Abstract
Two- and three-dimensional steady-flow heat-conduction problems are readily solved to any degree of approximation by application of the relaxation method introduced by Southwell. Except for the simplest geometric shapes and boundary conditions, the relaxation method is far superior to analytical methods of solution in point of time required to reach a given desired accuracy. The relaxation method has the further advantages of permitting the calculator to put into the calculation all the physical intuition he may have about the problem and, at the same time, to know at each step just how seriously his solution still differs from the correct answer. By an extension of the method one-, two-, and three-dimensional transient-heat-flow problems are easily solved. For one-dimensional problems, the new method is identical to the graphical method of Schmidt.
