A general exact solution for heat conduction in multilayer spherical composite laminates

In this study, an exact analytical solution for steady conductive heat transfer in multilayer spherical fiber reinforced composite laminates is presented as the first time. Here, the orthotropic temperature distribution of laminate is obtained under the general linear boundary conditions that are suitable for various conditions including combinations of conduction, convection, and radiation both inside and outside of the sphere. The temperature and heat flux continuity is applied between the laminas. In order to obtain the exact solution, the separation of variables method is used and the set of equations related to the coefficient of Fourier–Legendre series of temperature distribution is solved using the recursive Thomas algorithm. The capability of the present solution is examined by applying it on two industrial applications for different fiber arrangements of multilayer spherical laminates.