic diameter (m)


Design of experiments


Darcy friction factor


Heat transfer coefficient (W m−2 K−1)


Height of channel (m)


Current (A)


Thermal conductivity (W m−1 K−1)


Length of channel (m)


Mass flow rate (kg s−1)


Mean square error


Shape factor


Nusselt number


Pressure drop (Pa)


Performance evaluation criteria


Heat (W)




Response surface methodology


Reynolds number


Temperature (°C)


Time (s)


Velocity (m s−1)


Voltage (V)


Vortex generator


Width of channel (m)







Base fluid













Greek symbols


Viscosity (kg m−1 s−1)


Density (kg m−3)


Volume fraction


Weight fraction



  1. 1.
    Ahmed H, Mohammed H, Yusoff M. An overview on heat transfer augmentation using vortex generators and nanofluids: approaches and applications. Renew Sustain Energy Rev. 2012;16(8):5951–93.CrossRefGoogle Scholar
  2. 2.
    Sidik NAC, et al. An overview of passive techniques for heat transfer augmentation in microchannel heat sink. Int Commun Heat Mass Transf. 2017;88:74–83.CrossRefGoogle Scholar
  3. 3.
    Hafezisefat P, Esfahany MN, Jafari M. Erratum to: An experimental and numerical study of heat transfer in jacketed vessels by SiO2 nanofluid. Heat Mass Transf. 2017;53(7):2395–2405.CrossRefGoogle Scholar
  4. 4.
    Ramezanpour M, Siavashi M. Application of SiO2–water nanofluid to enhance oil recovery. J Therm Anal Calorim. 2018. Scholar
  5. 5.
    Keblinski P, Eastman JA, Cahill DG. Nanofluids for thermal transport. Mater Today. 2005;8(6):36–44.CrossRefGoogle Scholar
  6. 6.
    Chol S, Estman J. Enhancing thermal conductivity of fluids with nanoparticles. ASME Publ Fed. 1995;231:99–106.Google Scholar
  7. 7.
    Heris SZ, Etemad SG, Esfahany MN. Experimental investigation of oxide nanofluids laminar flow convective heat transfer. Int Commun Heat Mass Transf. 2006;33(4):529–35.CrossRefGoogle Scholar
  8. 8.
    Fazeli SA, et al. Experimental and numerical investigation of heat transfer in a miniature heat sink utilizing silica nanofluid. Superlattices Microstruct. 2012;51(2):247–64.CrossRefGoogle Scholar
  9. 9.
    Wang J, et al. Heat transfer and pressure drop of nanofluids containing carbon nanotubes in laminar flows. Exp Thermal Fluid Sci. 2013;44:716–21.CrossRefGoogle Scholar
  10. 10.
    Gireesha B, Gorla RSR, Mahanthesh B. Effect of suspended nanoparticles on three-dimensional MHD flow, heat and mass transfer of radiating Eyring–Powell fluid over a stretching sheet. J Nanofluids. 2015;4(4):474–84.CrossRefGoogle Scholar
  11. 11.
    Choi TJ, et al. A review of the internal forced convective heat transfer characteristics of nanofluids: experimental features, mechanisms and thermal performance criteria. J Mech Sci Technol. 2018;32(8):3491–505.CrossRefGoogle Scholar
  12. 12.
    Sarafraz M, Hormozi F. Experimental investigation on the pool boiling heat transfer to aqueous multi-walled carbon nanotube nanofluids on the micro-finned surfaces. Int J Therm Sci. 2016;100:255–66.CrossRefGoogle Scholar
  13. 13.
    Sarafraz M, Hormozi F. Comparatively experimental study on the boiling thermal performance of metal oxide and multi-walled carbon nanotube nanofluids. Powder Technol. 2016;287:412–30.CrossRefGoogle Scholar
  14. 14.
    Sarafraz M, et al. On the convective thermal performance of a CPU cooler working with liquid gallium and CuO/water nanofluid: a comparative study. Appl Therm Eng. 2017;112:1373–81.CrossRefGoogle Scholar
