Similarity analysis of the equations of motion is used in order to study forced convection turbulent boundary layers with and without pressure gradient. New scalings are found for both the inner and the outer temperature profiles, respectively. It is shown that by normalizing the temperature profiles using the new scalings, the effects from the Pe´clet number and pressure gradient can be removed completely from the profiles. Therefore, the asymptotic solutions can be obtained even at the finite Pe´clet number. Moreover, using the Near-Asymptotic principle, a power law solution is derived for the temperature profile in the overlap region. This power law solution is a consequence of the fact that the boundary layer depends on two different temperature scalings.
The Asymptotic Temperature Profile for Forced Convection Turbulent Boundary Layers With and Without Pressure Gradient
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Wang, X, & Castillo, L. "The Asymptotic Temperature Profile for Forced Convection Turbulent Boundary Layers With and Without Pressure Gradient." Proceedings of the ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. Volume 2: Symposia, Parts A, B, and C. Honolulu, Hawaii, USA. July 6–10, 2003. pp. 1485-1490. ASME. https://doi.org/10.1115/FEDSM2003-45451
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