Effect of axial vibration of boundary on wall shear stress and mass transfer in medium saturated with homogeneous rigid porous materials

Abstract

It is well established in the literature that oscillatory forcing enhances convection and, hence, assists mass transfer. We focus on a physical situation where the oscillations are induced via sinusoidal vibration of boundaries. We consider flow inside a cylindrical porous pipe that is governed by non-stationary Navier–Stokes equations, with a Brinkman term accounting for the resistance offered by the porous medium. The hydrodynamic problem is coupled with advection–diffusion inside the pipe. The analytical treatment used to solve the problem is based on the finite Hankel transformation. Mass transfer enhancement is studied via the ratio of the Sherwood numbers calculated in both the presence and absence of vibration. We introduce some dimensionless numbers, viz. the Womerseley number and the Strouhal number, to illustrate the mass transfer phenomenon. We establish a relation between the ratio of the Sherwood numbers which are calculated in the presence and the absence of vibration, with the dimensionless vibration parameters being the Womerseley number and Strouhal number, which in turn show that an increase in the frequency of the vibration results in an increase in the ratio of the Sherwood numbers which is much greater than one. Also, the said ratio increases as the medium permeability decreases. The present study indicates that vibration is responsible for the decay of the total convective mass transport in the axial direction.