Temperature-dependent nonlinear transient heat conduction using the scaled boundary finite element method

This paper presents a numerical framework for solving temperature dependent non-linear transient heat conduction problems using the Scaled Boundary Finite Element Method (SBFEM) combined with fixed point iteration. Non-linear terms are interpolated using SBFEM shape functions to capture non-linearity effectively. The flexibility of the proposed method is demonstrated through various discretization techniques, including polygonal meshes, a node relocation technique for inclusions in a non-linear medium, and a moving quadtree meshing technique for complex non-linear problems. The proposed method is validated through three numerical examples, encompassing both steady-state and transient heat conduction problems. Additionally, a moving heat source problem is solved using the moving quadtree meshing technique, and a comparative study is conducted with its linear counterpart. This research showcases the robustness and versatility of the SBFEM framework in addressing complex non-linear heat conduction problems.