Computation of high Prandtl number turbulent thermal fields by the analytical wall-function

The extended version of the analytical wall-function (AWF) for rough wall turbulence by Suga et al. [K. Suga, T.J. Craft, H. Iacovides, An analytical wall-function for turbulent flows and heat transfer over rough walls. Int. J. Heat Fluid Flow 27 (2006) 852–866] is improved for high Prandtl number flows. The original AWF assumes a linear profile of turbulent viscosity near a wall though it is widely recognised that a theoretically correct cubic profile of the turbulent viscosity is essential for heat transfer of high Prandtl number flows. In order to predict thermal boundary layer of high Prandtl number fluid flows, the present approach thus employs a correct limiting profile of the turbulent viscosity in the analytical integration process. The presently proposed version of the AWF proves its good performance for predicting turbulent high Prandtl number thermal flows at Pr ⩽ 4 × 104 for smooth wall cases, and at least at Pr ⩽ 10 for rough wall cases.