THERMAL SCIENCE
International Scientific Journal
Find this paper on
INFLUENCE OF THERMAL DISPERSION AND VARIABLE VISCOSITY ON MIXED CONVECTION FLOW IN NON-DARCY POROUS MEDIUM FILLED BY NANOLIQUID
ABSTRACT
In this current paper, a numerical analysis was performed to study the effects of variable viscosity and thermal dispersion considered for an Ergun-Darcy mixed convection flow on a heated horizontal plate from below by variable heat flux in a saturated porous medium filled with Tiwari and Das nanoliquid. The governing partial differential equations are transformed into coupled nonlinear ordinary differential equations using an appropriate similarity transformation and the resulting system of equations is then solved numerically by efficient finite-difference method. Numerical results are presented to illustrate how the physical parameters affect the flow field, temperature and concentration. Moreover, the interesting features of the solutions in terms of the number of Nusselt are presented graphically.
KEYWORDS
PAPER SUBMITTED: 2025-08-15
PAPER REVISED: 2026-05-20
PAPER ACCEPTED: 2026-06-01
PUBLISHED ONLINE: 2026-08-07
DOI REFERENCE: https://doi.org/10.2298/TSCI250815156A
[1] Khanafer, K., Vafai, K., Applications of nanofluids in porous media, Journal of Thermal Analysis and Calorimetry 135 (2019) pp. 1479-1492
[2] Vafai, K., handbook of porous media, CRC Press, New York, 2015, pp. 493-531
[3] Mahmoudi, Y., et al., Convective Heat Transfer in Porous Media, CRC Press, New York, 2019, pp. 55-83
[4] Nield, D.A., Bejan, A., Convection in Porous Media, fifth ed., Springer, New York, 2017
[5] Rashad, A.M., Chamkha, A.J., Modather, M., Mixed convection boundary-layer flow past a horizontal circular cylinder embedded in a porous medium filled with a nanofluid under convective boundary condition, Computers & Fluids, 86 (2013) pp. 380-388
[6] Ahmad, S., Pop, I., Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids, International Communications in Heat and Mass Transfer, 37 (2010) 987-991
[7] Rohni, A. M., et al., Mixed convection boundary-layer flow along a vertical cylinder embedded in a porous medium filled by a nanofluid, Transport in Porous Media, 96 (2013), 2, pp. 237-253
[8] Sedki, A. M., Effect of thermal radiation and chemical reaction on MHD mixed convective heat and mass transfer in nanofluid flow due to nonlinear stretching surface through porous medium, Results in Materials, 16 (2022) pp. 100334
[9] Kodi, R., et al., Influence of MHD mixed convection flow for maxwell nanofluid through a vertical cone with porous material in the existence of variable heat conductivity and diffusion, Case Studies in Thermal Engineering 44 (2023) pp.102875
[10] Kumari, P., et al., Magnetic field effect on non-darcy mixed convection from a horizontal plate in a nanofluid-saturated porous medium, Journal of Porous Media, 22(2019), 5, pp.599-610
[11] Trîmbiţaş, R., et al., Mixed convection boundary layer flow past vertical flat plate in nanofluid: case of prescribed wall heat flux, Applied Mathematics and Mechanics, 36(2015), 8, pp. 1091-1104
[12] Kameswaran, P. K., Sibanda, P., Thermal dispersion effects on convective heat and mass transfer in an Ostwald de Waele nanofluid flow in porous media, Boundary Value Problems, 2013, (2013) pp. 1-12
[13] Bouaziz, A. M., Hanini, S., Double Dispersion for Double Diffusive Boundary Layer in Non-Darcy Saturated Porous Medium Filled by a Nanofluid, Journal of Mechanics, 32 (2016), 4, pp. 441 - 451
[14] Sheremet, M.A., Effect of thermal dispersion on transient natural convection in a wavy-walled porous cavity filled with a nanofluid: Tiwari and Das' nanofluid model, International Journal of Heat and Mass Transfer, 92 (2016) pp.1053-1060
[15] RamReddy, Ch., Venkata Rao, Ch., Double dispersion effects on non-Darcy free convective boundary layer flow of a nanofluid over vertical frustum of a cone with convective boundary condition, Nonlinear Engineering, 6 (2017), 4, pp. 277-292
[16] Sudhagar, P., et al., Thermal dispersion effect on nanofluid: a revised model, Journal of Porous Media, 23, (2020), 9, pp. 923-941
