Numerical Investigation of Near-Wall Turbulent Heat Transfer Taking Into Account the Unsteady Heat Conduction in the Solid Wall

The deterministic near-wall turbulence model developed by Kasagi et al. (1984b) is used in a numerical analysis of turbulent heat transfer, in which the unsteady heat conduction inside the wall associated with the turbulent flow unsteadiness is taken into account. Unlike the typical methodology based on Reynolds decomposition, the algebraic expressions for the three fluctuating velocities given by the model are directly introduced into the governing energy equation. From the numerical results of the unsteady conjugate heat transfer, the statistical quantities, such as temperature variance, turbulent heat flux, and turbulent Prandtl number, are obtained for fluids of various Prandtl numbers. It is demonstrated that the near-wall behavior of these quantities is strongly influenced by the thermal properties and thickness of the wall. In addition, the budget of the temperature variance associated with coherent turbulence structure is calculated and, except for dissipation, each budget term is in qualitative agreement with the experiment.