ABSTRACT
This chapter focuses on the solution to 2-D, steady-state, heat conduction problems. The method of separation of variables is introduced to solve the 2-D heat conduction equation with various thermal boundary conditions (BCs). The separation of variables technique requires a set of homogeneous BCs; if more than one nonhomogeneous BC exists, the principle of superposition must be applied by dividing the problem into multiple subproblems. The separation of variables method is demonstrated in Cartesian and cylindrical coordinates. In addition, the solution method is expanded to 3-D problems. Examples of analytical solutions for a wide variety of BCs and geometries are included within the chapter.
