On the scaling of heat transfer using thermal flux gradients for fully developed turbulent channel and Couette flows

Wei et al. [T. Wei, P. Fife, J. Klewicki, P. McMurtry, Scaling heat transfer in fully developed turbulent channel flow, International Journal of Heat and Mass Transfer 48 (2005) 5284–5296; T. Wei, P. Fife, J. Klewicki, P. McMurtry, Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows, Journal of Fluid Mechanics 522 (2005) 303–327; P. Fife, T. Wei, J. Klewicki, P. McMurtry, Stress gradient balance layers and scale hierarchies in wall-bounded turbulent flows, Journal of Fluid Mechanics 532 (2005) 165–189] proposed a new scaling for fully developed turbulent channel flow with constant heat flux at the walls. Their analysis was based on the description of the physical layer structure of the thermal energy field in wall turbulence using the unintegrated form of the mean energy equation. The present communication examines the applicability of this analysis for different turbulent velocity fields (plane Couette and plane Poiseuille flow). The data, obtained using a Lagrangian computational method, show good agreement with the Wei et al. approach and extend the range of Peclet numbers that Wei and coauthors have investigated.