### Effect of Radiation and Magnetohydrodynamic Free Convection Boundary Layer Flow on a Solid Sphere with Convective Boundary Conditions

#### Abstract

In this paper, the effect of radiation on magnetohydrodynamic free convection boundary layer flow on a solid sphere with convective boundary conditions, in which the heat is supplied through a bounding surface of finite thickness and finite heat capacity, is considered. The basic equations of the boundary layer are transformed into a non-dimensional form and reduced to nonlinear systems of partial differential equations and solved numerically using an implicit finite difference scheme known as the Keller-box method. Numerical solutions are obtained for the wall temperature, the heat transfer coefficient, local Nusselt number and the local skin friction coefficient, as well as the velocity and temperature profiles. The features of the flow and heat transfer characteristics for various values of the Prandtl number Pr, magnetic parameter *M*, radiation parameter *N _{R}*, the conjugate parameter

*g*, and the coordinate running along the surface of the sphere,

*x*are analyzed and discussed.

doi:10.14456/WJST.2015.50

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