A General Sensitivity Equation Formulation for Turbulent Heat Transfer

ABSTRACT

This article presents a general formulation of the continuous sensitivity equation method for turbulent heat transfer. The standard k– ε model of turbulence with wall functions is used to model turbulence, while turbulent heat transfer is handled using an eddy conductivity. The formulation accounts for complex parameter dependence and is suitable for a wide range of problems. In addition to a detailed description of the formulation, we perform careful verification of the methodology on a problem possessing a closed-form solution. The methodology is then demonstrated by performing a detailed sensitivity analysis of the turbulent forced convection over a heated flat plate. Details include sensitivity of the Stanton number with respect to the closure coefficients of the k– ε model and the parameters appearing in the momentum and thermal wall functions.

This work was sponsored in part by NSERC (Government of Canada), FCAR (Government of Québec), the Canada Research Chair Program, and by the Air Force Office of Scientific Research under Grants AFOSR F49620-00-1-0299 and F49620-03-1-0243.