Thermal MHD Free Convection of a Nanofluid in a Square Porous Cavity Partially Heated and Cooled from Opposite Walls Using Buongiorno’s Two-Phase Model

¹ Cadi Ayyad University, Faculty of Sciences Semlalia, Department of Physics, LMFE, BP 2390 Marrakesh, Morocco
² LS2M Laboratory, Polydisciplinary Faculty of Khouribga, Sultan Moulay Slimane University, 25000 Khouribga, Morocco

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 22 May 2026

Abstract

This study focuses on natural convection within a square porous cavity that is partially heated/(cooled) along its left and bottom/(right and top) walls, filled with a nanofluid and subjected to an external horizontal magnetic field. All walls are assumed to be impermeable. The Buongiorno mathematical model has been employed to take into consideration Brownian and thermophoretic diffusion effect, in order to show the spatial distribution of the local nanoparticle concentration. Using the finite volume method and the SIMPLE algorithm, the governing equations have been discretized. The results are depicted in terms of streamlines, isotherms, and iso-concentration contours, as well as through the evaluation of the average Nusselt number for different values of Darcy number, Da, Hartmann number, Ha, Rayleigh number, R_T, thermophoresis number N_t, Brownian number N_b and Buoyancy ratio N_r. The Lewis and Prandtl numbers are assumed to remain constant, with Le=25 and Pr=7, and the porosity of the cavity is assumed to be 0.8 (a porosity of 0.8 corresponds to a moderately dense porous medium, typical of materials such as metal foams, fibrous layers, or certain granular media). All of these variables were discovered to have significant influences on the strength of nanofluid flows, as well as the flow structure and the rate of heat transfer.