  15. 15.
    Rashidi S, Mahian O, Languri EM. Applications of nanofluids in condensing and evaporating systems. J Therm Anal Calorim. 2018;131(3):2027–39.CrossRefGoogle Scholar
  16. 16.
    Bellos E, Tzivanidis C. A review of concentrating solar thermal collectors with and without nanofluids. J Therm Anal Calorim. 2018. Scholar
  17. 17.
    Subramani J, et al. Efficiency and heat transfer improvements in a parabolic trough solar collector using TiO 2 nanofluids under turbulent flow regime. Renew Energy. 2018;119:19–31.CrossRefGoogle Scholar
  18. 18.
    Mirzaei M, Dehghan M. Investigation of flow and heat transfer of nanofluid in microchannel with variable property approach. Heat Mass Transf. 2013;49(12):1803–11.CrossRefGoogle Scholar
  19. 19.
    Tang B, et al. Heat transfer performance of a novel double-layer mini-channel heat sink. Heat Mass Transf. 2017;53(3):929–36.CrossRefGoogle Scholar
  20. 20.
    Mohammadi A, Floryan J. Effects of longitudinal grooves on the Couette–Poiseuille flow. Theoret Comput Fluid Dyn. 2014;28(5):549–72.CrossRefGoogle Scholar
  21. 21.
    Rashidi S, et al. Combination of nanofluid and inserts for heat transfer enhancement. J Therm Anal Calorim. 2018. Scholar
  22. 22.
    Koo J, Kleinstreuer C. Laminar nanofluid flow in microheat-sinks. Int J Heat Mass Transf. 2005;48(13):2652–61.CrossRefGoogle Scholar
  23. 23.
    Moraveji MK, et al. Modeling of convective heat transfer of a nanofluid in the developing region of tube flow with computational fluid dynamics. Int Commun Heat Mass Transf. 2011;38(9):1291–5.CrossRefGoogle Scholar
  24. 24.
    Moraveji MK, Haddad SMH, Darabi M. Modeling of forced convective heat transfer of a non-Newtonian nanofluid in the horizontal tube under constant heat flux with computational fluid dynamics. Int Commun Heat Mass Transf. 2012;39(7):995–9.CrossRefGoogle Scholar
  25. 25.
    Moraveji MK, Ardehali RM. CFD modeling (comparing single and two-phase approaches) on thermal performance of Al2o3/water nanofluid in mini-channel heat sink. Int Commun Heat Mass Transf. 2013;44:157–64.CrossRefGoogle Scholar
  26. 26.
    Khoshvaght-Aliabadi M, Hormozi F, Zamzamian A. Effects of geometrical parameters on performance of plate-fin heat exchanger: vortex-generator as core surface and nanofluid as working media. Appl Therm Eng. 2014;70(1):565–79.CrossRefGoogle Scholar
  27. 27.
    Ghale ZY, Haghshenasfard M, Esfahany MN. Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models. Int Commun Heat Mass Transf. 2015;68:122–9.CrossRefGoogle Scholar
  28. 28.
    Sarafraz M, Hormozi F. Heat transfer, pressure drop and fouling studies of multi-walled carbon nanotube nano-fluids inside a plate heat exchanger. Exp Therm Fluid Sci. 2016;72:1–11.CrossRefGoogle Scholar
  29. 29.
    Hosseinirad E, Hormozi F. New correlations to predict the thermal and hydraulic performance of different longitudinal pin fins as vortex generator in miniature channel: utilizing MWCNT–water and Al2O3–water nanofluids. Appl Therm Eng. 2017;118:199–213.CrossRefGoogle Scholar
  30. 30.
    Tekin E, Sabuncuoglu I. Simulation optimization: a comprehensive review on theory and applications. IIE Trans. 2004;36(11):1067–81.CrossRefGoogle Scholar
  31. 31.
    Ahmed HE, et al. Optimization of thermal design of heat sinks: a review. Int J Heat Mass Transf. 2018;118:129–53.CrossRefGoogle Scholar
