Simple two-layer model for temperature distribution in the inner part of turbulent boundary layers in adverse pressure gradients

A simple one-point closure for the inner region of turbulent boundary layers subjected to adverse pressure gradient is introduced. The use of local wall variables leads to self-similarity for the temperature distribution but not the velocity. A turbulent velocity scale directly related to the pressure parameter that maintains constant the total shear stress in the inner layer is used to define an eddy viscosity and diffusivity. The predicted velocity and temperature profiles agree reasonably well with the experiments. The essence of the formulation explains why the turbulent heat flux scaled by the local inner variables is merely unaffected contrarily to the Reynolds shear stress distribution in wall units that is significantly sensitive to the imposed pressure gradient.