ABSTRACT
This chapter talks about integral transform methods. There are both advantages and disadvantages of the Laplace transform method as compared to the other integral transform methods. The Laplace transform method is particularly applicable to time-dependent problems and, in fact, is attractive for one-dimensional problems. If the method of Laplace transforms is used to solve two- or three-dimensional time-dependent problems, the resulting simpler problem would again involve partial derivatives with respect to space variables. Furthermore, with Laplace transforms, inversion may not be as easy as with integral transforms. The chapter examines the basic properties of Laplace transforms. It discusses the method of solution of various unsteady-state heat conduction problems by Laplace transforms in terms of various representative examples. The chapter reviews some of the important properties of Laplace transforms. The Laplace transform method is particularly convenient and efficient for solving one-dimensional unsteady-state heat conduction problems.