  32. 32.
    Ghasemi N, Aghayari R, Maddah H. Optimizing the parameters of heat transmission in a small heat exchanger with spiral tapes cut as triangles and aluminum oxide nanofluid using central composite design method. Heat Mass Transf. 2018;54(7):2113–30.CrossRefGoogle Scholar
  33. 33.
    Maddah H, et al. Experimental and numerical study of nanofluid in heat exchanger fitted by modified twisted tape: exergy analysis and ANN prediction model. Heat Mass Transf. 2017;53(4):1413–23.CrossRefGoogle Scholar
  34. 34.
    Ahmadi MH, et al. A proposed model to predict thermal conductivity ratio of Al2O3/EG nanofluid by applying least squares support vector machine (LSSVM) and genetic algorithm as a connectionist approach. J Therm Anal Calorim. 2018. Scholar
  35. 35.
    Korichi A, Oufer L. Numerical heat transfer in a rectangular channel with mounted obstacles on upper and lower walls. Int J Therm Sci. 2005;44(7):644–55.CrossRefGoogle Scholar
  36. 36.
    Naphon P, Nakharintr L. Heat transfer of nanofluids in the mini-rectangular fin heat sinks. Int Commun Heat Mass Transf. 2013;40:25–31.CrossRefGoogle Scholar
  37. 37.
    Hasan MI. Investigation of flow and heat transfer characteristics in micro pin fin heat sink with nanofluid. Appl Therm Eng. 2014;63(2):598–607.CrossRefGoogle Scholar
  38. 38.
    Ahmed HE, Ahmed M, Yusoff M. Heat transfer enhancement in a triangular duct using compound nanofluids and turbulators. Appl Therm Eng. 2015;91:191–201.CrossRefGoogle Scholar
  39. 39.
    Khoshvaght-Aliabadi M, Zangouei S, Hormozi F. Performance of a plate-fin heat exchanger with vortex-generator channels: 3D-CFD simulation and experimental validation. Int J Therm Sci. 2015;88:180–92.CrossRefGoogle Scholar
  40. 40.
    Esfe MH, et al. Mixed convection heat transfer from surface-mounted block heat sources in a horizontal channel with nanofluids. Int J Heat Mass Transf. 2015;89:783–91.CrossRefGoogle Scholar
  41. 41.
    Zhao H, et al. Pressure drop and friction factor of a rectangular channel with staggered mini pin fins of different shapes. Exp Thermal Fluid Sci. 2016;71:57–69.CrossRefGoogle Scholar
  42. 42.
    Sabaghan A, et al. Nanofluid flow and heat transfer in a microchannel with longitudinal vortex generators: two-phase numerical simulation. Appl Therm Eng. 2016;100:179–89.CrossRefGoogle Scholar
  43. 43.
    Hosseinirad E, Hormozi F. Influence of shape, number, and position of horizontal minifins on thermal-hydraulic performance of minichannel heat sink using nanofluid. Heat Transf Eng. 2017;38(9):892–903.CrossRefGoogle Scholar
  44. 44.
    Ali HM, Arshad W. Effect of channel angle of pin-fin heat sink on heat transfer performance using water based graphene nanoplatelets nanofluids. Int J Heat Mass Transf. 2017;106:465–72.CrossRefGoogle Scholar
  45. 45.
    Ahmed HE, et al. Turbulent heat transfer and nanofluid flow in a triangular duct with vortex generators. Int J Heat Mass Transf. 2017;105:495–504.CrossRefGoogle Scholar
  46. 46.
    Zhang J, et al. An experimental investigation of heat transfer enhancement in minichannel: combination of nanofluid and micro fin structure techniques. Exp Therm Fluid Sci. 2017;81:21–32.CrossRefGoogle Scholar
  47. 47.
