Mass Transfer Effects on Viscous Flow in an Expanding or Contracting Porous Pipe with Chemical Reaction

Abstract

In this paper, an analysis is performed to study the effects of mass transfer and chemical reaction on laminar flow in a porous pipe with an expanding or contracting wall. The pipe wall expands or contracts uniformly at a time dependent rate. The governing equations are reduced to ordinary differential equations by using a similarity transformation. An analytical approach, namely, the homotopy analysis method is applied in order to obtain the solutions of the ordinary differential equations. The convergence of the obtained series solutions is analyzed. The effects of various parameters on flow variables have been discussed. It is noticed that the wall expansion ratio significantly increases the axial velocity and the concentration for the case of wall expansion and it decreases the axial velocity for the case of wall contraction irrespective of injection or suction. Further, it is observed that the concentration (ϕ) decreases for a destructive chemical reaction () and increases for a generative chemical reaction (). The concentration reduces as Schmidt number () increases. The corresponding problem related to the porous pipe flow with a stationary wall can be recovered from the present analysis in the limiting case where the wall expansion ratio approaches to zero (i.e., ).