Chapter 11: Applied Solution Methods—Part 2: PDEs and Heat Transfer

In this chapter, we consider both ODEs and partial differential equations, or PDEs, solved using common methods encountered in nuclear engineering applications and related problems of interest. Fundamentally, PDEs are typically solved by applying methods similar to those used for ordinary differential equations, but with the added complexity of separating multivariate conditions, and applying orthogonality to yield a linearly independent solution basis. For this reason, we focus on solving the heat equation. Then, after covering essential concepts here, we will consider problems involving neutron transport and diffusion theory.