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.
Highlights
Swirling flows are one of the classical problems in fluid mechanics
The results show the various effects of the porosity and slip parameters on the velocity and temperature profiles
Increasing the porosity parameter γ induces a decrease of all velocity components and an increase of the temperature throughout the domain of integration
Summary
Swirling flows are one of the classical problems in fluid mechanics. They have many interesting features and industrial applications: rotating machineries, nuclear reactor or computer storage devices among other things. The steady flow of an incompressible viscous liquid due to an infinite rotating disk was first discussed by von Kármán in 1921 [3]. Attia [10] solved the system of differential equations for the steady flow over a rotating disk in porous medium with heat transfer. It has been extended in a later paper to the cases where the porosity parameter tends either to zero or infinity [11]. One will mainly focus on the combined effects of velocity slip and porosity on the von Kármán swirling flow and heat transfer of a viscous fluid for a rough rotating disk. The temperature jump arising due to the velocity slip has been considered
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