EFFECTS OF SLIP ON THE VON KÁRMÁN SWIRLING FLOW AND HEAT TRANSFER IN A POROUS MEDIUM

Abstract

Numerical solutions are obtained for the fully coupled and highly nonlinear system of differential equations, arising due to the steady Kármán flow and heat transfer of a viscous fluid in a porous medium. The conventional no-slip boundary conditions are replaced by partial slip boundary conditions owing to the roughness of the disk surface. Combined effects of the slip λ and porosity γ parameters on the momentum and thermal boundary layers are studied in detail. Both parameters produce the same effects on the mean velocity profiles, such that all velocity components are reduced by increasing either λ or γ. The temperature slip factor β has a dominating influence on the temperature profiles by decreasing the fluid temperature in the whole domain. The porosity parameter strongly decreases the heat transfer coefficient at the wall for low values of β and tends to an asymptotical limit around 0.1 for β ≃ 10. The porosity parameter γ increases the moment coefficient at the disk surface, which is found to monotonically decrease with λ.