A low-Reynolds-number, four-equation heat transfer model for turbulent separated and reattaching flows

An algebraic heat flux model is applied to predict turbulent heat transfer in separated and reattaching flows. Based on the prior low-Reynolds-number k-ε model of Park and Sung (1995), an improved version of the nonequilibrium heat transfer model is developed. The model performance is examined by solving the equations of the temperature variance k_θ and its dissipation rate ε_θ, together with the equations of k and ε. In the present model, the near-wall limiting behaviour close to the wall and the nonequilibrium effect away from the wall are incorporated. A tensor eddy-diffusivity is obtained to implement the orientation of mean temperature gradient in separated and reattaching flows. The validation of the model is applied to the turbulent flow over a backward facing step. The predictions of the present model are cross-checked with the existing measurements and direct numerical simulation (DNS) data. The model performance is shown to be generally satisfactory.