Analysis of immiscible Newtonian and non-Newtonian micropolar fluid flow through porous cylindrical pipe enclosing a cavity

Abstract

In the considered problem, we presented a model for the flow of immiscible fluids (non-Newtonian and Newtonian) through the cylindrical pipe. Cylindrical pipe is constituted by two porous cylindrical shell enclosing a cylindrical cavity. Non-Newtonian (micropolar) fluid is flowing through the middle porous cylindrical shell, and other immiscible Newtonian fluids are flowing through the cavity and outer porous cylindrical shell. The flow of fluid through the outer porous cylindrical shell and cavity is governed by well-known Brinkman and Stoke’s equation, respectively. However, the flow of micropolar fluid through the middle porous cylindrical shell is governed by the field equation given by Eringen (Springer, Berlin, 2001). An analytical solution of the problem has been obtained by using the justified boundary conditions. The effects of various non-dimensional parameters such as permeability parameters, micropolar parameter, and viscosity ratio on the linear flow velocity, microrotational flow velocity and flow rate are examined graphically. The results are validated with the help of previously established result.