On exact solutions for anisotropic heat conduction in composite conical shells

Abstract

In this paper, exact analytical solutions for anisotropic conductive heat transfer in composite conical shells are presented. To the knowledge of authors, the present work is the first exact study in the field of heat conduction in anisotropic cones. The shell has a full conical shape and the fibers are winded around the body. In order to obtain the most general solution, the general boundary condition is considered at the basis of shell and the effect of heat convection resulted from flow motion around the body and different kinds of non-axisymmetric radiative heat flux at outer side of shell is modeled. The exact solution of temperature distribution is obtained via separation of variables method for a general form and some special cases. Due to the existence of a dual second order derivative of temperature in heat transfer equation, it is not possible to obtain directly the temperature distribution using the analytical techniques. In order to cancel this term, the heat transfer equation is transformed to a canonical form using an innovative transformation. The present analytical solution is validated via numerical solution and some applied cases are considered to investigate the capability of current solution for solving the industrial problems.