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Bénard convection and the Cattaneo law of heat conduction

Published online by Cambridge University Press:  14 November 2011

B. Straughan  and
F. Franchi
B. Straughan
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
F. Franchi
Affiliation:
Istituto Matematico, Universita di Bologna, 40127 Bologna, Italy
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Synopsis

Critical Rayleigh numbers are obtained for the onset of convection when the Maxwell–Cattaneo heat flux law is employed. It is found that convection is possible in both heated above and below cases.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 1-2 , 1984 , pp. 175 - 178
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Lindsay, K. A. and Straughan, B.. Acceleration waves and second sound in a perfect fluid. Arch. Rational Mech. Anal. 68 (1978), 53–87.CrossRefGoogle Scholar
2Cattaneo, C.. Sulla conduzione del calore. Atti. Sem. Mat. Fis. Univ. Modena 3 (1948), 83–101.Google Scholar
3Maxwell, J. C.. On the dynamical theory of gases. Philos. Trans. Roy. Soc. London Ser. A 157 (1867), 49–88.Google Scholar
4Gurtin, M. E. and Pipkin, A. C.. A general theory of heat conduction with finite wavespeeds. Arch. Rational Mech. Anal. 31 (1968), 113–126.CrossRefGoogle Scholar
5Fox, N.. Low temperature effects and generalized thermoelasticity. J. Inst. Math. Applic. 5 (1969), 373–386.CrossRefGoogle Scholar
6Chandrasekhar, S.. Hydrodynamic and hydromagnetic stability (Oxford Univ. Press, 1961).Google Scholar
7Galdi, G. P. and Straughan, B.. Exchange of stabilities, symmetry and nonlinear stability. Arch. Rational Mech. Anal. In press.Google Scholar
8Wollkind, D. J. and Frisch, H. L.. Chemical instabilities: I. A heated horizontal layer of dissociating fluid. Phys. Fluids 14 (1971), 13–18.CrossRefGoogle Scholar
9Straughan, B., Bampi, F. and Morro, A.. Chemical convective instabilities and quasi-equilibrium thermodynamics. Submitted for publication.Google Scholar
10Green, A. E.. A note on “axioms of continuum mechanics”. Bull. Inst. Math. Applic. 18 (1982), 7–9.Google Scholar