Summary
The onset of instability, due to the combined effects of thermal and mass concentration gradients, is investigated in the hydrodynamic stability regime. It is found that the critical Rayleigh number, which determines the onset of instability, increases as the chemical reaction rate constant increases hyperbolically over a wide range of values at both moderate and high permeabilities. In addition, the instability grows with increase in porosity. Previous results show that the critical Rayleigh number rises linearly when only the mass concentration gradient is considered.
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References
Rayleigh J. W. S.,Philos. Mag.,32 (1916) 529.
Ukhovskii M. E. andIudovich V. I.,J. Appl. Math. Mech. PMM,27 (1963) 432.
Eckhaus W.,Studies in Non-Linear Stability Theory (Springer-Verlag, New York, N.Y.) 1965.
Chandrasekhar S.,Hydrodynamic and Hydromagnetic Stability (University Press, Oxford) 1961.
Matkowsky B. J.,Bull. Am. Math. Soc.,76 (1970) 620;SIAM J. Appl. Math.,18 (1972).
Sattinger D. H.,Topics in Stability and Bifurcation Theory (Springer-Verlag, New York, N.Y.) 1973.
Bestman A. R., ICTP Internal Report No. IC/87/102.
Brinkman H. C.,Appl. Sci. Res. A,1 (1947) 27; 81.
Joseph D. D.,Stability of Fluid Motion II (Springer-Verlag, New York, N.Y.) 1976.
Roberts P. H.,J. Math. Appl.,1 (1960) 195.
Bdzil J. andFrisch H. L.,Phys. Fluids,14 (1971) 475; 208; 2048.
Wolkind D. J. andFrisch H. L.,Phys. Fluids,14 (1971) 13; 482.
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Opara, F.E., Tay, G. Effect of the combined thermal and mass concentration gradients on the stability of a chemically reacting fluid in a porous medium. Il Nuovo Cimento D 18, 1031–1040 (1996). https://doi.org/10.1007/BF02457670
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DOI: https://doi.org/10.1007/BF02457670