Boundary layer convective heat transfer with pressure gradient using Homotopy Perturbation Method (HPM) over a flat plate

Convective heat transfer equations of boundary layer with pressure gradient over a flat plate are solved using Homotopy Perturbation Method (HPM). This variation method is able to study the effects of Prandtl number (Pr) and pressure gradient (m) on both temperature and velocity distributions in the boundary layer. To this aim, the nonlinear equations of momentum and energy are solved simultaneously. Results of HPM in the absence of pressure gradient are in good agreement with results obtained from numerical methods. In addition, a general equation in terms of Re number, Pr number, and pressure gradient is derived using Nu number definition which can be used to obtain heat transfer coefficient for various situations.