Heat Diffusion in an Anisotropic Medium with Central Heat Source

Abstract Anisotropy is a property of some materials in which the physical properties vary with different crystallographic orientations. In this study, the analytical steady state solution to the anisotropic heat conduction in an orthotropic sphere is presented. There is a point heat source in the center of the sphere which supply the constant thermal energy. Using a transformation can change the anisotropic problem to an isotropic one which can be solved by the change of variables. The results showed that the isothermal surfaces are concentric ellipsoids which approach spheres while the conductivities in different directions are close to each other. The analytical results were validated with the 2D experimental tests performed for quartz as an orthotropic material. Despite the isotropic materials, it can be seen that the vectors of temperature gradients T ∇ and the heat flux q are not parallel