Finite element simulation of magnetoconvection inside a sinusoidal corrugated enclosure with discrete isoflux heating from below

A numerical investigation of the steady magnetoconvection in a sinusoidal corrugated enclosure has been performed. In this analysis, two vertical sinusoidal corrugated walls are maintained at a constant low temperature whereas a constant heat flux source whose length is varied from 20 to 80% of the reference length of the enclosure is discretely embedded at the bottom wall. The Penalty finite element method has been used to solve the governing Navier–Stokes and energy conservation equation of the fluid medium in the enclosure in order to investigate the effect of discrete heat source sizes on heat transfer for different values of Grashof number and Hartmann number. The values of the governing parameters are the Grashof number Gr (103 to 106), Hartmann number Ha (0 to 100) and Prandtl number Pr (0.71). The present numerical approach is found to be consistent and the solution is obtained in terms of stream functions and isotherm contours.