An approximation technique for natural convection in a boundary layer

Abstract

An approximation technique, widely used by Meksyn for finding solutions in terms of asymptotic expansions to problems of flow in boundary layers, is extended to free convection flows, and applied to the classical problem of free convection at a uniformly heated vertical wall in fluid otherwise at rest, and to the rather less known problems of combined free and forced convection at a vertical wall in a fluid having a vertical velocity at a large distance from the wall. It is found that, in the problems considered, the first three terms of the asymptotic series provide a good approximation to known results, and since in this case the essential computational problem is that of finding the least root of a quartic equation in which the Prandtl number appears as a parameter, the method is a good deal more easy to use and of more general application than those used by previous workers on these problems. Other problems of free convection, or combined free and forced convection, in which similarity transformations may be used are at once amenable to the same technique.