    Thansekhar M, Anbumeenakshi C. Experimental investigation of thermal performance of microchannel heat sink with nanofluids Al2O3/water and SiO2/water. Exp Techn. 2017;41(4):399–406.CrossRefGoogle Scholar
  48. 48.
    Saeed M, Kim M-H. Heat transfer enhancement using nanofluids (Al2O3–H2O) in mini-channel heatsinks. Int J Heat Mass Transf. 2018;120:671–82.CrossRefGoogle Scholar
  49. 49.
    Duangthongsuk W, Wongwises S. A comparison of the thermal and hydraulic performances between miniature pin fin heat sink and microchannel heat sink with zigzag flow channel together with using nanofluids. Heat Mass Transf. 2018;54(11):3265–74.CrossRefGoogle Scholar
  50. 50.
    Zdaniuk GJ, Chamra LM, Walters DK. Correlating heat transfer and friction in helically-finned tubes using artificial neural networks. Int J Heat Mass Transf. 2007;50(23–24):4713–23.CrossRefGoogle Scholar
  51. 51.
    Jang J-Y, Hsu L-F, Leu J-S. Optimization of the span angle and location of vortex generators in a plate-fin and tube heat exchanger. Int J Heat Mass Transf. 2013;67:432–44.CrossRefGoogle Scholar
  52. 52.
    Salviano LO, Dezan DJ, Yanagihara JI. Optimization of winglet-type vortex generator positions and angles in plate-fin compact heat exchanger: response surface methodology and direct optimization. Int J Heat Mass Transf. 2015;82:373–87.CrossRefGoogle Scholar
  53. 53.
    Esfe MH, et al. Experimental investigation of thermal conductivity of CNTs-Al2O3/water: a statistical approach. Int Commun Heat Mass Transf. 2015;69:29–33.CrossRefGoogle Scholar
  54. 54.
    Izadi M, et al. Modeling of effective thermal conductivity and viscosity of carbon structured nanofluid. Transp Phenom Nano Micro Scales. 2015;3(1):1–13.Google Scholar
  55. 55.
    Esfe MH, et al. Estimation of thermal conductivity of CNTs–water in low temperature by artificial neural network and correlation. Int Commun Heat Mass Transf. 2016;76:376–81.CrossRefGoogle Scholar
  56. 56.
    Zhou J, et al. Design of microchannel heat sink with wavy channel and its time-efficient optimization with combined RSM and FVM methods. Int J Heat Mass Transf. 2016;103:715–24.CrossRefGoogle Scholar
  57. 57.
    Ghahdarijani AM, Hormozi F, Asl AH. Convective heat transfer and pressure drop study on nanofluids in double-walled reactor by developing an optimal multilayer perceptron artificial neural network. Int Commun Heat Mass Transf. 2017;84:11–9.CrossRefGoogle Scholar
  58. 58.
    Zhong G, Liu QS, Liu Y. Modeling of thermal-hydraulic characteristics of H-type finned tube using response surface methodology. Energy Procedia. 2017;105:5098–105.CrossRefGoogle Scholar
  59. 59.
    Esfe MH, et al. Design of a heat exchanger working with organic nanofluids using multi-objective particle swarm optimization algorithm and response surface method. Int J Heat Mass Transf. 2018;119:922–30.CrossRefGoogle Scholar
  60. 60.
    Esfe MH, et al. Prediction and optimization of thermophysical properties of stabilized Al2O3/antifreeze nanofluids using response surface methodology. J Mol Liquids. 2018;261:14–20.CrossRefGoogle Scholar
  61. 61.
    Esfe MH, Bahiraei M, Mahian O. Experimental study for developing an accurate model to predict viscosity of CuO–ethylene glycol nanofluid using genetic algorithm based neural network. Powder Technol. 2018;338:383–90.CrossRefGoogle Scholar
  62. 62.
    Amani M, et al. Hydrothermal optimization of SiO 2/water nanofluids based on attitudes in decision making. Int Commun Heat Mass Transf. 2018;90:67–72.CrossRefGoogle Scholar
