Stokes flow of an incompressible micropolar fluid past a porous spheroidal shell

Abstract

Abstract. Consider a pair of confocal prolate spheroids S0 and S1 where S0 is within S1. Let the spheroid S0 be a solid and the annular region between S0 and S1 be porous. The present investigation deals with a flow of an incompressible micropolar fluid past S1 with a uniform stream at infinity along the common axis of symmetry of the spheroids. The flow outside the spheroid S1 is assumed to follow the linearized version of Eringen's micropolar fluid flow equations and the flow within the porous region is assumed to be governed by the classical Darcy's law. The fluid flow variables within the porous and free regions are determined in terms of Legendre functions, prolate spheroidal radial and angular wave functions and a formula for the drag on the spheroid is obtained. Numerical work is undertaken to study the variation of the drag with respect to the geometric parameter, material parameter and the permeability parameter of the porous region. An interesting feature of the investigation deals with the presentation of the streamline pattern.

Flow of Stokesian fluid through a cellular medium and thermal effects

“…On the other hand, A. Cemal Eringen considers linear constitutive equations of anisotropic micropolar fluids [32], cf. also [33].…”

Cell Models for Non-Newtonian Fluid Past a Semipermeable Sphere

“…To solve Eq. ( 9)-( 11), on boundary of semipermeable sphere, normal velocity and pressure are continuous and vanishing of tangential velocity, no spin condition (Joseph and Tao, 1964;Saad, 2008;2012;Shapovalov, 2009;Iyengar and Radhika, 2011; are used. On cell surface, radial velocity is continuous, no spin condition, Happel's (Happel, 1958), Kuwabara's (Kuwabara, 1959), Kvashnin's (Kvashnin, 1979), and Cunningham's (Cunningham, 1910) boundary conditions, are valid.…”

“…Iyengar and Srinivasacharya (1993) studied the slow flow of micropolar fluid past an approximate sphere. Iyengar and Radhika (2011; investigated micropolar fluid flow past a porous spheroid and prolate spheroidal shell containing a solid core using spheroidal coordinate system. They have numerically studied the variation of drag exerted on the particle with respect to the geometric parameters.…”

Two theorems about Lorentz method for asymmetrical anisotropic regions

“…The results of force and torque calculations can also be treated as benchmarks for models of linear, cylindrical and spherical converters [12][13][14]. For the linear converter an acting force is calculated.…”