The transient behavior and heat transfer for the melting of ice in porous media within a rectangular enclosure is simulated by the numerical method SIMPLE C. The solid-liquid interface becomes irregular due to the presence of porous media. The mushy zone of the finite thickness is taken into consideration in this investigation. The entire flow held is modeled by the non-Darcy model which incorporates effects of convection, inertia and boundary friction. Based upon the numerical results, the non-linear factor due to temperature-dependent density of the molten liquid could be a significant contributor to temperature field, flow field, position of interface, and capacity of heat transfer. A temperature exists on the hot side where minimum heat transfer takes place. As the Darcy number gets larger, the heat transfer gets better, the rate of melting of ice goes faster, and the interface distorts more. As time goes on, heat transfer on the hot side worsens and that on the cold side gets better.