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[References: 23 tit.]

MHD natural convection melting in a square cavity with a local heater has been analyzed numerically. The domain of interest is an enclosure bounded by isothermal vertical walls of low constant temperature and adiabatic horizontal walls. A heat source of constant temperature is located on the bottom wall. An inclined uniform magnetic field affects the natural convective heat transfer and fluid flow inside the melt. The governing equations formulated in dimensionless stream function, vorticity 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 Rayleigh number, Stefan number, Hartmann number, magnetic field inclination angle and dimensionless time on streamlines, isotherms and Nusselt number at the heat source surface have been analyzed.