Transient mixed convection of a second-grade fluid past a backward-facing step

Abstract

A transient mixed convection of a second-grade viscoelastic fluid on a backward-facing step was studied numerically. The combined effects of the Reynolds number, the elastic number and the Richardson number on the flow and heat transfer were examined. The stream-vorticity equations and energy equation were discretized by a second-order accurate finite-difference method. The point and line Gauss–Seidel methods with successive over-relaxation (SOR) and alternative direction iteration were implemented with the finite-difference method to obtain the solutions. The results indicate that the size of the primary recirculation zone, as with the reattachment length, increases with a higher Richardson number and decreases with a higher elastic number at a Reynolds number of 75, and the results also imply that the buoyancy and the elasticity of the fluid have opposite influences on the flow. In general, only one secondary recirculation zone is present for the cases chosen in the present study. However, two secondary recirculation zones were noticed in the flow during the transient period for a case with a Reynolds number of 75, an elastic number of 0.001 and a Richardson number of 7. A steady-state secondary recirculation zone was present for a Reynolds number of 75, a Richardson number of 1, and an elastic number of 0.001. A reflex shape in the temperature profiles was observed to occur near the step, and the maximum local Nusselt number on the bottom wall was present in the vicinity and at the downstream side of the reattachment point.