Chapter 5 - Two-Dimensional and Transient Heat Conduction

Abstract

In many engineering systems, heat conduction exhibits predominantly in two- or three-dimensional nature. Engineering systems consist of multiple components where thermal properties could be significantly different, leading to two- or three-dimensional temperature gradient. In some cases, inhomogeneous temperature distributions could lead to significant thermal stress to the systems, causing deformation, crack, or even fracture. This chapter uses several numerical example to illustrate solutions to the two-dimensional heat conduction and transient gradients to assist engineers to optimize their designs in substantial heat conduction applications. Most engineering systems are designed for long-term operation, design considerations and hence engineers commonly focus on the steady state temperature distribution. The numerical analysis in this chapter provides solutions to application involving high-power devices where transient heat generation and conduction could incur significant temporal thermal load. In these cases, it is also important to resolve the transient heat conduction to obtain the time-dependent temperature generation and dissipation characteristics.