Numerical Study of Viscous Dissipation and Temperature-Dependent Viscosity on MHD Free Convection Flow over a Sphere with Heat Conduction
Md. M. Alam
Department of Mathematics, Dhaka University of Engineering and Technology, Gazipur-1707, Bangladesh.
Ruhul Imran
Department of Mathematics, Model Institute of Science and Technology, Gazipur-1707, Bangladesh.
Mohammad Mahfuzul Islam
Department of Mathematics, Dhaka University of Engineering and Technology, Gazipur-1707, Bangladesh.
M. H. Rashid *
Department of Mathematics, Dhaka University of Engineering and Technology, Gazipur-1707, Bangladesh.
*Author to whom correspondence should be addressed.
Abstract
The effect of viscous dissipation and temperature dependent viscosity on MHD free convection flow over a sphere with heat conduction has been analyzed in the article. The governing equations are transformed into dimensionless non-similar equations by using a set of useful transformations and solved numerically by 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 local Nusselt number, the velocity and the temperature profiles over the whole boundary layer are shown graphically by using Tecplot-10 and tabular form for different values of the Prandtl’s number Pr, magnetic parameter M, the temperature dependent viscosityε, viscous dissipation parameter N and the Joule heating parameter J.
Keywords: Free convection, Joule-heating, Magneto hydrodynamics, Variation viscosity and viscous dissipation.