Natural Convection Flow from an Isothermal Sphere with Temperature Dependent Thermal Conductivity

Abstract

Laminar free convection flow from an isothermal sphere immersed in a fluid with thermal conductivity proportional to linear function of temperature has been studied. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations is reduced to local non-similarity equations, which are solved numerically by very efficient implicit finite difference method together with Keller box scheme. Numerical results are presented by velocity and temperature distribution of the fluid as well as heat transfer characteristics, namely the heat transfer rate and the skin-friction coefficients for a wide range of thermal conductivity parameter γ (= 0.0, 0.5, 1.0, 2.0, 3.0, 5.0) and the Prandtl number Pr (= 0.7, 1.0, 3.0, 5.0, 7.0).  

Keywords: Natural convection, temperature dependent thermal conductivity, isothermal sphere.   

doi:10.3329/jname.v2i2.1872

 Journal of Naval Architecture and Marine Engineering 2(2005) 53-64