MHD flow and heat transfer in a porous enclosure heated by two inner cylinders using Darcy–Forchheimer–Brinkman extended model

Abstract

This study presents a numerical investigation of natural convection in a square enclosure filled with an electrically conducting fluid saturated in a Darcy-type porous medium. The system features two symmetrically embedded hot circular cylinders placed along the vertical centerline of the cavity. The enclosure is externally cooled, while a uniform vertical magnetic field is applied downward along the negative y-axis. The coupled momentum and energy equations are solved using the finite volume method based on the Brinkman Forchheimer extended Darcy model. A comprehensive analysis is performed to examine the effects of key dimensionless parameters namely, the Rayleigh number ([Formula: see text]), Hartmann number (Ha) and Darcy number (Da) on flow structures, thermal fields and heat transfer performance. Additionally, the influence of geometric parameters such as the cylinder diameter (D) and the spacing between cylinders ([Formula: see text]) is investigated to identify optimal thermal configurations. Results show that increasing magnetic field strength suppresses fluid circulation and reduces heat transfer, especially at high permeability. A predictive correlation for the average Nusselt number is proposed, achieving a high degree of accuracy ([Formula: see text]). The optimal thermal performance is obtained for [Formula: see text], [Formula: see text] and [Formula: see text], under a moderate magnetic field ([Formula: see text]).