Journal of Applied Mathematics
Volume 2008 (2008), Article ID 835380, 15 pages
doi:10.1155/2008/835380
Research Article
On the Asymptotic Approach to Thermosolutal Convection in Heated Slow Reactive Boundary Layer Flows
1Department of Mathematics and Applied Mathematics, University of Venda, Private Bag x5050, Thohoyandou 0950, South Africa
2School of Mathematical Sciences, University of KwaZulu Natal, Private Bag X01, Scottsville, Pietermaritzburg 3209, South Africa
3Mathematics Department, University of Swaziland, Private Bag 4, Kwaluseni, Swaziland
Received 22 April 2008; Revised 14 July 2008; Accepted 12 August 2008
Academic Editor: Jacek Rokicki
Copyright © 2008 Stanford Shateyi et al. 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.
Abstract
The study sought to investigate thermosolutal convection and stability of two dimensional disturbances
imposed on a heated boundary layer flow over a semi-infinite horizontal plate composed of a chemical species using a self-consistent asymptotic method. The chemical species reacts as it diffuses into the nearby fluid causing density stratification and inducing a buoyancy force. The existence of significant temperature gradients near the plate surface results in additional buoyancy and decrease in viscosity. We derive the linear neutral results by analyzing asymptotically the multideck structure of the perturbed flow in the limit of large Reynolds numbers. The study shows that for small Damkohler numbers, increasing buoyancy has a destabilizing effect on the upper branch Tollmien-Schlichting (TS) instability waves. Similarly, increasing the Damkohler numbers (which corresponds to increasing the reaction rate) has a destabilizing effect on the TS wave modes. However, for small Damkohler numbers,
negative buoyancy stabilizes the boundary layer flow.