3D natural convection melting in a cubical cavity with a heat source

Three-dimensional natural convection melting in a cubical cavity with a local heater has been analyzed numerically. The considered region is an enclosure bounded by two isothermal opposite vertical surfaces of low constant temperature and adiabatic other walls. A heat source of high constant temperature is located on the bottom wall. 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 Rayleigh number (5⋅10⁴ ≤ Ra ≤ 5⋅10⁷) and dimensionless time for Prandtl number (Pr = 48.36) and Stefan number (Ste = 5.53) on streamlines, isotherms, profiles of temperature and velocity as well as mean Nusselt number at the heat source surface have been analyzed.