Logarithmic Expansions for Reynolds Shear Stress and Reynolds Heat Flux in a Turbulent Channel Flow

Abstract

The heat and fluid flow in a fully developed turbulent channel flow have been investigated. The closure model of Reynolds shear stress and Reynolds heat flux as a function of a series of logarithmic functions in the mesolayer variable have been adopted. The interaction between inner and outer layers in the mesolayer (intermediate layer) arising from the balance of viscous effect, pressure gradient and Reynolds shear stress (containing the maxima of Reynolds shear stress) was first proposed by Afzal (1982, “Fully Developed Turbulent Flow in a Pipe: An Intermediate Layer,” Arch. Appl. Mech., 53, 355–377). The unknown constants in the closure models for Reynolds shear stress and Reynolds heat flux have been estimated from the prescribed boundary conditions near the axis and surface of channel. The predictions are compared with the DNS data Iwamoto et al. and Abe et al. for Reynolds shear stress and velocity profile and Abe et al. data of Reynolds heat flux and temperature profile. The limitations of the closure models are presented.