An exact analysis for transient anisotropic heat conduction in truncated composite conical shells
Abstract This paper presents an exact analytical solution for transient anisotropic heat conduction in a truncated composite conical shell for the first time. The fibers of composite conical shell are winded around the body in any arbitrary direction. Heat convection between the ambient fluid flow and composite conical shell is modeled and the exact solution of heat conduction equation is obtained by combining two popular analytical methods. First, by means of an integral transform in angular direction, the heat conduction equation is transformed and after that the transferred heat equation is solved using separation of variables method. Eventually, an inverse transformation is used in order to achieve the final exact solution of heat conduction equation. Validation of the present analytical solution is performed by comparing the analytical results with the solution of second order finite different method. Besides, the capability of present solution in solving the industrial cases is tested. The present solution is applicable in some industrial cases such as cooling pin fins and aeronautical instruments.