[en] We propose a variational principle applicable to the heat-transport equations derived some years ago by Guyer and Krumhansl [Phys. Rev. 133, 1411 (1964); 148, 766 (1966); 148, 778 (1966)] to describe heat-wave propagation in dielectric crystals at low temperature. The variational principle appears as a generalization of Prigogine's minimum-entropy production criterion. The analysis is based on extended irreversible thermodynamics, which is used to derive the Guyer-Krumhansl equations from macroscopic arguments.
Disciplines :
Physics
Author, co-author :
Lebon, Georgy ; Université de Liège - ULiège > Services généraux (Faculté des sciences) > Relations académiques et scientifiques (Sciences)
Dauby, Pierre ; Université de Liège - ULiège > Département d'astrophys., géophysique et océanographie (AGO) > Thermodynamique des phénomènes irréversibles
Language :
English
Title :
Heat transport in dielectric crystals at low temperature: A variational formulation based on extended irreversible thermodynamics
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Guyer R., Krumhansl J. Phys. Rev. 1964, 133:1411.
Guyer R., Krumhansl J. Phys. Rev. 1966, 148:766.
Guyer R., Krumhansl J. Phys. Rev. 1966, 148:778.
Tisza L. C. R. Acad. Sci. Paris 1938, 207:1035.
Landau L. J. Phys. (Moscow) 1941, 5:71.
Peshkov V. J. Phys. (Moscow) 1944, 8:381.
Ward J., Wilks J. Philos. Mag. 1951, 42:314.
Ward J., Wilks J. Philos. Mag. 1952, 43:48.
Tsai D., MacDonald R. Phys. Rev. B 1976, 14:4714.
Joseph D., Preziosi L. Rev. Mod. Phys. 1989, 61:41.
Joseph D., Preziosi L. Rev. Mod. Phys. 1990, 62:375.
Cattaneo C. Atti Semin. Mat. Fis. Univ. Modena 1948, 3:3.
Chester M. Phys. Rev. 1963, 131:2013.
Lebon G. Bull. Acad. Sci. Belg. 1978, 64:456.
Lebon G., Jou D., Casas-Vasquez J. J. Phys. A 1980, 13:275.
Lebon G., Jou D. J. Chem. Phys. 1982, 77:970.
Lebon G., Perez-Garcia C., Casas-Vasquez J. J. Chem. Phys. 1988, 88:5068.
Jou D., Llebot J., Casas-Vasquez J. Phys. Rev. A 1982, 25:3277.
Jou D., Casas-Vasquez J., Lebon G. Rep. Prog. Phys. 1988, 51:1104.
.
Prigogine I. Introduction to Thermodynamics of Irreversible Processes, Wiley Interscience, New York; 1961.
De Groot S., Mazur P. Nonequilibrium Thermodynamics, North-Holland, Amsterdam; 1962.
Glansdorff P., Prigogine I. Structure, Stability and Fluctuations, Wiley, New York; 1971.
Truesdell C. Rational Thermodynamics, McGraw-Hill, New York; 1969.
Mikhlin R. Variational Methods in Mathematical Physics, MacMillan, New York; 1964.
Lebon G. Variational Principles in Thermomechanics, in Vol. 262 of Centre International des Sciences Mecaniques Courses and Lectures , Springer, Berlin; 1980, 262:221-415.
Sewell M. Maximum and Minimum Principles, Cambridge University Press, Cambridge; 1989.
Biot M. Variational Principles in Heat Transfer, Oxford University Press, Oxford; 1970.
Gyarmati I. Nonequilibrium Thermodynamics, Springer, Berlin; 1971.
Rosen P. Phys. Fluids 1958, 1:251.
Lebon G., Lambermont J. (1973) Generalization of Hamilton's principle to continuous dissipative systems. The Journal of Chemical Physics 59:2929.
Ziegler H. Progress in Solid Mechanics , North-Holland, Amsterdam; 1963, 4:93-193.
Finlayson B. The Method of Weighted Residuals and Variational Principles, Academic, New York; 1972.
Similar publications
Sorry the service is unavailable at the moment. Please try again later.
This website uses cookies to improve user experience. Read more
Save & Close
Accept all
Decline all
Show detailsHide details
Cookie declaration
About cookies
Strictly necessary
Performance
Strictly necessary cookies allow core website functionality such as user login and account management. The website cannot be used properly without strictly necessary cookies.
This cookie is used by Cookie-Script.com service to remember visitor cookie consent preferences. It is necessary for Cookie-Script.com cookie banner to work properly.
Performance cookies are used to see how visitors use the website, eg. analytics cookies. Those cookies cannot be used to directly identify a certain visitor.
Used to store the attribution information, the referrer initially used to visit the website
Cookies are small text files that are placed on your computer by websites that you visit. Websites use cookies to help users navigate efficiently and perform certain functions. Cookies that are required for the website to operate properly are allowed to be set without your permission. All other cookies need to be approved before they can be set in the browser.
You can change your consent to cookie usage at any time on our Privacy Policy page.
