Steady-State Temperatures in an Anisotropic Strip

This article deals with the development of a rigorous solution to the steady-state temperature in an anisotropic strip. The solution is given with respect to a coordinate system (x, y), which conforms with the strip geometry but does not necessarily coincide with the principal directions of the anisotropic material. Using a partitioning–matching technique and the separation of variables method, exact expressions are obtained for temperatures in the strip under prescribed boundary temperature conditions. Numerical values of the temperatures and heat flux are provided in graphic form. Also, a discussion is presented regarding the solution method and the temperature distribution features in the heat conduction problem of an anisotropic medium.