Radiative magneto‐thermogravitational flow in a porous square cavity with viscous heating and Hall current effects: A numerical study of ψ–v scheme

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Abstract
A numerical study presented for the natural convection two‐dimensional incompressible flow of a magnetized fluid in a square enclosure filled with porous medium. Viscous dissipation, thermal radiation, and Hall current effects are included. The formulated computational domain comprising the mass, momentum, and energy conservation equations with appropriate boundary conditions, is rendered dimensionless via appropriate scaling transformations. The resulting nondimensional partial governing equations are solved by the ψ–v scheme. A detailed parametric investigation of the influence of Hartman number (magnetic body force parameter), Rayleigh number (thermal buoyancy parameter), Darcy number (permeability parameter), Eckart number for porous medium, Hall parameter, and radiation parameter on the streamline, temperature contours, local Nusselt number along the hot wall and mid‐section velocity profiles are computed. Thermal Rayleigh number can be a control key parameter on heat and flow in enclosures. In addition, the heat transfer rate is intensified with increasing thermal Rayleigh numbers. With increasing Darcy number (i.e., greater permeability of the porous medium and progressively lower Darcian drag force) there is a strong elevation in the average Nusselt number at the left hot wall.

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