Revisited results about the theory of steady laminar forced convection for 2D external boundary layer flows

Abstract

This paper is inspired by the observation in the literature that there was a lack of data about the knowledge of semi-analytical solutions of steady thermal state applied to laminar boundary layer flows in the case of forced convection. Thus, we have made a complete analysis and synthesized the results on both the surface temperature and the surface flux problems, from the development of integral and differential methods, in the range 10 −3 ≤ Pr ≤ 10 2. Moreover, it has been shown that the same ratio, δ T δ = 20 traduces the transition between boundary layer and slug flows, whatever the thermophysical considered case. Finally, we present a warning about the use of 2 and 3-order polynomial shapes by Pohlhausen method which induce a non-unicity of steady state thermal solutions.