New analysis of natural convection boundary layer flow on a horizontal plate with variable wall temperature

In this study, steady laminar free convection boundary layer flow on a horizontal plate is investigated through analytical solutions. By transforming the governing non-dimensional boundary layer equations into an ordinary differential equation, the application of the Homotopy Analysis Method can be practical. So in this case, the analytical results for different Prandtl numbers and constant $ M$ values which portray the power index are achieved. The trend goes on large amounts of $ (M\gg1)$ and the results are compared with other efforts. Furthermore, the effects of different values of Prandtl number and $ M$ values on temperature and velocity profiles are verified.