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An asymptotic analysis of convection in boundary-layer flows in the presence of a chemical reaction. (English) Zbl 1105.76027

Summary: We investigate the stability of two-dimensional disturbances imposed on a boundary-layer flow over a semi-infinite flat plate in the presence of reacting chemical species. Species concentration levels are assumed to be small, what is typical of many processes in water and in atmospheric air. We exploit the multi-deck structure of the flow in the limit of large Reynolds numbers to analyze asymptotically the perturbed flow. The neutral eigenrelations are obtained implicitly, and limiting cases for large buoyancy and reaction kinetics are investigated. The results show the effects of Damköhler number on the wave number and wave speed of the disturbed flows.

MSC:

76E06 Convection in hydrodynamic stability
76V05 Reaction effects in flows
76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics
76R10 Free convection
80A20 Heat and mass transfer, heat flow (MSC2010)
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