Improved solution for laminar thermal boundary layers

Abstract

first case was that of a heated plate with uniform temperature in the midst of an incompressible fluid with uniform velocity and temperature at infinity. The second case was that of an adiabatic plate also in a steady uniform flow of a fluid with uniform temperature. In a literature search, no previous work could be found, except for an analysis by L. Prandtl [2] in which no calculations of temperature distributions were included. Pohlhausen's analysis has become a classic of boundary layer methodology, but, for the calculations of temperature distributions, he used the data available at the time for the velocity distribution in the boundary layer [3]. This did not affect the expected qualitative trend of the temperature profiles which he determined for the two particular cases mentioned above. It is only when Pohlhausen's results are used to eonstruet the general solution for the thermal boundary layer that the inaceuracies in the veloeity profiles are large enough to distort some of the temperature profiles [4]. This occurs in a manner that can be easily deteeted as anomalous even by a relatively inexperienced observer. To facilitate the discussion, we summarize first the classieal treatment of the problem, and then show how possible wrong trends can be deteeted through a simplified qualitative analysis. This is aecomplished by establishing basie properties that the solution must possess. The governing equations for laminaI' flat-plate boundary layers without pressure gradient and buoyaney effeets, but with dissipation of energy, are: Introduction