On the asymptotic approach to thermosolutal convection in heated slow reactive boundary layer flows. (English) Zbl 1158.76013

Shateyi, Stanford; Sibanda, Precious; Motsa, Sandile S.

J. Appl. Math. 2008, Article ID 835380, 15 p. (2008).

Summary: Using a self-consistent asymptotic method, we 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. 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 Damköhler numbers, increasing buoyancy has a destabilizing effect on the upper branch Tollmien-Schlichting (TS) instability waves. Similarly, increasing the Damköhler 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.

MSC:

76E06	Convection in hydrodynamic stability
76V05	Reaction effects in flows
76M45	Asymptotic methods, singular perturbations applied to problems in fluid mechanics
80A20	Heat and mass transfer, heat flow (MSC2010)

Keywords:

density stratification; buoyancy force; multideck structure

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