Developing flow near a semi-infinite vertical wall with ramped temperature

The buoyancy-driven boundary layer flow and heat transfer in a viscous incompressible fluid bounded by a semi-infinite vertical wall has been considered. It is assumed that the bounding wall has a ramped temperature profile with respect to time. The solutions of the coupled nonlinear momentum and energy equations have been obtained using an implicit finite difference method of Crank-Nicolson type. The variations of velocity and temperature in the boundary layer, at a fixed cross section, as well as the skin friction and Nusselt number along the heated surface, have been discussed. Some contour curves of temperature distributions have also been shown.