Creeping flow of fluid sphere contained in a spherical envelope: magnetic effect

Abstract

The characteristic of creeping flow past a fluid sphere enclosed in a spherical envelope bearing fluid of different viscosity has been studied under the impact of transverse magnetic field. Stream functions related to modified Bessel functions are used in order to calculate the solution in closed form. The problem is considered to be parted into two flow regions as inner fluid and outer fluid region respectively, which are supposed to be governed using Stokes equations with different Hartmann number. At the contact layer of outer and inner fluid sphere, we assume the vanishing of normal components of velocity along with continuity of tangential components of velocity and stress respectively as boundary conditions. The condition of vanishing of vorticity (Kuwabara model) is considered to be applicable at the outer layer of fluid envelope. Expression for drag acting on the inner fluid sphere is presented. In limiting cases, several significant results accessible in literature are evaluated.

Archive of Mechanical Engineering

“…Motivated by the developments in this area of research, recently numerous works addressing the problem concerning transport in porous media have been explored. Applying Happel's along with Kuwabara's boundary conditions, the MHD flow over a sphere containing fluid immersed in a spherical cell was handled by Prasad and Bucha [24]. In the latest articles by Prasad and Bucha [25,26], an analytical study was made to examine the effect of imposed magnetic forces on the motion through a weakly permeable spherical and cylindrical particle in a cell, respectively.…”