Viscous Dissipation Effects on MHD Natural Convection Flow Over a Sphere in the Presence of Heat Generation

M A A Alim,Md M M Alam,Md M K M K Chowdhury

doi:10.15388/na.2007.12.4.14676

Abstract

In this paper, the viscous dissipation effects on magnetohydrodynamic natural convection flow over a sphere in the presence of heat generation have been described. The governing boundary layer equations are first transformed into a nondimensional form and the resulting nonlinear system of partial differential equations are then solved numerically using finite-difference method together with Keller-box scheme. The numerical results of the surface shear stress in terms of skin friction coefficient and the rate of heat transfer in terms of local Nusselt number, velocity as well as temperature profiles are shown graphically and tabular form for a selection of parameters set consisting of heat generation parameter Q, magnetic parameter M, viscous dissipation parameter N and the Prandlt number Pr.

Highlights

The study of the flow of electrically conducting fluid in the presence of magnetic field is important from the technical point of view and such types of problems have received much attention by many researchers
The influence of the magnetic field on the boundary layer is exerted only through induced forces within the boundary layer itself, with no additional effects arising from the free stream pressure gradient
The stress work effects in laminar flat plate natural convection flow have been studied by Ackroyd [1]

Summary

Introduction

The study of the flow of electrically conducting fluid in the presence of magnetic field is important from the technical point of view and such types of problems have received much attention by many researchers. The influence and importance of viscous stress work effects in laminar flows have been examined by Gebhart [2] and Gebhart and Mollendorf [3] In both of the investigations, special flows over semi-infinite flat surfaces parallel to the direction of body force were considered. To the best of our knowledge, viscous dissipation effects on magnetohydrodynamics free convection flow from an isothermal sphere in presence of heat generation has not yet been studied and the present work demonstrate the issue. Natural convection boundary layer flow over a sphere of a viscous incompressible electrically conducting fluid in the presence of magnetic field and heat generation with the effects of viscous dissipation has been investigated. Numerical results have been shown graphically as well as in tabular form

Formulation of the problems

Method of solution

Results and discussion

Conclusions