STEADY-STATE HEAT CONDUCTION PROBLEMS FOR NON-HOMOGENEOUS HOLLOW ELLIPTICAL TWO-DIMENSIONAL DOMAIN

The paper deals with a two-dimensional boundary value problem of steady-state heat conduction in non-homogeneous hollow elliptical domain. First one is the layered elliptical domain, the thermal conductance in each elliptical rings is constant. The layered non-homogeneous domain is considered as a union of elliptical rings which have different material properties. The boundary curves of elliptical rings are confocal ellipses. In the second case, the functionally graded type of non-homogeneity is considered, the thermal conductance is a smooth function of a curvilinear coordinate. All results of the paper are based on Fourier's theory of heat conduction in non-homogeneous solid bodies.