COMPARISON OF APPROXIMATE METHODS FOR SOLVING NON-LINEAR CONVECTIVE DIFFUSION PROBLEMS

Abstract

A comparison is made of the approximate methods of solving a high Schmidt number non-linear convective diffusion equation and boundary conditions similar to those which arise in various separation problems including reverse osmosis and directional solidification. The series expansion method gives the best agreement with exact numerical solutions. The film theory, which provides very simple results, yields surprisingly good estimates which are second in accuracy only to the series expansion. Several more sophisticated techniques including rapidly varying boundary conditions, the integral method and local non-similarity yield results of somewhat disappoinling accuracy. The linear problem, B ₂ = 0, for which exact analytical and numerical solutions exist, provides a discriminating test of the accuracy of the methods.

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Notes on contributors

WILLIAM N. GILL

To whom correspondence should be addressed.