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Approximations to the temperature in a heated thermoelastic fluid

Part of: Thermodynamics and heat transfer

Published online by Cambridge University Press:  26 February 2010

W. A. Day
W. A. Day
Affiliation:
Hertford College, Oxford.
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Extract

It has been shown in [1, 2] that it is sometimes possible to justify the uncoupled and quasi-static approximations which are commonly invoked to simplify the solution of initial and boundary value problems in the linear theory of thermoelasticity. The justification involves showing, among other things, that the temperature predicted by the coupled dynamic theory is approximated by a solution of the classical heat equation.

MSC classification

Secondary: 80A20: Heat and mass transfer, heat flow
Type
Research Article
Information
Mathematika , Volume 31 , Issue 1 , June 1984 , pp. 47 - 64
Copyright
Copyright © University College London 1984

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References

1.Day, W. A.. Justification of the uncoupled and quasi-static approximations in a problem of dynamic thermoelasticity. Arch. Rational Mech. Anal., 77 (1981), 387.CrossRefGoogle Scholar
2.Day, W. A.. Further justification of the uncoupled and quasi-static approximations in thermoelasticity. Arch. Rational Mech. Anal., 79 (1982), 85.CrossRefGoogle Scholar
3.Day, W. A.. A comment on approximations to the temperature in dynamic linear thermoelasticity. Arch. Rational Mech. Anal. To appear.Google Scholar
4.Carlson, D. E.. Linear Thermoelasticity. Vol. VIa/2 of the Handbuch dcr Phvsik (Springer-Verlag, Berlin, 1972).Google Scholar
5.Sigillito, V. G.. Explicit a priori inequalities with applications to boundary value problems. Research Notes in Mathematics No. 13 (Pitman, London, 1977).Google Scholar
6.Bramble, J. H. and Payne, L. E.. Bounds in the Neumann problem for second order uniformly elliptic operators. Pacific J. Math., 12 (1962), 823.CrossRefGoogle Scholar