Hall Current Effects on Unsteady MHD Flow in a Rotating Parallel Plate Channel Bound-ed by Porous Bed on the Lower Half—Darcy Lapwood Model

M Veera Krishna,Jagdish Prakash

doi:10.4236/ojfd.2015.54029

Abstract

We discussed the unsteady flow of an incompressible viscous fluid in a rotating parallel plate channel bounded on one side by a porous bed under the influence of a uniform transverse magnetic field taking hall current into account. The perturbations are created by a constant pressure gradient along the plates in addition to the non-torsional oscillations of the upper plate. The flow in the clean fluid region is governed by Navier-Stoke’s equations while in the porous bed the equations are based on Darcy-Lapwood model. The exact solutions of velocity in the clean fluid and the porous medium consist of steady state and transient state. The time required for the transient state to decay is evaluated in detail and ultimate quasi-steady state solution has been derived analytically and also its behaviour is computationally discussed with reference to different flow parameters. The shear stresses on the boundaries and the mass flux are also obtained analytically and their behaviour is computationally discussed.

Highlights

Flow of a viscous fluid in rotating channels is of considerable importance due to the occurrence of various natu-How to cite this paper: Krishna, M.V. and Prakash, J. (2015) Hall Current Effects on Unsteady MHD Flow in a Rotating Parallel Plate Channel Bounded by Porous Bed on the Lower Half—Darcy Lapwood Model
The slip velocity uB enhances with its magnitude with increasing in E, m, M and D−1 for the smaller and larger thickness of porous bed (Table 1)
The slip velocity vB enhances with its magnitude increase in E or m while reduces with increases in M D−1 for the irrespective thickness of porous bed (Table 2)

Summary

Introduction

How to cite this paper: Krishna, M.V. and Prakash, J. (2015) Hall Current Effects on Unsteady MHD Flow in a Rotating Parallel Plate Channel Bounded by Porous Bed on the Lower Half—Darcy Lapwood Model. V. Krishna et al [19] discussed the unsteady flow of an incompressible viscous fluid in a rotating parallel plate channel bounded on one side by a porous bed under the influence of a uniform transverse magnetic field making use of Darcy Lapwood model. Krishna et al [22] studied the steady hydro magnetic flow of a couple stress fluid through a composite medium in a rotating parallel plate channel with porous bed on the lower half subjected to subjected to normal to the channel and extended the problem taking hall current into account by M. Motivated in view of the above discussions, in this paper, we discuss the unsteady flow of an incompressible viscous fluid in a rotating parallel plate channel bounded on one side by a porous bed under the influence of a uniform transverse magnetic field taking hall current into account. The flow in the clean fluid region is governed by Navier-Stoke’s equations while in the porous bed the equations are based on Darcy-Lapwood model

Formulation and Solution of the Problem

B Coshλ1h

Results and Discussion

Conclusions