## Journal of Applied Mathematics

### On the Asymptotic Approach to Thermosolutal Convection in Heated Slow Reactive Boundary Layer Flows

#### 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.

#### Article information

Source
J. Appl. Math., Volume 2008 (2008), Article ID 835380, 15 pages.

Dates
First available in Project Euclid: 10 February 2009

https://projecteuclid.org/euclid.jam/1234298350

Digital Object Identifier
doi:10.1155/2008/835380

Mathematical Reviews number (MathSciNet)
MR2448777

Zentralblatt MATH identifier
1158.76013

#### Citation

Shateyi, Stanford; Sibanda, Precious; Motsa, Sandile S. On the Asymptotic Approach to Thermosolutal Convection in Heated Slow Reactive Boundary Layer Flows. J. Appl. Math. 2008 (2008), Article ID 835380, 15 pages. doi:10.1155/2008/835380. https://projecteuclid.org/euclid.jam/1234298350

#### References

• S. Ostrach, Natural convection with combined buoyancy forces,'' Physico Chemical Hydrodynamics, vol. 1, pp. 233--247, 1980.
• J. S. Turner, Double-diffusive phenomena,'' Annual Review of Fluid Mechanics, vol. 6, pp. 37--54, 1974.
• B. Gerbhart and L. Pera, The nature of vertical natural convection flows resulting from the combined buoyancy effects of thermal and mass diffusion,'' International Journal of Heat and Mass Transfer, vol. 14, no. 12, pp. 2025--2050, 1971.
• E. W. Mureithi, J. P. Denier, and J. A. K. Stott, The effect of buoyancy on upper-branch Tollmien-Schlichting waves,'' IMA Journal of Applied Mathematics, vol. 58, no. 1, pp. 19--50, 1997.
• F. T. Smith and R. J. Bodonyi, Nonlinear critical layers and their development in streaming-flow stability,'' Journal of Fluid Mechanics, vol. 118, pp. 165--185, 1982.
• S. Shateyi, P. Sibanda, and S. S. Motsa, An asymptotic analysis of convection in boundary layer flows in the presence of a chemical reaction,'' Archives of Mechanics, vol. 57, no. 1, pp. 25--41, 2005.
• S. S. Motsa, J. S. B. Gajjar, and P. Sibanda, The effect of heating/cooling on the upper-branch stability of boundary layer flows over a compliant boundary,'' Computer Assisted Mechanics and Engineering Sciences, vol. 9, no. 2, pp. 163--181, 2002.
• M. Pons and P. Le Quéré, Modeling natural convection with the work of pressure-forces: a thermodynamic necessity,'' International Journal of Numerical Methods for Heat & Fluid Flow, vol. 17, no. 3, pp. 322--332, 2007.
• Y. Azizi, B. Benhamou, N. Galanis, and M. El-Ganaoui, Buoyancy effects on upward and downward laminar mixed convection heat and mass transfer in a vertical channel,'' International Journal of Numerical Methods for Heat & Fluid Flow, vol. 17, no. 3, pp. 333--353, 2007.
• P. W. Carpenter and J. S. B. Gajjar, A general theory for two- and three-dimensional wall-mode instabilities in boundary layers over isotropic and anisotropic compliant walls,'' Theoretical and Computational Fluid Dynamics, vol. 1, no. 6, pp. 349--378, 1990.
• J. S. B. Gajjar and F. T. Smith, On the global instability of free disturbances with a time-dependent nonlinear viscous critical layer,'' Journal of Fluid Mechanics, vol. 157, pp. 53--77, 1985.