Validation of a Central-Difference Finite Volume Method for Analysing Wall Turbulent Heat Transfer Using Transport Equations for Turbulent Heat Fluxes

Abstract The aim of this study is to validate the finite volume method approach using the transport equations for turbulent heat fluxes in turbulent heat transfer at the wall surface. The finite volume method technique is a numerical analysis based on conservation laws of physical quantities in the flow field, with particular emphasis on the conservation of velocity fluctuation intensity in the flow field. The behaviour of turbulent heat flows is analysed in detail using this method and its validity is tested. In the study, heat transfer in channel turbulence is analysed under a constant heat flux heating condition. The individual terms of the temperature variance equation are analysed and the results are shown to be in agreement with a previous study. The residual is small, confirming the high accuracy of the results. The present study analyses the transport equation for the dissipation of the temperature variance. The transport equations for turbulent heat fluxes in the flow direction and in the vertical wall direction are analysed and show good agreement with those of the previous study. The results show that in the vertical wall direction, non-zero terms such as the pressure diffusion term appear to contribute and reduce the accuracy of the transport equations.