Closed-Form Analytical Solution of Transient Heat Conduction in a Multi-Layer Hollow Cylinder with Time-Dependent Heat Transfer Coefficient

Numerous practical engineerings involve the problem of heat conduction in a multi-layer hollow cylinder. It is meaningful for forming a deeper physical insight to derive an analytical solution of the heat conduction in composite hollow cylinders. However, heat transfer coefficient is commonly fixed as a constant in previous researches. This is not practical in some circumstances, such as heat conduction in casting. As a result, applications of numerous previous solutions are limited to some extent. Therefore, this work aims to propose a new closed-form analytical solution of transient heat conduction in a multi-layer hollow cylinder with time-dependent heat transfer coefficient. Shifting function method is introduced to our solution and new shifting functions are employed in the derivation. Besides, finite integral transform technique is used to deal with the governing equations and the homogenized BCs. The new solution suits for arbitrary initial temperature distribution, time-dependent temperature boundary conditions, time-dependent heat source and time-dependent heat transfer coefficient. Three examples with constant heat transfer coefficient are implemented to verify our new solution. Then a seven-layer example with time-dependent heat transfer coefficient is computed to show the capability of our solution. The results imply the explicitness and the operability of the proposed analytical method, demonstrating the high-efficiency and precision of the solution.