Comparative Solutions to the Integral-Approximate Thermal Boundary Layer Equations for a Flat Plate

Abstract

The flat plate in fluid flow is the paradigm of heat transfer problems. The polynomial approximation of Pohlhausen to the Blasius solution for the flow leads to messy expressions in the integral formulation for the associated heat transfer between plate and flow, together with a continuation of the paradoxical results that the termination in the approximate solution implies. If the distribution is approximated in exponential form, the required integrals are easy — and may safely be attempted by a lecturer at the board or screen — and the anomalies eliminated. The results are perhaps less accurate than the Pohlhausen approximation but in either case would be replaced with exact values of the flow equations, obtained with considerably more difficulty.