A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition

The problem of a steady forced convection thermal boundary-layer past a flat plate with a prescribed surface heat flux is investigated both analytically and numerically. In view of the present formulation, the governing equations reduce to the well-know Blasius similarity equation and to the full boundary-layer energy equation with two parameters: Prandtl number and surface heat flux parameter. The range of existence of solutions is considered. The asymptotic solutions are derived and compared with the numerical solutions of the full boundary-layer equation. A very good agreement between these asymptotic solutions and numerical simulations are found in the range of Prandtl numbers considered.