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International Journal of Mathematics and Mathematical Sciences
Volume 23, Issue 5, Pages 319-334

Similarity analysis for natural convection from a vertical plate with distributed wall concentration

Department of Applied Mathematics, Daltech, Dalhousie University, P.O. Box 1000, NS, Halifax B3J 2X4, Canada

Received 10 July 1998

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Steady laminar natural convection flow over a semi-infinite vertical plate is examined in this paper. It is assumed that the concentration of a species along the plate follows some algebraic law with respect to chemical reaction. Similarity solutions may then be obtained for different orders of reaction. The fundamental parameters of this problem are the Schmidt number, Sc, and reaction order, n. Numerical results, based on the fourth order Runge-Kutta method, for Schmidt number ranging from 0.0 to 100.0 and reaction order from 0.0 to 1.5 are presented. When chemical reaction occurs, diffusion and velocity domains are seen to expand out from the plate. For large values of n, one may expect a smaller diffusion layer which, at fixed Schmidt number, is associated with increased velocity and reduced convection-layer.