MHD natural convective flow in a porous corrugated enclosure: Effects of different key parameters and discrete heat sources

Present work deals with an unsteady two-dimensional magneto-hydrodynamics natural convection flow problem in a porous-corrugated enclosure. The vertical side walls are insulated, and the top wall is non-uniformly heated; while square-shaped undulations at the bottom wall are discretely heated. Five different cases are considered depending on the discrete heat sources and various key parameters. A transformation-free higher-order compact (HOC) scheme is used to discretize the non-linear coupled transport equations, and an advanced iterative solver, like the hybrid-bi-conjugate-gradient stabilized technique, is used to solve the system of algebraic equations generated from the numerical discretization. Present higher-order compact scheme is fourth-order accurate in space coordinates and second-order accurate in the time variable. At first, the developed code is validated with existing experimental and numerical computed results for the case of a square enclosure associated with and without a heat source. Then, the computed results are analysed over a range of key parameters, like Rayleigh number (10(3) <= Ra <= 10(6)), Darcy Number (10(-5) <= Da <= 10(-1)), Hartmann number (25 <= Ha <= 150), with a fixed Prandtl number (Pr = 6.1), to study the effects of these key parameters on the fluid flow behaviour and isotherm patterns in the porous-corrugated enclosure. It is found that at high Rayleigh-Darcy numbers with different Hartmann numbers, the effect of the permeability of the porous medium is significant; whereas the flow resistance from the boundary friction is gradually reduced, and the flow behaviour is similar to the pure buoyancy-induced flow. These simulated results are presented in the form of streamlines, isotherms, local and averaged Nusselt number plots, etc. The presented results show various flow features that have not been analysed before.