Convection, diffusion and reaction inside a spherical porous pellet in the presence of oscillatory flow

The problem of convection, diffusion and reaction inside a spherical porous pellet is investigated analytically. Unsteady Stokes equation is used for the flow outside the porous pellet and Darcy's law is used inside the pellet. A solenoidal decomposition method is employed for the hydrodynamic problem. Following the above findings, the convection-diffusion-reaction problem is formulated and solved analytically for a first order reaction. The behavior of the nutrient transport is discussed with respect to various parameters like Darcy number, Peclet number, frequency and Thiele modulus. Also the effectiveness factor corresponding to the first order reaction is computed.