MHD natural convection flow in a porous medium-filled corrugated enclosure: Effect of heat sources with different heights

Abstract

A two-dimensional natural convection flow problem in a porous medium-filled enclosure with electrically conducting fluids and solid heat sources of different heights is numerically investigated in this study. The top boundary is cold, and the vertical side boundaries are insulated, while rectangular-shaped corrugations at the lower boundary are generated by placing heat sources. Three distinctive cases are considered concerning the height of the solid rectangular-shaped heat sources. The nonlinear coupled transport equations are discretized by using a higher-order compact (HOC) finite difference scheme. First, existing numerical and experimental data are used to validate the developed code. Then, the effect of key parameter values, like Hartmann number (25–150), Rayleigh number (103–106), Darcy number (10−5–10−1), and Prandtl number (0.015–10), on the convective flow in the corrugated enclosure is analysed. The influence of the permeability of the porous medium is abundantly seen for a range of significant parameter values with a fixed high Rayleigh-Darcy number. The formation of primary, secondary, tertiary, and quaternary vortices affects the thickness of the thermal boundary layer on both hot and cold surfaces in both symmetric and asymmetric patterns. In addition, possible multiple steady states are observed in the Case 2 at Pr=10.0. The local and average Nusselt numbers remains constant on the bottom cold surfaces of the corrugated enclosure, while significant variations are observed on the upper surfaces of the heat sources. These findings are analysed by conducting stream-function (ψ), isotherms (T), local (Nuh,Nuv), and average (Nū) Nusselt number plots. The intensities of heat transfer rate are also examined by analysing Nusselt numbers as a function of Prandtl, Darcy, Rayleigh and Hartmann numbers. Analysing natural convective heat transfer fluid flow in an enclosure with heat sources is prominent for ample engineering applications such as solar collectors, designing nuclear reactors, chemical energy production systems, building constructions and microelectronic equipment, to name a few.