Analytical Study of Thermal Heat Conduction inside Two Orthotropic Mediums in Cylindrical Geometry

Abstract

The present work focuses on the two-dimensional steady-state thermal behavior of two orthotropic mediums in a coaxial cylindrical geometry. The whole lateral surface is subjected to a flux density while the end sections are maintained at prescribed temperatures. The resolution of the problem is carried out analytically by the variable separation technique, taking into account the boundary conditions and the continuity of temperatures and flux at the interface between the two mediums. The resolution in dimensionless form, expressed in terms of the Bessel functions, made it possible to identify the parameters of the study, namely the ratio of the main thermal conductivities for each medium as well as the ratio of the radial thermal conductivities of the two mediums. A numerical code was developed, in order to simulate the effect of the study parameters on heat transfer within the two mediums, in terms of isotherms.