Unsteady MHD elastico-viscous fluid flow of second order type in a tube of hyperbolic cross section on the porous boundary

Abstract
Exact solution of an unsteady flow of elastico-viscous fluid through a porous media in a tube of hyperbolic 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 After attaining the steady state, the pressure gradient is suddenly withdrawn and the resulting fluid motion in a tube of hyperbolic cross section by taking into account of the magnetic parameter and porosity factor of the bounding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 ( ), magnetic parameter(M) and elastico-viscosity parameter ( ), which depends on the Non-Newtonian coefficient. The flow parameters are found to be identical with that of Newtonian case as , K and . It is seen that the effect of elastico-viscosity parameter ( ), Magnetic parameter(M) and the porosity parameter ( ) of the bounding surface has significant effect on the velocity parameter.

Keywords
Elastico -viscous fluid, second order fluid, Elliptic cross-section, porous media, Separation of variables, Magentic parameter

Cite this paper
S. B. Kulkarni, Unsteady MHD elastico-viscous fluid flow of second order type in a tube of hyperbolic cross section on the porous boundary, SCIREA Journal of Mechanics. Vol. 1 , No. 1 , 2016 , pp. 48 - 63 .

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