**C. Y. Zhao **
*Mechanical Engineering Department The Hong Kong Polytechnic University Hung Horn, Kowloon, Hong Kong*

**Ronald M. C. So**
*Dept. of Mech. Engineering, Arizona State University, Tempe, AZ 85287; Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Horn, Kowloon, Hong Kong*

### Abstract

Near-Wall modeling of the turbulent temperature field is much more complicated, because the boundary conditions are not as well defined as those for the velocity field. Up to now, most computational and theoretical investigations are still based on the hypothesis of a constant turbulent Prandtl number in order to remove the uncertainty of the turbulent temperature boundary condition. However, strictly speaking, the physical arguments for these assumptions are applicable only for fluids whose Prandtl number, Pr, is approximately 1. Near-wall asymptotes of the turbulence statistics show that these properties are Pr dependent. Another difficult in the modeling of near-wall heat transfer is the irregular geometries often encountered in heat transfer problems. If the heat-flux models fail to reflect the Pr dependence and are geometry dependent, they would not be able to replicate the thermal asymptotes correctly as a wall is approached. The main objective of this paper is to develop a geometry independent near-wall two-equation heat-flux model for fluids with different Pr. In this paper, a geometry independent near-wall Reynolds stress turbulence model and the proposed two-equation heat-flux model are used to calculate heat transfer problems. As a first attempt, the proposed model is validated against fully developed turbulent channel flow with variable Pr. The mean temperature, turbulent kinetic energy, temperature variance, heat flux and the time scale ratio together with the near-wall characteristics are calculated and compared with direct numerical simulation (DNS) data. Good correlation with data is obtained.