Turbulent flow and heat tranfer in the vicinity of a backward-facing step

A numerical procedure is provided and evaluated for the calculation of the turbulent flow and heat transfer in the region downstream of a backward-facing step. The elliptic form of the momentum, mass and energy equations were solved numerically together using a finite difference method to calculate the flow field and temperature patterns. Utilizing the constant-property concept, the momentum and mass conservation equations were solved first to calculate the flow field, then the energy equation was solved using the calculated flow field to obtain the temperature distribution and the heat transfer parameters. The present calculations provide the influence of the Reynolds number, the step height and the Prandtl number on the flow and turbulence patterns and local and average heat transfer coefficients. The results are expressed in the form of two-dimensional stream function and local and average Nusselt numbers. The results indicate that the strength and size of the recirculation region as well as the levels of the turbulence kinetic energy are increased sharply by the increase in the step height. Along the surface to which the step is attached, the results indicate that the local Nusselt number increases towards a maximum value at a distance from the step which is dependent on the step height. On the opposite side of the step, the local Nusselt number is found to increase rapidly at the step edge and is then reduced gradually towards a fully-developed channel-flow value. The average Nusselt number is shown to increase to 3.5 times its fully-developed channel-flow value as a result of increasing the step height, the Reynolds number and the Prandtl number.