A study on non Newtonian fluid past axisymmetrical bodies

Abstract

An analysis is performed to explore the uniform Stokes flow of an incompressible newlinecouple stress fluid which surrounds the spherical droplet of Newtonian fluid encased newlinewith a penetrable layer under steady symmetric axis. The porous region and non-porous newlineregion s flow fields are governed by the equation of Brinkman and Stokes, respectively. newlineExplicit terms are examined for stream functions, velocities, and components of couple newlinestresses. The stream function solutions are obtained in terms of Gegenbauer functions newlineand modified Bessel functions for both external and internal flow fields. We have dealt newlinewith the creeping flow of a couple stress fluid past a porous sphere that includes a solid newlinecore embedded in a permeable medium by presuming stress jump boundary condition newlinefor the shear stresses. We have studied the slow, steady and viscous fluid through a couple newlinestress fluid sphere covered by a porous medium using the cell model technique. The newlineBrinkman equation for the flow outside the permeable layer in their stream function formulation newlineis used. We utilize a unit cell in which each spherical particle is covered by a newlineporous spherical container of suspending fluid. The boundary conditions namely radial newlinevelocity, Happel, Kuwabara, Kvashnin, and Mehta-Morse are considered on the cell newlinesurface. The effect of various fluid parametric factors such as viscosity, permeability, newlineand parameter of couple stress on the drag, is described and discussed in graphical and newlinenumerical forms. We found that the drag force diminishes rapidly as the couple stress newlineparametric quantity increases. There are attempts to compare different cases which conclude newlinethat the flow of couple stress fluid through a porous sphere enclosed by a rigid newlinespherical core, discontinuity of shear stress (presence of stress jump condition) having newlineless drag compared to continuous case of shear stress. The consequences of Hartmann newlinenumber, coupling number, and micropolarity parameter on the fluid flow are examined newlinein the problem of micropolar fluid past a fluid cylinder under m