Effects of non-uniform nanoparticle concentration on entropy generation


  • Ahmer Mehmood International Islamic University, Islamabad
  • Sajid Khan International Islamic University, Islamabad
  • Muhammad Usman University of Education Lahore, Vehari Campus




Nanofluid, non-homogeneous modeling, entropy generation, moving surface


The entropy generation analysis of a thermal process is capable of determining the efficiency of that process and is therefore helpful to optimize the thermal system operating under various conditions. There are several ingredients upon which the phenomenon of entropy generation can depend, such as the nature of flow and the fluid, the assumed conditions, and the material properties of the working fluid. However, the dependence of entropy generation phenomenon upon such properties has so far not been fully realized, in view of the existing literature. On the other hand, based upon the existing studies, it has been established that the non-uniform concentration of nanoparticles in the base fluid does cause to enhance the heat transfer rate. Therefore, it is logical to investigate the entropy production under the impact of non-homogenous distribution of nanoparticles. Based upon this fact the aim of current study is to explore a comprehensive detail about the influence of non-homogeneous nanoparticles concentration on entropy production phenomenon by considering a laminar viscous flow past a moving continuous flat plate. Non-uniform concentration is considered in the nanofluid modeling in which the Brownian and thermophoretic diffusions are considered which impart significant effects on velocity and temperature profiles. An exact self-similar solution to this problem is observed to be possible and is reported. The effects of various controlling physical parameters such as Brinkman number, Schmidt number, Prandtl number, diffusion parameter, and concentration parameter on both local as well as total entropy generation number and Bejan number are elaborated by several graphs and Tables. The obtained results reveal a significant impact of all aforementioned parameters on entropy generation characteristics. It is observed that by a 20% increase in nanoparticles concentration the total entropy generation is increased up to 67% for a set of fixed values of remaining parameters.


A. Bejan, A study of entropy generation in fundamental convective heat transfer, J. Heat Transfer, 101 (1979) 718. https://doi.org/10.1115/1.3451063.

A. Bejan, Second law analysis in heat transfer, Energy, 5 (1980) 720, https://doi.org/10.1016/0360-5442(80)90091-2.

A. Bejan, Entropy generation through heat and fluid flow, (Wiley, New York, 1982)

J.Y. San, W.M. Worek, and Z. Laven, Entropy generation in convective heat transfer and isothermal mass transfer, J. Heat Trans. 109 (1987) 647, https://doi.org/10.1115/1.3248137.

B. Yilbas, Entropy analysis of concentric annuli with rotating outer cylinder, Int. J. Energy, 1 (2001) 60. https://doi.org/10.1016/S1164-0235(01)00011-5.

S. Mahmud, and R.A. Fraser, The second law analysis in fundamental convective heat transfer problems Int. J. Therm. Sci. 42 (2003) 177. https://doi.org/10.1016/S1290-0729(02)00017-0.

A.S. Butt, S. Munawar, A. Ali, and A. Mehmood, Entropy generation in the Blasius flow under thermal radiation, Phys. Scr. 85 (2012) 035008, https://doi.org/10.1088/0031-8949/85/03/035008.

O. D. Makinde, Second law analysis for variable viscosity hydromagnetic boundary layer flow with thermal radiation and newtonian heating, Entropy 13 (2011) 1446, https://doi.org/10.3390/e13081446.

A.S. Butt, S. Munawar, A. Ali, and A. Mehmood, Entropy generation in hydrodynamic slip flow over a vertical plate with convective boundary, J. Mech. Sci. Tech. 26 (2012) 2977, https://doi.org/10.1007/s12206-012-0701-3.

A. Mehmood, M.S. Iqbal, S. Khan, and S. Munawar, Entropy analysis in moving wavy surface boundary layer, Therm. Sci. 23 (2019) 233, https://doi.org/10.2298/TSCI161029029M.

