Abstract
This article contains the free convective flow in a rectangular cavity having partially heated vertical wall. Further it is assumed that flow and thermal profiles are influenced by Lorentz forces applied in the perpendicular direction to the flow distribution. This physical setup is translated in mathematical form, which is expressed as differential equation. Finite element method is adopted to get the solution of these partial differential equations, the results against various flow controlling variables are presented in contour plots and line graphs. Results depict that at various heated length streamlines distribution gets stronger due to stronger buoyancy effects. Higher values of Rayleigh number correspond to maximum Nusselt number and temperature profile. Moreover, the streamlines pattern is reduced by increasing Hartman number and resulting the conduction mode of heat transportation.