A non-Newtonian liquid sphere embedded in a polar fluid saturated porous medium: Stokes flow

Abstract

The selection of interface boundary conditions between porous-medium and clear-fluid regions is vital for the extensive range of applications in engineering. As such, present paper reports an analytically investigating Stokes flow over Reiner–Rivlin liquid sphere embedded in a porous medium filled with micropolar fluid using Brinkman’s model and assuming uniform flow away from the obstacle. The stream function solution of Brinkman equation is obtained for the flow in porous region, while for the inner flow field the solution is obtained by expanding the stream function in a power series of S. The flow fields are determined explicitly by matching the boundary conditions at the interface of porous region and the liquid sphere. Relevant quantities such as velocity and pressure on the surface of the liquid sphere are determined and exhibited graphically. The mathematical expression of separation parameter SEP is also calculated which shows that no flow separation occurs for the considered flow configuration and also validated by its pictorial presentation. The drag coefficient experienced by a liquid sphere embedded in a porous medium is evaluated. The useful features of the Stokes flow for numerous values of parameters are analyzed and discussed. The dependence of the drag force and stream line pattern on permeability parameter(η2), viscosity ratio(λ), micropolar parameter(m), coupling number(N), and dimensionless parameter S is presented graphically and discussed. The analysis also aims at the explanation of velocity overshoot behavior. Some previous noted results are then also obtained from the ongoing analysis.