Chapter 12 - Heat Transfer

Abstract

This chapter presents the finite element modeling of heat transfer problems. It starts with the fundamental knowledge of the conduction (for isotropic and orthotropic materials) and convection heat transfer and proceeds with the development of the heat transfer matrices using a variational method. The “stiffness” matrices derivation is carried out for one-dimensional (1D) heat transfer element, for linear triangular heat transfer element, for bilinear quadrilateral heat transfer isoparametric element, for eight-node isoparametric heat transfer two-dimensional (2D) element, and for eight-node isoparametric heat transfer tree-dimensional (3D) element. Detailed solutions are provided for temperature distribution and heat flux calculation in 1D multilayered materials and 2D heat transfer problems regarding heat exchangers. A step-by-step instruction of ANSYS implementation for the solution of an electronic chip-cooling system is also given.