Calculation of turbulent heat flux distributions in a square duct with one roughened wall by means of algebraic heat flux models

Calculations have been performed for fully developed turbulent flow and heat transfer in a square duct with one roughened wall. This paper focuses on the application of two algebraic models of the turbulent heat flux transport equation to predict turbulent heat flux component behavior. The convection and diffusion terms in this transport equation are modeled in a manner similar to Rodiʹs approximation for corresponding terms in the Reynolds stress transport equations. The pressure–temperature gradient term is simulated by means of two models: one a composite based on the “slow” and “rapid” interaction models proposed by Lumley and Launder (LL), respectively, and the other, the model proposed by Jones and Musonge (JM). Both the LL and JM models lead to predicted mean temperature distributions in the duct cross plane that are in relatively good agreement with experimentally measured distributions. The LL model, however, yields predicted distributions that agree better with experiment near both the smooth and roughened walls of the duct. Calculated turbulent heat flux component distributions in the cross plane show that both the LL and JM models predict experimentally observed features in the flow, with the LL model providing the best overall accuracy.