Closed-form analytical solutions of transient heat conduction in hollow composite cylinders with any number of layers

Conventional analytical methods for transient heat conduction solutions, due to complicated derivations and formidable calculations, have been limited to composite bodies with two or three layers. Developed in this work is a new analytical solution method for transient heat conduction in hollow composite cylinders with an arbitrary number of layers and subject to general boundary conditions. In this method, a distributed transfer function formulation gives an s-domain solution of a composite cylinder and inverse Laplace transform of the s-domain solution via a newly derived residue formula yields the transient solution of the cylinder in an explicit and closed form. Unlike conventional analytical methods, the proposed method does not require different derivations for different cylinder configurations (such as number of layers, boundary conditions and thermal resistance at layer interfaces). Because it only involves two-by-two matrices in the solution process, the proposed method is highly efficient in computation, as demonstrated in numerical examples.