A Two-Equation Model for Heat Transport in Wall Turbulent Shear Flows

A new proposal for closing the energy equation is presented at the two-equation level of turbulence modeling. The eddy diffusivity concept is used in modeling. However, just as the eddy viscosity is determined from solutions of the k and ε equations, so the eddy diffusivity for heat is given as functions of temperature variance t², and the dissipation rate of temperature fluctuations ε_t, together with k and ε. Thus, the proposed model does not require any questionable assumptions for the “turbulent Prandtl number.” Modeled forms of the t² and ε_t equations are developed to account for the physical effects of molecular Prandtl number and near-wall turbulence. The model is tested by application to a flat-plate boundary layer, the thermal entrance region of a pipe, and the turbulent heat transfer in fluids over a wide range of the Prandtl number. Agreement with the experiment is generally very satisfactory.