ABSTRACT
This chapter examines how to solve transient problems, in which the temperature or species concentration within a domain varies with both position and time. The transient heat conduction and mass diffusion problems have numerous important applications in materials processing, such as melting and solidification, crystal growth, casting, heat treatment, and welding processes. The chapter considers one-dimensional transient heat conduction problems in case of no heat generation. Consider one-dimensional transient heat conduction problems in a steel plate, hollow cylinder and hollow sphere. The integral form of transient heat conduction equation, which will be used in the finite volume approach. The first step in the finite volume method is to divide the computational domain into discrete control volumes. In general, three types of error are introduced into the solution of finite difference equations: truncation error, round-off and discretization errors. Stability analysis is essential for obtaining a successful solution of a finite difference equation.
