ABSTRACT
This chapter explores the method of solution of linear heat conduction problems by the application of various integral transforms, such as Fourier and Hankel transforms. These transforms remove the partial derivatives with respect to space variables and are equally attractive for both steady- and unsteady-state problems. The chapter examines the solution of unsteady-state linear heat conduction problems posed in the rectangular coordinate system by the application of Fourier transforms. It introduces the method of solution by solving a one-dimensional unsteady-state problem. For two- and three-dimensional unsteady-state problems the method of solution is the same: partial derivatives with respect to space variables are removed from the problem by repeated application of Fourier transforms. The chapter considers the extensions of the theory and introduces integral transforms in the semi-infinite and infinite regions. Integral transforms whose kernels are Bessel functions are called Hankel transforms, and they are obtained from the expansion of an arbitrary function in an infinite series of Bessel functions.
