Abstract: Exact solution of an unsteady flow of elastico-viscous
fluid through a porous media in a tube of ellipsoidal cross section
under the influence of constant pressure gradient has been obtained in
this paper. Initially, the flow is generated by a constant pressure
gradient. After attaining the steady state, the pressure gradient is
suddenly withdrawn and the resulting fluid motion in a tube of
ellipsoidal cross section by taking into account of the porosity factor
of the bounding surface is investigated. The problem is solved in twostages
the first stage is a steady motion in tube under the influence of
a constant pressure gradient, the second stage concern with an
unsteady motion. The problem is solved employing separation of
variables technique. The results are expressed in terms of a nondimensional
porosity parameter (K) and elastico-viscosity parameter
(β), which depends on the Non-Newtonian coefficient. The flow
parameters are found to be identical with that of Newtonian case as
elastic-viscosity parameter tends to zero and porosity tends to
infinity. It is seen that the effect of elastico-viscosity parameter and
the porosity parameter of the bounding surface has significant effect
on the velocity parameter.