Study of melting of a pure gallium under influence of magnetic field in a square cavity with a local heat source

Numerical analysis of the unsteady natural convection with phase transitions inside the pure galluim under the influence of a uniform magnetic field with a heat source of constant temperature has been conducted in the presence of magnetic field. The vertical walls of the cavity are kept at low constant temperatures whereas the top and bottom horizontal walls are adiabatic with the exception of the heat source of high constant temperature. The mathematical model formulated in dimensionless stream function, vorticity and temperature variables is solved using the implicit finite difference schemes of the second order. The governing parameters are the Rayleigh and Hartmann numbers, and the dimensionless time. The effects of these parameters on the streamlines and isotherms are analyzed.