The sudden melting of a thin vertical flat plate in a Darcian free convection flow (Q584010)

The unsteady free convection boundary layer equations for sudden melting of a thin vertical flat plate in steady fluid-saturated porous media are solved with the corresponding steady free convection solutions as initial values. Asymptotic solutions at very small time t and very large time t are obtained analytically, in which inner and outer solutions for small time case are matched. Starting from the small time solution, a numerical solution to join up both asymptotic solutions is made by marching method for parabolic type differential equation. Good agreement between analytical solution and numerical solution at large values of time is shown.