magneto-hydrodynamic flow in a two-dimensional inclined rectangular enclosure heated and cooled on adjacent walls

Steady, laminar, natural-convection flow in the presence of a magnetic field in an inclined rectangular enclosure heated from one side and cooled from the adjacent side was considered. the governing equations were solved numerically for the stream function, vorticity and temperature using the finite-volume method for various grashof and hartman numbers and inclination angles and magnetic field directions. the results show that the orientation and the strength and direction of the magnetic field have significant effects on the flow and temperature fields. counterclockwise inclination induces the formation of multiple eddies inside the enclosure significantly affecting the temperature field. circulation inside the enclosure and therefore the convection become stronger as the grashof number increases while the magnetic field suppresses the convective flow and the heat transfer rate