Numerical Investigation of the Influence of the Coolant’s Prandtl Molecular Numbers and the Permeability of the Pipe Wall on Turbulent Heat Transfer

A technique for modeling turbulent flow in a channel with impermeable and permeable walls in the presence of heat supply to the wall is proposed. To close the equations of the boundary layer, a three-parameter differential model of shear turbulence is used, which is supplemented by a transfer equation for a turbulent heat flux. Calculations are carried out for a developed turbulent flow in a round pipe with impermeable and permeable walls for air and binary gas mixtures with a low molecular Prandtl number with parameters corresponding to those in earlier experiments. The results of studies on the effect of the Prandtl number on heat transfer in a pipe with impermeable walls for a coolant with constant physical properties are consistent with the experimental data and empirical dependences of W.M. Kays and B.S. Petukhov for the Nusselt number in the range of Prandtl numbers of 0.2–0.7. It is shown that a positive pressure gradient arising in a pipe under strong gas suction leads to a violation of the similarity of the velocity and temperature profiles and, as a consequence, to a violation of the Reynolds analogy. The use of the transport equation for a turbulent heat flux makes it possible to take into account the complex dependence of the turbulent Prandtl number on the molecular Prandtl number in the viscous sublayer and in the logarithmic boundary layer. The influence of the variability of thermophysical properties and the turbulent Prandtl number on the characteristics of heat transfer in a pipe is estimated. Thus, the difference between the Nu number determined under the assumption of a constant turbulent Prandtl number and the results obtained in calculations using the equation for turbulent heat flux increases with a decrease in the molecular Prandtl number and an increase in the intensity of gas suction.