The present work shows how perturbation techniques can be used to find analytical solutions for turbulent boundary layer problems when several complex factors such as, transpiration, roughness, transfer of heat and compressibility are present. The asymptotic structures, of both the thermal and the dynamic boundary layers, were derived by an intermediate variable technique analysis of the equations of motion, and the influence of the dissipation function was shown to become important when E = 0(uτ), E = Eckert number, Uτ = non-dimensional friction velocity. For turbulent boundary layers subject to normal injection or suction of fluid, the universal laws were studied and two Stanton number equations were proposed. The universal laws for boundary layer flows over “k” and “d” type rough surfaces were also studied. The analysis shows that the similarity parameter used to describe the velocity boundary layer, the displacement in origin, can also be used to describe the temperature boundary layer. Finally, the results derived for incompressible transpired flow were extended to compressible flow.
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