Investigation of Friction Factor and Nusselt Number Distributions for Zno-water Nanofluid under Forced, Mixed and Free Convection with Varying Eckert Numbers

Document Type : Original Research Paper

Author

University of Bonab

Abstract

This study investigates the behavior of the friction factor and Nusselt number in fluid flow across forced, mixed, and free convection regimes, with a specific emphasis on the influence of the Eckert number. Numerical simulations were performed for a moving lid configuration, maintaining a constant Reynolds number (Re=100) while systematically varying the Grashof numbers (Gr=103,104,105) and Eckert numbers. The analysis reveals distinct trends: In forced (Gr=103) and mixed (Gr=104) convection, the mean friction factor remains largely constant across different Eckert numbers, while the mean Nusselt number shows a significant increase with Eckert number. This suggests that viscous dissipation primarily enhances heat transfer without substantially altering wall shear stress in these regimes. Conversely, under free convection (Gr=105), both mean friction factor and Nusselt number exhibit a substantial increase with rising Eckert number, highlighting the dominant role of buoyancy forces and viscous dissipation in governing both heat transfer and energy losses. Detailed friction factor distribution profiles further illustrate these phenomena, revealing unique behaviors, particularly the emergence of a near-zero slope region in free convection at higher Eckert numbers.

Keywords

References

[1] M. Nawaz, "Numerical study of hydrothermal characteristics in nano fluid using KKL model with Brownian motion," (in en), Scientia Iranica, vol. 26, no. 3, pp. 1931-1943, 2019, doi: 10.24200/sci.2019.50073.1494.
[2] N. Amar and N. Kishan, "The influence of radiation on MHD boundary layer flow past a nano fluid wedge embedded in porous media," Partial Differential Equations in Applied Mathematics, vol. 4, p. 100082, 2021/12/01/ 2021, doi: https://doi.org/10.1016/j.padiff.2021.100082.
[3] T. Gong and Y. Wang, "An artificial neural networkbased quadratic constitutive Reynolds stress model for separated turbulent flows using data-augmented field inversion and machine learning," Physics of Fluids, vol. 37, no. 3, p. 035153, 2025, doi: 10.1063/5.0263211.
[4] T. Adibi and S. E. Razavi, "A Data-Driven PhysicsInformed Neural Network for Correcting Structural Errors in RANS Turbulence Models," (in en), Computational Sciences and Engineering, 2026, doi: 10.22124/cse.2026.32957.1159.
[5] M. A. Jamil, N. Imtiaz, K. C. Ng, B. B. Xu, H. Yaqoob, M. Sultan, and M. W. Shahzad, "Experimental and parametric sensitivity analysis of a novel indirect evaporative cooler for greener cooling," Thermal Science and Engineering Progress, vol. 42, p. 101887, 2023/07/01/ 2023, doi: https://doi.org/10.1016/j.tsep.2023.101887.
[6] N. V. K, "Opportunities, challenges, and state of the art of flexible heat-pipe heat exchangers: A comprehensive review," Heat Transfer, vol. 53, no. 2, pp. 893-938, 2024/03/01 2024, doi: https://doi.org/10.1002/htj.22978.
[7] M. H. Shojaeefard and S. Saremian, "Analyzing the impact of blade geometrical parameters on energy recovery and efficiency of centrifugal pump as turbine installed in the pressure-reducing station," Energy, vol. 289, p. 130004, 2024/02/15/ 2024, doi: https://doi.org/10.1016/j.energy.2023.130004.
[8] X. Liang, M. Min, K. Bian, and J. Cheng, "Study on the enhanced heat transfer and exergy performance of the finned tube heat exchanger with vortex generator," International Journal of Thermal Sciences, vol. 210, p. 109639, 2025/04/01/ 2025, doi: https://doi.org/10.1016/j.ijthermalsci.2024.109639.
[9] R. D. Alsemiry, H. M. Sayed, and N. Amin, "Mathematical analysis of Carreau fluid flow and heat transfer within an eccentric catheterized artery," Alexandria Engineering Journal, vol. 61, no. 1, pp. 523-539, 2022/01/01/ 2022, doi: https://doi.org/10.1016/j.aej.2021.06.029.
[10]S. Shukla, R. P. Sharma, T. M. Agbaje, and S. Mondal, "Investigation of thermodynamics characteristics of ternary hybrid nanofluid flow over a stretching sheet," Modern Physics Letters B, vol. 38, no. 12, p. 2450079, 2024/04/30 2023, doi: 10.1142/S0217984924500799.
[11]C. M. Mohana and B. R. Kumar, "Numerical and semi-analytical approaches for heat transfer analysis of ternary hybrid nanofluid flow: A comparative study," Mathematics and Computers in Simulation, vol. 226, pp. 66-90, 2024/12/01/ 2024, doi: https://doi.org/10.1016/j.matcom.2024.06.019.
[12]T. A. Seyed Esmail Razavi , Hussein Hassanpour, " Thermo-flow Analysis of Cylinder with Crossed Splitter Plates with a Characteristics-based Scheme," International Journal of Thermodynamics, vol. 24, no.
2, pp. 83-91, 2021, doi: 10.5541/ijot.783614.
