Closed-form analytical solutions of transient heat conduction in hollow composite cylinders with any number of layers. (May 2017) - Yang, Bingen; Liu, Shibing
Highlights: An analytical method for composite cylinders of any number of layers is proposed. The analytical method relies on a distributed transfer function formulation. Transient solutions are obtained by a residue formula in exact and explicit form. Different configurations of composite cylinders are treated in a unified manner. Highly efficient computation only needs operations of two-by-two matrices. Abstract: 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.