ABSTRACT
This chapter discusses one-dimensional steady-state heat conduction problems and observed that formulations of such problems involve ordinary differential equations. Formulations of two- or three-dimensional steady-state and one-dimensional or multidimensional unsteady-state heat conduction problems, on the other hand, involve partial differential equations. When the boundary surfaces correspond to the coordinate surfaces in a specific system of coordinates, such as rectangular, cylindrical, or spherical coordinates, we may then employ, among several different techniques, separation of variables, Fourier transforms, or Laplace transforms as the method of solution to obtain analytical solutions. The chapter also discusses the basic mathematical concepts related to several methods. The Fourier sine and cosine series that we have discussed in this section can be used in solving certain heat conduction problems. These two series were developed by considering two special cases of the boundary conditions of the Sturm–Liouville problem.
