ABSTRACT
This chapter introduces the constitutive relation between heat flux and temperature that is known as Fourier's law. The temperature distribution in solids is needed, for example, to predict thermal stresses that can develop in constrained bodies. Under steady-state conditions, the temperature field no longer depends on time, but it can vary spatially throughout the body. The temperature field dictates the thermal strain distribution in the solid, which in turn gives rise to thermal stresses when the solid is constrained. In other words, the thermal strain distribution loads the solid, and the resulting displacement, elastic strains, and stresses are obtained by performing a separate finite element analysis. The chapter begins by deriving the partial differential equation that governs steady-state heat conduction. It also includes a discussion of symmetry, which under certain circumstances can be exploited, reducing computational costs. Symmetry can often be exploited in steady-state heat conduction problems, reducing the computational cost.