[17] Awad, F. G., et al., A Note on Double Dispersion Effects in a Nanofluid Flow in a Non-Darcy Porous Medium, Journal of Heat Transfer, 137, (2015), 10, pp.104501-104506
[18] Meena, Om P., et al., Mixed convection flow over a vertical cone saturated porous medium with double dispersion effect, Applied Mathematics and Computation, 430 (2022) pp.127072
[19] Khashi'iea, N. S., et al., Non-Darcy mixed convection of hybrid nanofluid with thermaldispersion along a vertical plate embedded in a porous medium, International Communications in Heat and Mass Transfer, 118 (2020) pp. 104866
[20] Jayanthi, S., Kumari, M., Effect of variable viscosity on non-Darcy free or mixed convection flow on a vertical surface in a non-Newtonian fluid saturated porous medium, Applied mathematics and computation, 186 (2007) pp. 1643-1659
[21] Soares, A. A., et al., Effect of temperature-dependent viscosity on forced convection heat transfer from a cylinder in crossflow of power-law fluids, International Journal of Heat and Mass Transfer, 53 (2010) pp. 4728-4740
[22] Kandasamy, R., Hashim, I., Thermophoresis and chemical reaction effects on non-Darcy mixed convective heat and mass transfer past a porous wedge with variable viscosity in the presence of suction or injection, Nuclear Engineering and Design, 238(10) pp. 2699-2705
[23] Pal, D., Mondal, H., Influence of Soret and Dufour on MHD buoyancy-driven heat and mass transfer over a stretching sheet in porous media with temperature-dependent viscosity, Nuclear Engineering and Design, 256 (2013) pp. 350-357
[24] Pal, D., Mondal, H., Hydromagnetic convective diffusion of species in Darcy-Forchheimer porous medium with non-uniform heat source/sink and variable viscosity, International Communications in Heat and Mass Transfer, 39 (7) pp. 913-917
[25] Makinde, O. D., et al., MHD variable viscosity reacting flow over a convectively heated plate in a porous medium with thermophoresis and radiative heat transfer, International journal of heat and mass transfer, 93 (2016) pp. 595-604
[26] Umavathi, J. C., et al., Combined effect of variable viscosity and thermal conductivity on mixed convection flow of a viscous fluid in a vertical channel in the presence of first order chemical reaction, European Journal of Mechanics-B/Fluids 58 (2016), pp. 98-108
[27] Tiwari, R.K., et al., Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids, International Journal of Heat and Mass Transfer, 50 (2007) pp. 2002-2018
[28] Ergun, S., Fluid flow through packed columns, Chemical Engineering Progress, 48 (1952) pp. 89- 94
[29] Plumb, O., The effect of thermal dispersion on heat transfer in packed bed boundary layers Proc. First ASME/JSME Thermal Engineering Joint Conference 2, (1983) pp. 17-21
[30] Hong, J. T., et al., Analysis of thermal dispersion effect on vertical plate natural Convection in porous media, International Journal of Heat and Mass Transfer, 30 (1987) pp.143-150
[31] Lai, F. C., et al., Thermal dispersion effect on non-Darcy convection from horizontal surface in saturated porous media, International Journal of Heat and Mass Transfer, 32 (1989), pp.971-976
[32] Rosca, A. V., et al., non-Darcy mixed convection from a horizontal plate embedded in a nanofluid saturated porous media, International Communications in Heat and Mass Transfer, 39 (2012), pp.1080-1085
[33] Ali Agha, H., et al., Magnetohydrodynamic thermal radiation and convective boundary effects of free convection flow past a vertical plate embedded in a porous medium saturated with a nanofluid, Journal of Mechanics 31 (2015), 5, pp. 607-616
[34] Hussain, M., et al., Numerical investigation of ohmically dissipated mixed convective flow, Case Studies in Thermal Engineering, 31 (2022), 101809
[35] Shampine, L. F., et al., Solving ODEs with matlab, first ed., Cambridge university press, United Kingdom, 2003
[36] M. Guedda, M., et al., Exact similarity solutions for forced convection flow over horizontal plate in saturated porous medium with temperature-dependent viscosity, The European Physical Journal Plus, 132(2017), 9, pp. 376-392
© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International licence


