An analytical method to solve heat conduction in layered spheres with time-dependent boundary conditions

An analytical method is proposed to solve the equation of heat conduction in a layered sphere subject to a time-dependent boundary temperature. It is well known that for such problems in general, eigenvalue and residue computation poses a challenge, which can become too complicated to handle with many layers. In this Letter, the proposed analytical method is free of eigenvalue and residue calculations. A closed-form approximate solution is derived with high accuracy.