Conjugate Effects of Viscous Dissipation and Dependent Viscosity on Natural Convection Flow over a Sphere with Joule Heating and Heat Conduction

In the present paper, the effect of viscous dissipation and dependent viscosity on free convection flow over a sphere has been investigated. Joule heating and heat conduction over a sphere are considered as well in this investigation. With a goal to attain similarity solutions of the problem being posed, the developed equations are made dimensionless by using suitable transformations. The non-dimensional equations are then transformed into non-linear equations introducing a non- similarity transformation. The resulting non-linear similar equations together with their corresponding boundary conditions based on conduction and convection are solved numerically by using the finite difference method along with Newton’s linearization approximation. The numerical results detailing the velocity profiles, temperature profiles, skin friction coefficient and the local heat transfer coefficient are shown both in graph and tabular forms for the different values of the parameters associated with the problem.