A local thermal non-equilibrium analysis for convective and radiative heat transfer in gaseous transpiration cooling through a porous wall

Abstract

A local thermal non-equilibrium analysis has been proposed for the gaseous transpiration cooling in which a coolant gas is driven from a coolant reservoir through a wall of porous structure to remove heat from a hot gas passing over the wall. For the first time, the effects of both radiation and gas expansion on the performance of the transpiration cooling were fully taken into consideration, on the basis of equal pumping power needed to supply the coolant, by introducing the Rosseland and low Mach approximations. The present analysis valid for all cases, in which both radiation and gas expansion are present, was validated against the existing analyses for the cases of incompressible transpiration gas flows in the absence of radiation. The radiative heat transfer tends to reduce the overall cooling effectiveness, but, at the same time increase the total removable of heat from the hot gas. The low Mach approximation is found quite effective to account for the gas expansion effects on the pressure drop across the wall. Furthermore, the analysis reveals that the overall Nusselt number exhibits its peak at a certain value of the pumping power, which turns out to be useful information in operating a transpiration cooling system effectively around its optimal flow rate.