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

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Abstract
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 εt, 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 εt 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.

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