ABSTRACT
This chapter introduces a very powerful mathematical tool, the method of separation of variables, to solve typical two-dimensional heat conduction problems with various thermal boundary conditions (BCs). In the undergraduate-level heat transfer, one normally employs the finite-difference energy balance method to solve the two-dimensional heat conduction problems with various thermal BCs. The chapter focuses on the analytical methods and solutions for various two-dimensional heat conduction problems. In general, all kinds of two-dimensional heat conduction problems with various BCs can be solved analytically by using superposition of separation of variables. The most important thing for applying separation of variable is that one has to set up the problem where only one nonhomogeneous BC is allowed. In real-life engineering applications, the convection heat transfer coefficients normally are varied along the solid surface. This will cause additional complexity for the separation of variables because one normally assumes the uniform convection BCs to simplify the problem.
