Heat-transfer and temperature-defect laws in a turbulent boundary layer on a plate with injection

Abstract

For a thermal turbulent boundary layer on a permeable flat plate, similarity laws for the heat flux at the wall and flow temperature are established. According to the universal temperature-defect law, the profiles of this quantity for any injection and sufficiently large Reynolds numbers everywhere outside the viscous sublayer may be described by a single curve, which is known from experimental data for an impermeable plate. The universal heat-transfer law in the form of the generalized Reynolds analogy allows one to represent the heat flux distributions that correspond to various Reynolds numbers and various injection velocities as a function of one variable. The results are obtained without the formulation of special closure hypotheses. 1. We consider an incompressible heat-conducting turbulent boundary layer flow over a smooth flat plate in a uniform stream with constant velocity U e and temperature θ e . The transpiration (injection or suction) velocity v w directed along the normal to the surface and the temperature on the wall θ w are also considered to be constant. The turbulent flow is assumed to develop directly from the leading edge of the plate. We also assume that the level of velocity and temperature fluctuation in the free stream is negligibly small and does not affect the flow and heat transfer in the boundary layer. Temperature is treated as a passive contaminant exerting no influence on the liquid motion.