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

摘要

Exact solution of an unsteady MHD flow of elastico-viscous 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 After attaining the steady state, the pressure gradient is suddenly withdrawn and the resulting fluid motion in a tube of spherical cross section by taking into account of the porosity factor and magnetic parameter of the bounding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, magnetic parameter, angle of inclination 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 elastic-viscosity parameter and magnetic parameter tends to zeroand 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.