ABSTRACT
This chapter explores the solutions of various two- and three-dimensional steady-state linear heat conduction problems by the method of separation of variables and introduces the method in terms of examples. It considers some representative examples in the rectangular coordinate system and investigates the conditions under which the method of separation of variables is applicable. The chapter also considers similar problems in the cylindrical and spherical coordinate systems. It explains nonhomogeneities in boundary conditions and discusses nonhomogeneities in differential equations. The chapter introduces the superposition techniques which are general in the sense that they can equally be applied to problems in the cylindrical and spherical geometries, as well as to unsteady problems. It also considers the solutions of Legendre's differential equation and then explains the expansion of an arbitrary function in a series of Legendre polynomials.
