Natural convection heat transfer combined with melting process in a cubical cavity under the effects of uniform inclined magnetic field and local heat source

Natural convective heat transfer combined with melting in a cubical cavity filled with a pure gallium under the effects of inclined uniform magnetic field and local heater has been studied numerically. The domain of interest is an enclosure bounded by two isothermal opposite vertical surfaces of low constant temperature and adiabatic other walls. A heat source of constant temperature is located on the bottom wall. An inclined uniform magnetic field affects the melting process inside the cavity. The governing equations formulated in dimensionless vector potential functions, vorticity vector and temperature with corresponding initial and boundary conditions have been solved using implicit finite difference method of the second-order accuracy. The effects of the Hartmann number, magnetic field inclination angle and dimensionless time on streamlines, isotherms, profiles of temperature and velocity as well as mean Nusselt number at the heat source surface have been analyzed. The obtained results revealed that a growth of magnetic field intensity reflects the convective flow suppression and heat transfer rate reduction. High values of Hartmann number homogenize the liquid flow and heat transfer inside the melting zone.