ABSTRACT
This chapter presents some of the standard analytical approximation methods for phase change problems. It focuses on four widely used analytical methods, commonly referred to as the quasistationary approximation method, the Megerlin method, the heat balance integral and perturbation methods. Several mechanisms, such as radioactive decay, electrical resistance heating or irradiation, provide energy directly to each point of the material, thus generating internal heating. Perturbation methods utilize series expansions in small parameters to reduce a problem to a sequence of simpler problems which, hopefully, may be explicitly solvable. Typically only the first few terms in the expansion can actually be found, due to the increasing complication of the problems. In some fields, such as fluid dynamics, quantum physics, the perturbation approach has proved to be extremely successful and, as a result, the theory and practice of perturbation methods in those fields is very advanced.
