Conjugate Effects of Radiation and Joule Heating on Magnetohydrodynamic Free Convection Flow along a Sphere with Heat Generation

Md Miraj Ali,Md Abdul Alim,Laek Sazzad Andallah

doi:10.4236/ajcm.2011.11003

Abstract

The conjugate effects of radiation and joule heating on magnetohydrodynamic (MHD) free convection flow along a sphere with heat generation have been investigated in this paper. The governing equations are transformed into dimensionless non-similar equations by using set of suitable transformations and solved numerically by the finite difference method along with Newton’s linearization approximation. Attention has been focused on the evaluation of shear stress in terms of local skin friction and rate of heat transfer in terms of local Nusselt number, velocity as well as temperature profiles. Numerical results have been shown graphically for some selected values of parameters set consisting of heat generation parameter Q, radiation parameter Rd, magnetic parameter M, joule heating parameter J and the Prandtl number Pr.

Highlights

The conjugate effects of radiation and joule heating on magnetohydrodynamic (MHD) free convection boundary layer on various geometrical shapes such as vertical flat plate, cylinder, sphere etc, have been studied by many investigators and it has been a very popular research topic for many years
The variation of the local skin friction coefficient Cf and local rate of heat transfer Nu for different values of Prandtl number Pr while radiation parameter Rd = 1.00, heat generation parameter Q = 0.10, magnetic parameter M = 2.00 and joule heating parameter J = 0.50 are shown in Figures 8(a) and 8(b)
Solutions are obtained for some test values of Prandtl number Pr = 2.00, 5.00, 7.00, 9.00; radiation parameter Rd =1.00, 2.00, 3.00, 4.00, 5.00; heat generation parameter Q = 0.00, 0.05, 0.10, 0.15, 0.20; magnetic parameter M = 0.50, 1.00, 1.50, 2.00, 3.00 and joule heating parameter J = 0.10, 0.50, 1.00, 1.50, 2.00 in terms of velocity and temperature profiles, skin friction coefficient and heat transfer coefficient

Summary

Introduction

The conjugate effects of radiation and joule heating on magnetohydrodynamic (MHD) free convection boundary layer on various geometrical shapes such as vertical flat plate, cylinder, sphere etc, have been studied by many investigators and it has been a very popular research topic for many years. Miraj et al [4] studied the effect of radiation on natural convection flow on a sphere in presence of heat generation. Hossain [6] studied viscous and joule heating effects on magnetohydrodynamic (MHD) free convection flow with variable plate temperature. Alam et al [7] studied the viscous dissipation effects with MHD natural convection flow on a sphere in presence of heat generation. The results have been shown in terms of the velocity, temperature profiles, the skin friction and surface heat transfer

Formulation of the Problem

Results and Discussion

Conclusions