MHD Couple stress fluid between two concentric spheres with slip regime

Abstract

The problem of the axisymmetric steady flow of an incompressible couple stress fluid within two concentric spheres is analyzed analytically in this study. In the interior of the solid sphere, translation takes place with a uniform velocity, and in the exterior, translation takes place with a fixed velocity. A study of slip conditions was carried out on the surfaces of the two spheres. In terms of stream functions, modified Bessel functions provide an analytical solution to the problem. As the outer sphere remains stationary, the inner sphere experiences the normalized drag force. A graphic representation of drag is provided based on the slip and spin slip parameters, the couple stress parameter, the separation distance, and the MHD parameter. In addition, the results are compared with earlier results for special cases of translation of one rigid sphere through an unbounded magnetic medium, viscous fluid flow, and Couple stress fluid without MHD between two concentric spheres.