Natural convection in a cavity filled with porous medium under the effect of a partial magnetic field

Natural convection flow in presence of partially applied magnetic field in a porous medium is investigated in this study. Partial magnetic field is applied horizontally in the direction of positive x-axis, and vertical walls of unit square cavity are differentially heated. Fluid flow in the porous medium is modelled by Brinkman-Forchheimer-extended Darcy equation of motion. Pseudo spectral method based on polyharmonic spline radial basis function f = r(7) is numerically performed for discretization of space derivatives and backward Euler method is carried out for time derivatives in governing dimensionless equations. The variation of the length of the partial magnetic field, Hartmann number, Rayleigh number, Darcy number and the location of the center of the partial magnetic field is presented in terms of streamlines, isotherms and vorticity contours. Central vortex in streamlines is pushed as the length of partial magnetic field increases in case of a top centered applied partial magnetic field. Convective heat transfer is suppressed if middle centered magnetic field is applied partially. Partial magnetic field may control fluid flow and heat transfer at required parts of the cavity.