Solving Transient Heat Conduction Problems by Means of Finite Element Method (FEM)

Abstract

Theoretical fundamentals and the application of finite element method (FEM) [1–3, 6, 7, 9, 11–18, 20, 21] are presented in Chap. 11 for solving steady-state heat conduction problems. In this chapter, the authors discuss how FEM is applied when solving transient heat conduction problems. They also present the methods for integrating ordinary differential equation systems after time, which describe body temperature changes in nodes in the function of time and the differences between Galerkin- method-based FEM and the FEM based on the heat balance method, which was discussed in Chap. 21. Furthermore, the authors describe FEM-based finite volume method and the difference between this method and the Galerkin-method-based FEM, in which the finite elements are regarded as bodies with a lumped thermal capacity. Also the transformation of coordinates will be discussed as it facilitates the calculation of integrals in FEM. The authors also give a practical example in which FEM is used to determine transient temperature distribution in a complex-shape fin.