Suction/Injection Effects on the Swirling Flow of a Reiner-Rivlin Fluid near a Rough Surface

Bikash Sahoo,Fotini Labropulu,Sébastien Poncet

doi:10.1155/2015/253504

Abstract

The similarity equations for the Bödewadt flow of a non-Newtonian Reiner-Rivlin fluid, subject to uniform suction/injection, are solved numerically. The conventional no-slip boundary conditions are replaced by corresponding partial slip boundary conditions, owing to the roughness of the infinite stationary disk. The combined effects of surface slip (λ), suction/injection velocity (W), and cross-viscous parameter (L) on the momentum boundary layer are studied in detail. It is interesting to find that suction dominates the oscillations in the velocity profiles and decreases the boundary layer thickness significantly. On the other hand, injection has opposite effects on the velocity profiles and the boundary layer thickness.

Highlights

The problem of Newtonian and non-Newtonian swirling flows near a rotating or stationary disk has occupied a central position in the field of fluid mechanics due firstly to the fact that similarity solutions to the Navier-Stokes equations may be found in some idealized infinite configurations and secondly to its industrial and technical applications in rotating machinery, chemical engineering, or oceanography among other things.Recently, Sahoo [1] and Sahoo and Poncet [2] have obtained numerical solution to similarity equations arising due to steady revolving flow of a non-Newtonian Reiner-Rivlin fluid near an infinite rough stationary disk
It is customary to mention that similar scheme has been used by Sahoo et al [13] to solve the Bodewadt flow problem for a viscous fluid with Navier’s slip boundary conditions
A local overshoot in the tangential velocity increases the centrifugal force locally, which tends to induce a radial outflow. This radial outflow convects an angular momentum defect to force an undershoot in the tangential velocity profile, and the above process is repeated to yield oscillatory approach to infinity

Summary

Introduction

The problem of Newtonian and non-Newtonian swirling flows near a rotating or stationary disk has occupied a central position in the field of fluid mechanics due firstly to the fact that similarity solutions to the Navier-Stokes equations may be found in some idealized infinite configurations and secondly to its industrial and technical applications in rotating machinery (centrifugal pumps, turbines, or computer storage devices), chemical engineering (spinning disk reactors, crystal growth processes, or rheometers), or oceanography among other things. Sahoo [1] and Sahoo and Poncet [2] have obtained numerical solution to similarity equations arising due to steady revolving flow (known as Bodewadt flow [3]) of a non-Newtonian Reiner-Rivlin fluid near an infinite rough stationary disk In this short note, the flow problem studied by Sahoo and Poncet [2] has been reconsidered, including uniform suction/injection at the surface of the stationary disk. Domairry and Aziz [9] investigated by a homotopy perturbation method the MHD flow between two parallel stationary disks with suction or injection through one of the two disks None of these previous works considered the Bodewadt flow of a non-Newtonian fluid over a stationary rough disk with mass transfer through it. The objective is to check if suction or injection is an effective way to reduce the chances of separation of the boundary layer

Formulation of the Problem

Numerical Solution of the Problem

Results and Discussions

Conclusions