[13]T. Adibi, S. E. Razavi, S. F. Ahmed, S. C. Saha, and N. A. Shah, "Role of a Hinged Single Separator in Heat Transfer Enhancement and Drag Reduction in Circular Cylinder Flow," Arabian Journal for Science and Engineering, 2024/08/18 2024, doi: 10.1007/s13369-024-09435-2.
[14]T. Adibi, S. E. Razavi, S. F. Ahmed, S. M. Shakor, and G. Liu, "Effects of Elastic Walls on the Thermal Performance of a Counterflow Heat Exchanger," International Journal of Energy Research, vol. 2024, no. 1, p. 8895936, 2024/01/01 2024, doi: https://doi.org/10.1155/er/8895936.
[15]N. Hedayati and A. Ramiar, "Investigation of two phase unsteady nanofluid flow and heat transfer between moving parallel plates in the presence of the magnetic field using GM," (in en), Challenges in Nano and Micro Scale Science and Technology, vol. 4, no. 1, pp. 52-58, 2016, doi: 10.7508/tpnms.2016.01.007.
[16]S. M. Ibrahim, p. Vijaya Kumar, and C. S. K. Raju, "Possessions of viscous dissipation on radiative MHD heat and mass transfer flow of a micropolar fluid over a porous stretching sheet with chemical reaction," (in en), Challenges in Nano and Micro Scale Science and Technology, vol. 6, no. 1, pp. 60-71, 2018, doi: 10.22111/tpnms.2018.3523.
[17]G. A. Sheikhzadeh, A. Aghaei, and S. soleimani, "Effect of nanoparticle shape on natural convection heat transfer in a square cavity with partitions using water-SiO2 nanofluid," (in en), Challenges in Nano and Micro Scale Science and Technology, vol. 6, no. 1, pp. 27-38, 2018, doi: 10.22111/tpnms.2018.3520.
[18]A. Shahriari, "Lattice Boltzmann method for MHD natural convection of CuO/water nanofluid in a wavywalled cavity with sinusoidal temperature distribution," (in en), Challenges in Nano and Micro Scale Science and Technology, vol. 5, no. 2, pp. 111- 129, 2017, doi: 10.7508/tpnms.2017.02.005.
[19]A. A. Abbasian Arani, M. Abbaszadeh, and A. Ardeshiri, "Mixed convection fluid flow and heat transfer and optimal distribution of discrete heat sources location in a cavity filled with nanofluid," (in en), Challenges in Nano and Micro Scale Science and Technology, vol. 5, no. 1, pp. 30-43, 2016, doi: 10.7508/tpnms.2017.01.004.
[20]R. P. Sharma, P. K. Pattnaik, S. R. Mishra, S. Tinker, and S. R. Allipudi, "Enhancing heat transfer on the free convection of conducting hybrid nanofluid through stretching/shrinking surface," Pramana, vol. 98, no. 3, p. 96, 2024/07/11 2024, doi: 10.1007/s12043-024-02762-x.
[21]R. P. Sharma, S. Baag, S. R. Mishra, and P. Sahoo, "Illustration of thermal radiation on the mixed convection of Williamson nanofluid over an inclined cylindrical surface," Modern Physics Letters B, vol. 38, no. 25, p. 2450141, 2024/09/10 2024, doi: 10.1142/S0217984924501410.
[22]Z. Iqbal et al., "Thermal convection and entropy generation analysis of hybrid nanofluid slip flow over a horizontal poignant thin needle with an inclined magnetic field: A numerical study," Modern Physics Letters B, vol. 38, no. 05, p. 2450004, 2024/02/20 2023, doi: 10.1142/S0217984924500040.
[23]S. E. Razavi, T. Adibi, and H. Hassanpour, "Sensitivity Analysis on Thermal Performance of Gas Heater with Finned and Finless Tubes using Characteristics-based Method," (in en), International Journal of Engineering, vol. 34, no. 6, pp. 1537-1544, 2021, doi: 10.5829/ije.2021.34.06c.18.
[24]T. Adibi, S. E. Razavi, O. Adibi, M. Vajdi, and F. Sadegh Moghanlou, "The response of nano-ceramic doped fluids in heat convection models: A characteristics-based numerical approach," (in en), Scientia Iranica, vol. 28, no. 5, pp. 2671-2683, 2021, doi: 10.24200/sci.2021.56574.4794.
[25]S. E. Razavi and T. Adibi, "Simulation of fluid flow in a counter-flow heat exchanger with partly elastic intermediate walls," (in en), Computational Sciences and Engineering, 2026, doi: 10.22124/cse.2026.32640.1149.
[26]T. Adibi and S. E. Razavi, "A novel multidimensional characteristic modeling of incompressible convective heat transfer," (in en), Journal of Solid and Fluid Mechanics, vol. 5, no. 4, pp. 283-296, 2015, doi: 10.22044/jsfm.2015.683.
[27]S. E. Razavi and T. Adibi, "A novel multidimensional characteristic modeling of incompressible convective heat transfer," Journal of Applied Fluid Mechanics, vol. 9, no. 4, pp. 1135-1146, 2016 2016, doi: 10.18869/acadpub.jafm.68.228.24295.
[28]T. Adibi and S. E. Razavi, "A new characteristic approach for incompressible thermo-flow in Cartesian and non-Cartesian grids," International Journal for Numerical Methods in Fluids, vol. 79, no. 8, pp. 371-393, 2015, doi: 10.1002/fld.4053.
[29]R. Iwatsu, J. M. Hyun, and K. Kuwahara, "Mixed convection in a driven cavity with a stable vertical temperature gradient," International Journal of Heat and Mass Transfer, vol. 36, no. 6, pp. 1601-1608, //1993, doi: http://dx.doi.org/10.1016/S0017-9310(05)80069-9.
Challenges in Nano and Micro Scale Science and Technology
Volume 14, Issue 2
September 2026
Pages 16-30

Files

Share

How to cite

Statistics