M.M. Rashidi, S. Abelman, and N.F. Mehr, Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid, Int. J. Heat Mass Tran. 62 (2013) 515, https://doi.org/10.1016/j.ijheatmasstransfer.2013.03.004.

A. Noghrehabad, M.R. Saffarian, R. Pourrajab, and M. Ghalambaz, Entropy analysis for nanofluid flow over a stretching sheet in the presence of heat generation/absorption and partial slip, J. Mech. Sci. Tech. 27 (2013) 927, https://doi.org/10.1007/s12206-013-0104-0.

M.M. Rashidi, M.M. Bhatti, M.A. Abbas, and M.E. Ali, Entropy generation on MHD blood flow of nanofluid due to peristaltic waves, Entropy 18 (2016) 117, https://doi.org/10.3390/e18040117.

M. Almakki, S. Dey, S. Mondal, and P. Sibanda, On unsteady three-dimensional axisymmetric MHD nanofluid flow with entropy generation and thermo-diffusion effects on a non-linear stretching sheet, Entropy 19 (2017) 168, https://doi.org/10.3390/e19070168.

S.E.B. Magia, C.T. Nugyen, N. Glanis, and G. Roy, Heat transfer behaviours of nanofluids in a uniformly heated tube, Supperlattices Microstruct. 35 (2004) 543, https://doi.org/10.1016/j.spmi.2003.09.012.

A.A. Avramenko, D.G. Blinov, and I.V. Shevchuk, Self-similar analysis of fluid flow and heat-mass transfer of nanofluids in boundary layer, Phys. Fluids 23 (2011) 082002, https://doi.org/10.1063/1.3623432.

A.A. Avramenko, D.G. Blinov, I.V. Shevchuk, and A.V. Kuznetsov, Symmetry analysis and self-similar forms of fluid flow and heat-mass transfer in turbulent boundary layer flow of a nanofluid, Phys. Fluids 24 (2012) 092003, https://doi.org/10.1063/1.4753945.

A. Mehmood, and M. Usman, Non-uniform nanoparticle concentration effects on moving plate boundary layer, Can. J. Phys. 94 (2016) 1222, https://doi.org/10.1139/cjp-2016-0129.

M. Frank, D. Anderson, E.R. Weeks, and J.F. Morris, Particle migration in pressure driven low of a Brownian suspension, J. Fluid Mech. 493 (2003) 363, https://doi.org/10.1017/S0022112003006001.

D. Mehri, E. Lemaire, G. Bossis, and F. Moukalled, Particle migration in a concentrated suspension flowing between rotating parallel plates: investigation of diffusion flux coefficients, J. Rheol. 49 (2005) 1429, https://doi.org/10.1122/1.2079247.

Y.L. Ding, and D. Wen, Particle migration in a flow of nanoparticle suspensions, Powder Tech. 149 (2005) 84, https://doi.org/10.1016/j.powtec.2004.11.012.

J. Buongiorno, Convective transport in nano-fluids, ASME J. Heat Tran. 128 (2006) 240, https://doi.org/10.1115/1.2150834.

R.K. Tiwari, and M.K. Das, Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids, Int. J. Heat Mass Tran. 50 (2007) 2002, https://doi.org/10.1016/j.ijheatmasstransfer.2006.09.034.

N. Dalir, M. Dehsara, and S.S. Nourazar, Entropy analysis for magnetohydrodynamic flow and heat transfer of a Jeffrey nanofluid over a stretching sheet, Energy 79 (2015) 351, https://doi.org/10.1016/j.energy.2014.11.021.

V. Bianco, O. Manca, S. Nardini, and K. Vafai, Heat Transfer Enhancement with Nanofluids (CRC Press, Boca Raton, 2015),





How to Cite

A. Mehmood, S. Khan, and M. Usman, “Effects of non-uniform nanoparticle concentration on entropy generation”, Rev. Mex. Fís., vol. 68, no. 1 Jan-Feb, pp. 010601 1–, Jan. 2022.