Unsteady MHD Flow of Elastico-Viscous Incompressible Fluid through a Porous Medium between Two Parallel Plates under the Influence of a Magnetic Field

S. B. Kulkarni

doi:10.14429/dsj.65.7958

S. B. Kulkarni Finolex Academy of Management and Technology, Ratnagiri

DOI: https://doi.org/10.14429/dsj.65.7958

Keywords: Elastico-viscous fluid, second order fluid, elastico-viscous parameter, porous media, magnetic parameter

Abstract

An unsteady flow of elastico-viscous incompressible and electrically conducting fluid through a porous medium between two parallel plates under the influence of transverse magnetic field is examined. Initially, the flow is generated by a constant pressure gradient parallel to the bounding fluids. After attaining the steady state, the pressure gradient is suddenly withdrawn and the resulting fluid motion between the parallel plates under the influence of magnetic field is then to be investigated. The problem is solved in two stages: the first stage is a steady motion between the parallel plates under the influence of a constant pressure gradient and the magnetic parameter. The momentum equation of steady state does not involve the elastic-viscosity parameter; however, the influence Darcian friction would appear in it. The solution of the momentum equation at this stage will be the initial condition for the subsequent flow. The second stage concerns with an unsteady motion for which the initial value for the velocity will be that obtained in stage one together with the no-slip condition on the boundary plates. The problem was solved employing Laplace transformation technique. It was found that the effect of the applied transverse magnetic field has significant contribution on the velocity profiles.

Defence Science Journal, Vol. 65, No. 2, March 2015, pp.119-125, DOI:http://dx.doi.org/10.14429/dsj.65.7958

Author Biography

S. B. Kulkarni, Finolex Academy of Management and Technology, Ratnagiri

Dr Sanjay Baburao Kulkarni obtained his MSc (Applied Mathematics) from the Gulbarga University Gulbarga, in 1995 and PhD from Dr Babasaheb Ambedkar Technological University, Lonere, in 2010. Presently, he is Associate Professor and Head, Department of Applied Mathematics at Finolex Academy of Management and Technology, Ratnagiri. He has published several research papers in national and international journals. He has also published international book on elastico-viscous fluid flows. His areas of interest include: Applied mathematics elastico-viscous fluid flow problems and operation research.