ABSTRACT
Transient heat conduction problems are found in my engineering applications. In this chapter, several very powerful mathematical tools such as similarity method, Laplace transform method, and separation of variables method are introduced to solve time-dependent conduction problems. The separation of variables method is convenient to solve transient conduction problems with finite-length dimensions such as the plate, cylinder, and sphere with various thermal boundary conditions (BCs). However, the similarity method and Laplace transform method are more appropriate to solve the transient conduction problems with a semiinfinite solid material for various thermal BCs. More advanced topics include 1-D transient heat conduction with a moving boundary, transient heat conduction with a time-dependent BC, and time-dependent nonhomogeneous problems. For these problems, both Duhamel’s theorem and Green’s function method are demonstrated.
