Asymptotic solutions in forced convection turbulent boundary layers

Abstract

A similarity analysis has been developed for a 2D forced convection turbulent boundary layer with and without a pressure gradient. Two new inner and outer temperature scalings are derived by means of similarity analysis of the equations of motion. The new scalings will be verified by the experimental data with adverse pressure gradient, favourable pressure gradient and zero pressure gradient respectively. It will be shown that the mean temperature profiles are dependent on the external pressure gradient and the upstream conditions. However, using the new scaling in inner variables or in outer variables, the temperature profiles collapse into a single curve. Thus, the true asymptotic solution for the temperature field exists even at a finite Péclet number. These results are confirmed by using the existing experimental data and compared with the results from various scalings. The asymptotic temperature profile or the self-similar profile found in the present analysis is in agreement with the fact that an asymptotic velocity profile exists if the mean velocity deficit profile is normalized by the Zagarola and Smits scaling (Zagarola and Smits 1998 J. Fluid Mech. 373 33-79).