This work provides a comprehensive theoretical analysis of a two-dimensiona
l unsteady free convection flow of an incompressible, visco-elastic fluid p
ast an infinite vertical porous plate. Solutions for the zero order perturb
ation velocity profile, the first order perturbation velocity and temperatu
re profiles in closed form are obtained with the help of Laplace transform
technique. The numerical solutions are carried out for the Prandtl number 0
.1, 0.72, 1.0, 1.5 and 2.0 which are appropriate for different types of liq
uid metals and for different values of magnetic field parameter, M.