Numerical solution of two‐dimensional heat‐flow problems

Abstract

Abstract Two‐dimensional heat flow frequently leads to problems not amenable to the methods of classical mathematical physics; thus, procedures for obtaining approximate solutions are desirable. A recently introduced finite‐difference method, known to be applicable to problems in a rectangular region and involving much less calculation than previous methods, is extended by example to cases of more practical interest. Although all three examples given are steady state, unsteady state problems may also be attacked successfully by the method. The first example is that of flow around a corner and indicates that a more complicated region than a rectangle can be treated. Then a problem involving a radiation‐boundray condition is given; as this condition is nonlinear, the method is extended to more general equations. The last example involves point heat sources and sinks in an elliptical region and so extends the method to treat curved boundaries (as distinguished from polygonal domains) and singular points. It is believed that materially less calculation is necessary by this method than for previous procedures.