External heating of a flat plate in a convective flow (Q1057749)

The steady-state and transient processes of the external heating of a flat plate under a convective flow is studied in this paper, with inclusion of the axial heat conduction through the plate. The balance equations reduce to a single integro-differential equation with only one parameter, \(\alpha\), denoting the ratio of the ability of the plate to carry heat in the streamwise direction to the ability of the gas to carry heat out of the plate. The two limits of a good conducting plate (\(\alpha\) \(\to \infty)\) and a bad conducting plate (\(\alpha\) \(\to 0)\) are analysed through the application of a regular perturbation procedure for the first case and a singular perturbation technique for the latter. The existence of two boundary layers at both edges of the plate is shown and their structures are analysed. The evolution of the temperature of the plate is then obtained for a constant external energy flux input.