Viscous Flow Past a Porous Spherical Shell—Effect of Stress Jump Boundary Condition

Using the stress jump boundary condition for the tangential stresses at the porous liquid interface along with the continuity of the velocity components and normal stress, the uniform viscous flow past a porous spherical shell with external radius r1, internal radius r2 is studied. The flow inside the porous region is governed by Brinkman equation. The flow in the liquid region is governed by the Stokes equation. The flow field is computed by matching the boundary conditions at the porous-fluid interface. The effect of stress jump coefficient (beta) on the flow field is very much felt. An increase in the drag with permeability is found for different R , different ratio of r1/r2, and also a change in magnitude of the drag for different values of stress jump coefficient (beta) is observed. Also, the variation of torque and shear stress with permeability and the stress jump coefficient is discussed.