A Steady-State Heat Conduction Problem in a Composite Solid Square Two-Dimensional Body

Studying inhomogeneous structural elements is a very important task.Many studies deal with inhomogeneity of the type whose introduction into an originally homogeneous body does not change its physical fields belonging to the prescribed boundary conditions.This type of inhomogeneity is called neutral inhomogeneity.In the relevant literature, we find several examples of this, mainly in the mathematical theory of elasticity.A prime example is the Saint-Venant's torsion problem of prismatic bars.In the present paper a steady-state heat conduction problem is considered in a two-dimensional square-body.The Cartesian orthotropic solid square body consists of a circular inclusion.The circular inclusion is placed at the center of the square and it has two parts, a core and a coating component, both of which are cylindrically orthotropic.The paper deals with the determination of the thermal conductance of component bodies such that the temperature distribution in originally homogeneous Cartesian orthotropic solid square body does not change.All results of the paper is based on the Fourier's theory of heat conduction in solid body.