Eur. Phys. J. Plus (2015) 130: 163
https://doi.org/10.1140/epjp/i2015-15163-8

Regular Article

Rotary oscillation of a composite sphere in a concentric spherical cavity using slip and stress jump conditions

¹ Department of Mathematics and Computer Science, Faculty of Science, Beirut Arab University, Beirut, Lebanon
² Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt

^* e-mail: eaashmawy@alexu.edu.eg

Received: 29 August 2014
Revised: 1 June 2015
Accepted: 14 July 2015
Published online: 14 August 2015

Abstract

The rotary oscillation of a composite sphere, consisting of a solid core surrounded by a porous shell, in an incompressible viscous fluid bounded by a concentric spherical cavity is investigated using the Brinkman model. The stress jump condition is applied on the porous-fluid interface and the slip boundary condition is proposed on the surface of the spherical cavity. The couple exerted by the fluid on the porous surface is obtained analytically and its imaginary and real coefficients are represented graphically. The effects of slip parameter, permeability coefficient, stress jump coefficient and effective viscosity ratio on the torque are discussed and special cases are deduced.