ABSTRACT
A variety of techniques are available for solving multidimensional heat conduction problems, including analytical, graphical, analogical, and numerical methods. The analytical solution is generally restricted to systems having a somewhat simple shape. Because two-dimensional steady-state conduction problems are governed by a partial differential equation, instead of an ordinary differential equation, the analytical solution techniques that are required are somewhat more complicated than the techniques required by one-dimensional problems. The separation of variables method is not applicable for every two-dimensional conduction problem. Some requirements that assure that the separation of variables will work for a particular partial differential equation include the following. The integral of the product of two different eigenfunctions between limits that correspond to the homogeneous boundary conditions will always be zero, while the integral of any eigenfunction multiplied by itself between the same boundary conditions will not be zero.
