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

A transient mixed convection of a second-grade viscoelastic fluid on a back ward-facing step was studied numerically. The combined effects of the Reyno lds number, the elastic number and the Richardson number on the flow, and h eat transfer were examined. The stream-vorticity equations and energy equat ion were discretized by a second-order accurate finite-difference method. T he point and line Gauss-Seidel methods with successive over-relaxation (SOR ) and alternative direction iteration were implemented with the finite-diff erence method to obtain the solutions. The results indicate that the size o f the primary recirculation zone, as with the reattachment length, increase s with a higher Richardson number and decreases with a higher elastic numbe r 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 ge neral, only one secondary recirculation zone is present for the cases chose n in the present study. However, two secondary recirculation zones were not iced in the flow during the transient period for a case with a Reynolds num ber of 75, an elastic number of 0.001 and a Richardson number of 7. A stead y-state secondary recirculation zone was present for a Reynolds number of 7 5, 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 m aximum local Nusselt number on the bottom wall was present in the vicinity and at the downstream side of the reattachment point; (C) 1999 Published by Elsevier Science Ltd. All rights reserved.