Thermal conduction in an orthotropic sphere with circumferentially varying convection heat transfer

Heat transfer due to fluid flow past a sphere is encountered commonly in engineering applications. In this case, the local convective heat transfer coefficient on the surface of the sphere is known to change with azimuthal and polar angles due to various flow phenomena. While surface-averaged convective heat transfer coefficient is commonly used for engineering analysis, however, not much work exists for modeling the temperature field inside the sphere while accounting for the spatially varying convective heat transfer, especially in the context of a sphere with orthotropic thermal conduction properties. This paper presents an analytical approach for a steady state solution of this problem by deriving a set of algebraic equations for coefficients of a series solution of the temperature distribution. The problem is solved using two different approaches, which are shown to lead to equivalent results. Temperature distribution based on the analytical approach is found to be in excellent agreement with finite-element simulation results. The effect of various parameters, such as thermal conduction orthotropic ratio, heat generation rate, power density, flow rate, etc. on temperature distribution in the sphere is presented. Results discussed in this paper contribute towards the fundamental understanding of an important heat transfer problem, and in the design of thermal management techniques for engineering applications involving convective cooling of spherical systems.