A general analytical solution for heat conduction in cylindrical multilayer composite laminates

This paper presents a steady analytical solution for heat conduction in a cylindrical multilayer composite laminate in which the fiber direction may vary between layers. The analytical solution is obtained for general linear boundary conditions that are suitable for various conditions including combinations of conduction, convection, and radiation both inside and outside the cylinder. The Sturm–Liouville theorem is used to derive an appropriate Fourier transformation for this problem. The temperature distribution is obtained by applying this transformation to the governing equation. The coefficients of the solution are obtained by solving a set of equations generated by applying the boundary conditions inside and outside the cylinder, and the continuity of temperature and heat flux at boundaries between adjacent layers. The recursive Thomas algorithm is used to obtain the solution of this set of equations. The applicability of the current solution for a wide range of applied problems is confirmed by considering two industrial examples.

► An exact solution for heat conduction in multilayer composite is obtained. ► The most linear general boundary conditions in cylindrical shape are considered. ► When the fiber angles are θ=90°θ=90°, the highest cooling rate of pin fin occurs.