A new approach for generating approximate analytic solutions of transient nonlinear heat conduction problems is presented. It is based on an effective combination of Lie symmetry method, homotopy perturbation method, finite element method, and simulation based error reduction techniques. Implementation of the proposed approach is demonstrated by applying it to determine approximate analytic solutions of real life problems consisting of transient nonlinear heat conduction in semi-infinite bars made of stainless steel AISI 304 and mild steel. The results from the approximate analytical solutions and the numerical solution are compared indicating good agreement.
Mustafa, M. T., Arif, A. F. M., & Masood, K. (2014). Approximate Analytic Solutions of Transient Nonlinear Heat Conduction with Temperature-Dependent Thermal Diffusivity. Abstract and Applied Analysis, 2014, 1–12. https://doi.org/10.1155/2014/423421