In this paper, we develop numerical methods for the natural convection flow from a vertical Bat plate with a surface temperature oscillation. In the steady case, numerical results for the Grashof numbers 0-625 an obtained using an iterative approach and the results for small Grashof numbers are validated using a perturbation method. For larger values of the Grashof numbers, an unsteady numerical scheme is constructed and the results obtained at large times are compared with the steady solutions. Further, the results for very large Glashof numbers, up to 10 000, show that the unsteady solution approaches a steady solution. All the results obtained show that the proposed methods are very efficient and accurate.