Magneto-Hydrodynamic Flow of a Viscous Fluid in a Channel with a Porous Bounding Wall of Different Permeabilities

Nidhi Pandya,R P Pandey,Pravin Kumar Srivastava,Ramesh Yadav

doi:10.33889/ijmems.2019.4.3-056

Abstract

In this paper, the effects of permeability parameter on the magneto-hydrodynamic laminar flow of a viscous incompressible fluid in a channel with a porous bounding wall have been investigated. A transverse magnetic field has been applied in the channel flow of viscous fluid and the stream function is used to reduce the governing partial differential equations into non-linear ordinary differential equation which is solved by applying Perturbation method. Numerical simulation is used to analyze the problem and the graphs have been plotted using MATLAB. It has been observed that an increase of magnetic parameter increases the velocity of the viscous fluid while the velocity decreases with the increase of permeability parameter. The flow of viscous fluid has also been investigated with the variation of Reynolds number and the slip coefficient.

Highlights

The study of a steady laminar flow of electrically conducting viscous fluids confined in a channel with the porous walls has been subject of intensive study because of its applications in industrial and geophysical situations such as the prevention of the boundary layer separation with injection or suction, magneto hydrodynamics generators, membrane separation, the filtration process, electrochemical engineering and other biological transport systems such as plasma studies, blood flow problems etc
Berman (1953) has analyzed the laminar flow of a viscous fluid in a channel with the porous bounding walls and solved the Navier-Stokes equations with suitable boundary conditions. He has discussed a complete description of the flow of viscous fluid flowing in a channel with porous walls having a rectangular cross-section and found that the velocity components and the pressure depend on position coordinates, channel dimensions, and fluid properties
In order to get a physical significance of this problem, graphs are plotted with the help of MATLAB software by giving numerical values to various parameters which are present in the mathematical formulation of the problem

Summary

Introduction

The study of a steady laminar flow of electrically conducting viscous fluids confined in a channel with the porous walls has been subject of intensive study because of its applications in industrial and geophysical situations such as the prevention of the boundary layer separation with injection or suction, magneto hydrodynamics generators, membrane separation, the filtration process, electrochemical engineering and other biological transport systems such as plasma studies, blood flow problems etc. Many researchers have solved the problem of laminar flow of incompressible viscous fluids over and through porous walls of different permeabilities under steady-state situations. Berman (1953) has analyzed the laminar flow of a viscous fluid in a channel with the porous bounding walls and solved the Navier-Stokes equations with suitable boundary conditions. Terrill and Shrestha (1966) have investigated a laminar flow through a channel with uniformly porous walls of different permeabilities They have obtained a perturbation solution for the case of suction at one wall and injection at the other wall by choosing the velocity differences of two walls as a perturbation parameter.

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