5.3 Two-Dimensional Heat Equation: Solution

5.3 Two-Dimensional Heat Equation: Solution

• In order to see the technique of solution for a two-dimensional problem, we need to consider the diffusion of heat in a rectangular plate of isotropic material.

• The problem has a partial differential equation and boundary conditions.

• We are not out of trouble yet.
• It is clear that the partial differential equation and the boundary conditions are both linear.

• There are two independent eigenvalue problems.

• The solution will be assembled.

• We can form linear combinations to get other solutions.

• The initial condition remains.

• We may say that the problem has been solved.
• Each term in the series is reassuring.

• The solution is shown on a CD.

• The double series should be converted into single series.

• The first terms in the single series are the most significant.

• The first few terms of the series should be written.

• The details of the separation of variables are provided.

• Sec tion 5.1 is Exercise 1.