MHD natural convection in a corrugated enclosure with discrete isothermal heating

In this study, we numerically examine the unsteady two-dimensional natural convective heat transfer flow problem in a corrugated enclosure containing an electrically conducting fluid whose top wall is non-uniformly heated. The vertical sidewalls of the corrugated enclosure are kept isothermally cold, while square-shaped undulations at the bottom wall are discretely heated. Five different cases are considered depending upon the location of the heat sources. A higher-order compact scheme is used to discretize the governing equations, and an advanced iterative solver, like the hybrid biconjugate gradient stabilized method, is used to solve the system of algebraic equations generated by the numerical discretization. We first validate our results with existing experimental and numerically computed results for the case of a square cavity with and without a heat source. Then, the computed results are analyzed over a range of key parameters, like Rayleigh number (10(3) <= Ra <= 10(6)), Hartmann number (10 <= Ha <= 150), and Prandtl number (0.015 <= Pr <= 10), to study the effect of these parameters on the characteristics of heat transfer and the flow field in the corrugated enclosure. Computed results are presented in the form of streamlines, isotherms, local and averaged Nusselt number plots, and so forth. It is found that, with the increase in the heat sources, the convection rate becomes stronger in the core region of the corrugated enclosure at higher Rayleigh numbers. Variations in the Hartmann and Prandtl numbers also have significant effects on the temperature distribution and flow field. Our simulated results show various flow features that have not been studied before.