On thermal boundary layers on a flat plate subjected to a variable heat flux

Abstract

The problem of a steady forced convection thermal boundary-layer past a flat plate with a prescribed surface heat flux proportional to (1+x2)^m (m a constant) is investigated both analytically and numerically. In view of the present formulation, the governing equations reduce to the well-known Blasius similarity equation and to the full boundary-layer energy equation with two parameters: the wall flux exponent m and Prandtl number Pr. The range of existence of solutions is considered, it being shown that solutions for both x small and x large exist only for m>−1/2. However, for m−1/2 the asymptotic structure for x large is found to be different for m<−1/2 and m=−1/2, respectively. These asymptotic solutions for large x are derived and compared with 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.