  63. 63.
    Bezerra MA, et al. Response surface methodology (RSM) as a tool for optimization in analytical chemistry. Talanta. 2008;76(5):965–77.CrossRefGoogle Scholar
  64. 64.
    Yang SM, Tao WQ. Heat transfer. 3rd ed. Beijing: Higher Education Press; 1998.Google Scholar
  65. 65.
    Buongiorno J. Convective transport in nanofluids. J Heat Transf. 2006;128(3):240–50.CrossRefGoogle Scholar
  66. 66.
    Sarviya R, Fuskele V. Review on thermal conductivity of nanofluids. Mater Today Proc. 2017;4(2):4022–31.CrossRefGoogle Scholar
  67. 67.
    Guo W, et al. Measurement of the thermal conductivity of SiO2 nanofluids with an optimized transient hot wire method. Thermochim Acta. 2018;661:84–97.CrossRefGoogle Scholar
  68. 68.
    Bashirnezhad K, et al. A comprehensive review of last experimental studies on thermal conductivity of nanofluids. J Therm Anal Calorim. 2015;122(2):863–84.CrossRefGoogle Scholar
  69. 69.
    White FM. Fluid mechanics. 7th ed. New York: McGraw Hill; 2011.Google Scholar
  70. 70.
    Kline S, Mcclintock F. Describing uncertainty in single sample experiments. Mech Eng. 1953;75:3–8.Google Scholar
  71. 71.
    Yang L, et al. Recent developments on viscosity and thermal conductivity of nanofluids. Powder Technol. 2017;317:348–69.CrossRefGoogle Scholar
  72. 72.
    Hamilton RL, Crosser O. Thermal conductivity of heterogeneous two-component systems. Ind Eng Chem Fundam. 1962;1(3):187–91.CrossRefGoogle Scholar
  73. 73.
    Nabil M, et al. An experimental study on the thermal conductivity and dynamic viscosity of TiO2–SiO2 nanofluids in water: ethylene glycol mixture. Int Commun Heat Mass Transf. 2017;86:181–9.CrossRefGoogle Scholar
  74. 74.
    Timofeeva EV, et al. Thermal conductivity and particle agglomeration in alumina nanofluids: experiment and theory. Phys Rev E. 2007;76(6):061203.CrossRefGoogle Scholar
  75. 75.
    Brinkman H. The viscosity of concentrated suspensions and solutions. J Chem Phys. 1952;20(4):571–81.CrossRefGoogle Scholar
  76. 76.
    Song S, et al. Study on hydration layers near nanoscale silica dispersed in aqueous solutions through viscosity measurement. J Colloid Interface Sci. 2005;287(1):114–20.CrossRefGoogle Scholar
  77. 77.
    Moldoveanu GM, et al. Viscosity estimation of Al2O3, SiO2 nanofluids and their hybrid: an experimental study. J Mol Liquids. 2018;253:188–96.CrossRefGoogle Scholar
  78. 78.
    Ahmed HE, et al. Experimental study of heat transfer augmentation in non-circular duct using combined nanofluids and vortex generator. Int J Heat Mass Transf. 2015;90:1197–206.CrossRefGoogle Scholar
  79. 79.
    Streeter VL, Wylie EB, Bedford KW. Fluid mechanics. 7th ed. New York: McGraw Hill; 1998.Google Scholar
  80. 80.
    Sarafraz M, et al. Fouling formation and thermal performance of aqueous carbon nanotube nanofluid in a heat sink with rectangular parallel microchannel. Appl Therm Eng. 2017;123:29–39.CrossRefGoogle Scholar
  81. 81.
    Sarafraz M, et al. Thermal performance of a heat sink microchannel working with biologically produced silver–water nanofluid: experimental assessment. Exp Thermal Fluid Sci. 2018;91:509–19.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of Chemical, Petroleum, and Gas EngineeringSemnan UniversitySemnanIran

Personalised recommendations