Analytical solution of heat transfer in heterogeneous composite conical shells with temperature dependent conduction coefficients

This paper presents an analytical solution for heat transfer in heterogeneous composite conical shells with temperature dependent conduction coefficients for the first time. The geometry of the shell is completely conical shaped and the fibers are winded around the laminate in the desired direction. In order to achieve 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. Heterogeneous effect in this case is the results of the dependency in conduction heat transfer coefficient on temperature. Therefore, the heat transfer equation should first be transformed using the Kirchhoff transform to a solvable equation using integral transformation, then, the partial differential equation becomes an ordinary differential equation Fourier transformation. Finally, the transformed differential equation can be solved Green's functions. In the end, the reversal integral transformation and reversal Kirchhoff conversion are applied to obtain heterogeneous temperature distribution. Validation of the this analytical solution is performed by comparing the analytical results with the solution of second order finite different method and some applied cases are considered to investigate the capability of current solution for solving the industrial problems in the production of composite conical pressure vessels.