ABSTRACT
This chapter explains 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. The solution of linear problems, such as heat conduction problems with constant properties, may often be reduced to the solution of a number of simpler problems by employing the principle of superposition. Temperature distributions in several representative problems have been obtained. Once the temperature distribution is known, the heat transfer rate across any area A can be calculated by using Fourier's law of heat conduction.
