Transpired Turbulent Boundary Layers Subject to Forced Convection and External Pressure Gradients

The problem of forced convection transpired turbulent boundary layers with external pressure gradient has been studied by using different scalings proposed by various researchers. Three major results were obtained: First, for adverse pressure gradient boundary layers with suction, the mean deficit profiles collapse with the free stream velocity, $U∞,$ but into different curves depending on the strength of the blowing parameter and the upstream conditions. Second, the dependencies on the blowing parameter, the Reynolds number, and the strength of pressure gradient are removed from the outer flow when the mean deficit profiles are normalized by the Zagarola/Smits [Zagarola, M. V., and Smits, A. J., 1998, “Mean-Flow Scaling of Turbulent Pipe Flow,” J. Fluid Mech., 373, 33–79] scaling, $U∞δ*/δ.$ Third, the temperature profiles collapse into a single curve using the new inner and outer scalings proposed by Wang and Castillo [Wang, X., and Castillo, L., 2003, “Asymptotic Solutions in Forced Convection Turbulent Boundary Layers,” J. Turbulence, 4(006)], which produce the true asymptotic profiles even at finite Pe´clet number.