Power Law Velocity and Temperature Profiles in a Fully Developed Turbulent Channel Flow

Abstract

The power law temperature distribution in a fully developed turbulent channel flow for large Peclet numbers has been proposed in the present work. The analysis of the power law velocity profile in a fully developed mean turbulent channel flow would be used for carrying out the analysis of the power law temperature profile. The Reynolds mean thermal energy equation in a fully developed mean turbulent channel flow has been analyzed. The mean turbulent thermal flow is divided in the inner and outer thermal layers that have been matched by Izakson–Millikan–Kolmogorov hypothesis to get the power law temperature profiles and the power law heat transfer law in the overlap region, in addition to traditional log laws for temperature profiles and heat transfer. It has been shown that the envelope of the heat transfer power law gives the heat transfer log law. Further, it is shown that the temperature power law index and prefactor are functions of the friction Peclet number, as well as function of an alternate variable, the nondimensional friction temperature. It is shown that for large Peclet numbers the power law temperature profile is equivalent to the log law temperature profile. The direct numerical simulation velocity profile data of fully developed turbulent flow provide good support for the power law temperature profile theory.