Transient temperature and elastic response of a space-based mirror in the radiation-conduction environment
Author:
Bejoy K. Choudhury
Journal:
Quart. Appl. Math. 64 (2006), 201-228
MSC (2000):
Primary 74B05, 74F05, 42B05
DOI:
https://doi.org/10.1090/S0033-569X-06-00970-7
Published electronically:
May 3, 2006
MathSciNet review:
2243860
Full-text PDF Free Access
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Abstract: The problem of the one-dimensional heat equation with radiation boundary conditions is studied. Steady state and transient solutions for a space-based mirror are obtained under a broad class of boundary specification. Associated elastic stress and displacement are investigated. Time-varying heat flux at the boundary is also considered. The method requires solving equations of the type $\tan \lambda =\left (Bi_1+Bi_2\right )\lambda /\!\left (\lambda ^2-Bi_1Bi_2\right )$ for the eigenvalues $\lambda$, for which complete asymptotic solutions are given. Selected transient response results for temperature and stresses are presented.
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Birkhoff G. Birkhoff and G-C. Rota, Ordinary Differential Equations, 4th ed, John Wiley, New York, 1989.
Boelter L. M. K. Boelter, V. H. Cherry, H. A. Johnson, R. C. Martinelli, Heat Transfer Notes, McGraw–Hill, New York, 1965.
Boley B. A. Boley and J. H. Weiner, Theory of Thermal Stresses, Mineola (Dover reprint), New York, 1997.
Carlson D. E. Carlson, Linear Thermoelasticity, in Handbuch der Physik, Bd. VIa/2, Springer-Verlag, Berlin, 1972.
Carslaw H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, 2nd ed, Clarendon Press, Oxford, 1973; Reprint of 2nd ed., 1988.
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Schneider P. J. Schneider, Temperature Response Charts, John Wiley, New York, 1963. [A total of 120 uniformly sized charts (mostly 10.5 cm $\times$ 21 cm) were specially prepared for this book.]
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Titchmarsh E. C. Titchmarsh, The Theory of Functions, 2nd ed, Clarendon Press, Oxford, 1985.
Tolstov G. P. Tolstov, Fourier Series (English translation by Richard. A. Silverman), Dover reprint, New York, 1962.
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Additional Information
Bejoy K. Choudhury
Affiliation:
Lockheed Martin Space Systems, Sunnyvale, California 94089
Email:
bejoy.choudhury@lmco.com
Keywords:
Heat conduction,
thermoelasticity,
Fourier series
Received by editor(s):
December 10, 2004
Published electronically:
May 3, 2006
Article copyright:
© Copyright 2006
Brown University
The copyright for this article reverts to public domain 28 years after publication.
