Chapter 12, Problem 39P

Mechanical/Aerospace Engineering

The steady-state distribution of temperature on a heated plate can be modeled by the Laplace equation,

$0=\frac{{\partial }^{2}T}{\partial x^2}+\frac{{\partial }^{2}T}{\partial y^2}$

If the plate is represented by a series of nodes (Fig. P12.39), centered finite-divided differences can be substituted for the second derivatives, which results in a system of linear algebraic equations. Use the Gauss-Seidel method to solve for the temperatures of the nodes in Fig. P12.39.

FIGURE P12.39