Transient analytical solution to heat conduction in multi-dimensional composite cylinder slab

The analytical solution for the problem of transient heat conduction in multi-dimensional composite cylinder slab is developed for a time-dependent boundary condition. For such problems, numerical programs are needed to obtain eigenvalues and residues in most of the published papers. The numerical schemes may become unstable due to the existence of imaginary eigenvalues in multi-dimensional cases. In this paper, the proposed analytical method involves no numerical complications. By a novel application of the methods of the Laplace transform and separation of variables together with variable transformations, the residue calculation is avoided. The developed analytical method is powerful which represents extension of the analytical approach derived for the heat conduction problem in Cartesian coordinates. A closed form solution is provided. Calculation examples show that the analytical solutions predict good agreement with the numerical results.