Theoretical analysis of convective heat flux structure in the incompressible turbulent boundary layer on a porous plate with uniform injection and suction

Abstract

Although many experimental and numerical studies on thermal convection exist for turbulent transpiration boundary layer flows on a porous structure, the general convective heat flux formula is urgently needed to clarify the influence of injection or suction on the energy transfer mechanism of turbulent heat convection. The two-dimensional (2D) theoretical convective heat flux structure obtained previously is therefore applied to the incompressible turbulent thermal boundary layer on a porous flat plate with uniform injection and suction. The energy balance relationship between the streamwise and wall-normal heat flux components is established and the effects of injection and suction on turbulent convective heat fluxes are analyzed. The explicit analytical expressions of turbulent skin friction factor, convective heat transfer coefficient and Stanton number are obtained based on the heat flux theory and verified by the previously experimental measurements. The turbulence characteristics of convective heat transfer with uniform injection and suction are revealed by the proposed key parameters. A hybrid control volume analysis for energy transfer inside the porous media plate is performed and applied to the cases of transpiration cooling and enhancing heat transfer, respectively, and a novel calculation formula for convective heat transfer is proposed in the form of heat flux instead of the heat transfer coefficient. It is also found that the direction of the resultant convective heat flux combining the conduction with advection is not always to remain that of the negative temperature gradient, and it depends not only on the temperature difference direction as well as velocity direction, but also on the magnitude contrast of the conductive and advective heat fluxes.