RANS modelling of a new turbulent energy equation with variable and fluctuating thermal conductivity.

This work presents numerical results for turbulent flow of a fluid with variable and fluctuating thermal conductivity. The equations solved numerically are the classical ones for the mean motion, i.e. mass conservation, turbulent kinetic energy and dissipation rate, and the new energy conservation equation. This new energy equation, obtained with mathematical and physical considerations in [1], contains a new term for heat flux due to the variation of thermal conductivity, i.e. the product of the square of fluctuating temperature and the temperature gradient of thermal conductivity. This new heat flux term, obtained in conservative form, transfers energy from large to small scales of turbulence. The present model, to be considered as a new three-equation-RANS model, has never been proposed before in the classical RANS modelling. The aim of the present paper is to investigate the influence of Prandtl number in the two-dimensional turbulent flow between parallel plates.