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Chemical convective instability and quasi-equilibrium thermodynamics. (English) Zbl 0567.76048

A nonlinear stability analysis is described for the Bénard problem for a chemically reacting fluid heated from above; the findings ar compared with those of D. J. Wollkind and H. L. Frisch [Phys. Fluids 14, 13-18 (1971)]. Next an energy stability analysis is given for the model of Wollkind and Frisch and it is shown that instabilities may occur.

MSC:

76E15 Absolute and convective instability and stability in hydrodynamic stability
80A32 Chemically reacting flows
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[1] Wollkind D.J., Frisch H.L.,Chemical instabilities: I. A heated horizontal layer of dissociating fluid, Phys. Fluids, vol. 14, 1971, pp. 13–18. · doi:10.1063/1.1693263
[2] Morro A., Straughan B.,Highly unstable solutions to completely nonlinear diffusion problems, J. Nonlinear Analysis, vol. 7, 1983, pp. 231–237. · Zbl 0516.35042 · doi:10.1016/0362-546X(83)90085-8
[3] Joseph D.D.,Stability of Fluid Motions, vol.II, Springer, Berlin, 1976. · Zbl 0345.76023
[4] Wollkind D.J., Bdzil J.,Comments on chemical instabilities, Phys. Fluids, vol. 14, 1971, pp. 1813–1814. · doi:10.1063/1.1693685
[5] Lighthill M.J.,Dynamics of a dissociating gas. Part 2. Quasiequilibrium transfer theory, J. Fluid Mech., vol. 8, 1960, pp. 161–182. · Zbl 0126.42001 · doi:10.1017/S0022112060000529
[6] Truesdell C., Toupin R.,The Classical Field Theories, inHandbuch der Physik, vol. III/1, Springer, Berlin, 1960.
[7] Galdi G.P.,Straughan B.,Exchange of stabilities, symmetry and nonlinear stability, Arch. Rational Mech. Anal., to be published. · Zbl 0622.76061
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