Chapter 1 discussed the analytical and numerical solution of 1-D, steady-state problems. These are problems where the temperature within the material is independent of time and varies in only one spatial dimension (e.g., x). Examples of such problems are the plane wall studied in Section 1.2, which is truly a 1-D problem, and the constant cross section fin studied in Section 1.6, which is approximately 1-D. The governing differential equation for these problems is an ordinary differential equation and the mathematics required to solve the problem are straightforward.

In this chapter, more complex, 2-D steady-state conduction problems are considered where the temperature varies in multiple spatial dimensions (e.g., x and y). These can be problems where the temperature actually varies in only two coordinates or approximately varies in only two coordinates (e.g., the temperature gradient in the third direction is negligible, as justified by an appropriate Biot number). The governing differential equation is a partial differential equation and therefore the mathematics required to analytically solve these problems are more advanced and the bookkeeping required to solve these problems numerically is more cumbersome. However, many of the concepts that were covered in the context of 1-D problems continue to apply.