Unsteady MHD Flow of an Incompressible Elastico-Viscous Fluid in a Tube of Spherical Cross Section on a Porous Boundary

Exact solution of an unsteady MHD flow of elasticoviscous
fluid through a porous media in a tube of spherical cross
section under the influence of magnetic field and 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state, the pressure gradient is suddenly withdrawn and the resulting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 spherical cross section by taking into
account of the porosity factor and magnetic parameter of the
bounding surface is investigated. The problem is solved in two-stages
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 non-dimensional
porosity parameter (K), magnetic parameter (m) and elasticoviscosity
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 and magnetic
parameter tends to zero and porosity tends to infinity. It is seen that
the effect of elastico-viscosity parameter, porosity parameter and
magnetic parameter of the bounding surface has significant effect on
the velocity parameter.





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