ABSTRACT
This chapter presents the analytical methods of solution, including Duhamel's method, the method of similarity transformation, the integral method, and the variational method. It introduces the integral method is especially important because it can also be implemented to solve nonlinear problems. That is, nonlinear heat conduction problems need not be linearized because this method is elastic enough to encompass all sorts of nonlinearities associated with such problems. The chapter also introduces Duhamel's method by applying it to the solution of a representative heat conduction problem. It discusses the basics of the similarity method and the solution procedure by solving a representative heat conduction problem. The integral method can also be used to obtain approximate solutions to problems with nonlinear boundary conditions. The chapter illustrates the use of the method by solving a heat conduction problem in a semi-infinite solid with a nonlinear boundary condition.
