Heat Transfer Engineering

Chapter 9: Numerical heat transfer

Abstract

In this chapter, we present a brief overview of why numerical solutions are required for heat transfer problems. Three popular approaches in numerical methods in heat transfer—namely, the finite difference method, the finite volume method, and the finite element method—are introduced. Classification of the governing equations is presented based on (1) linearity and order and (2) propagation of information. Based on the Taylor series approximation, the first- and second-order accurate derivations of finite difference approximations to derivatives are presented. The finite difference method is then demonstrated for (1) steady and (2) unsteady state conduction problems. The chapter ends with a note on practical ...