Abstract
The exact solution of an unsteady flow of elastico-viscous fluid through a porous media in a tube of elliptical cross section under the influence of a constant pressure gradient has been obtained in this paper. Initially, the flow is generated by a constant pressure gradient. After attaining steady state, the pressure gradient is suddenly withdrawn and the resulting fluid motion in the tube of elliptical cross section is investigated by taking into account the porosity factor of the bounding surface. The problem is solved in two stages. The first stage is the steady motion in the tube under the influence of the constant pressure gradient and the second stage is concerned with unsteady motion. The problem is solved by employing the separation of variables technique. The results are expressed in terms of the non-dimensional porosity (K) and elastico-viscosity (β) parameters, which depend on the non-Newtonian coefficient. The flow parameters are found to be identical with that of the Newtonian case as β → 0 and K →∞. It is seen that the effects of elastico-viscosity (β) and porosity (K) parameters of the bounding surface have a significant effect on the velocity parameter.
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