Abstract
This chapter is devoted to the problem of heat conduction in rigid bodies. A representative collection of variational principles is examined. According to the nature of the problem to be handled, these criteria will be classical or not.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Biot, M., Variational principles in heat transfer, Oxford Univ. Press, Oxford, 1970.
Vujanovic, B., An approach to linear and non-linear heat transfer problems using a Lagrangian, Journal, 9, 131, 1971.
Glansdorff, P. and Prigogine, I., On a general evolution criterion in macroscopic physics, Physica, 30, 351, 1964.
Glansdorff, P. and Prigogine, I., Structure, Stability and fluctuations, J. Wiley, New-York, 1971.
Lebon, G. and Lambermont, J., Some variational principles pertaining to non-stationary heat conduction and coupled thermoelasticity, Acta Mech., 15, 121, 1972.
Lebon, G., A new variational principle for the non-linear unsteady heat conduction problem, Quart. J. Mech. Appl. Math., 29, 499, 1976.
Gurtin, M., Variational principles for linear initial value problems, Quart. Appl. Math, 22, 252, 1964.
Tonti, E., On the variational formulation for linear initial value problems, Annali di Math. pura ed appl., 95, 331, 1973.
Reddy, J., A note on mixed variational principles for initial-value problems, Quart. J. Mech. Appl. Math., 28, 123, 1975.
Maxwell, J., On the dynamical theory of gases, Phil. Trans. Roy. Soc. London, 157, 49, 1867.
Cattaneo, C., Sur une forme de l’équation de la chaleur éliminant le paradoxe d’une propagation instantanée, C.R.Acad. Sc. Paris, 247, 431, 1958.
Vernotte, P., Les paradoxes de la théorie continue de l’équation de la chaleur, C.R.Acad. Sc. Paris, 247, 3154, 1958.
Onsager, L., Reciprocal relations in irreversible processes, Phys. Rev., 37, 405, 1931.
Gyarmati, I., Non-equilibrium thermodynamics, Springer-Verlag, Berlin, 1971.
Rosen, P., Variational approach to magnetohydrodynamics, Phys. Fluids, 1, 251, 1958.
Djukic, D. and Vujanovic, B., On a new variational principle of Hamiltonian type for classical field theory, Z.A.M.M., 21, 611, 1971.
Djukic, D., Vujanovic, B., Tatic, N. and Strauss, A., On two variational methods for obtaining solutions to transport problems, Chem. Eng. J., 5, 145, 1973.
Djukic, D., Hiemenz magnetic flow of power-law fluids, J. Appl. Mech., September 1974, 822, 1974.
Prigogine, I., Etude thermodynamique des phénomènes irréversibles, Desoer, Liège, 1947.
Lebon, G. and Lambermont, J., A rather general variational principle for purely dissipative processes, Annalen Phys., 7, 15, 1972.
Lebon, G. and Lambermont, J., Generalization of Hamilton’s principle to continuous dissipative systems, J. Chem. Phys., 59, 2929, 1973.
Lebon, G., Distribution non-stationnaire de la température dans les milieux dont la conductibilité thermique dépend de la température, Ann. Soc. Sc. Bruxelles, 84, 304, 1970.
Lardner, T.J., Biot’s variational principle in heat conduction, J. A. I. A. A. 1, 1, 1963.
Richardson, P.D., Unsteady heat conduction with a non-linear boundary condition, J. Heat Transfer, 86, 298, 1964.
Finlayson, B.A. and Scriven, L., On the search for variational principles, Int. J. Heat Mass Transfer, 10, 799, 1967.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1980 Springer-Verlag Wien
About this chapter
Cite this chapter
Lebon, G., Perzyna, P. (1980). Variational Theory of Heat Conduction. In: Lebon, G., Perzyna, P. (eds) Recent Developments in Thermomechanics of Solids. International Centre for Mechanical Sciences, vol 262. Springer, Vienna. https://doi.org/10.1007/978-3-7091-3351-4_15
Download citation
DOI: https://doi.org/10.1007/978-3-7091-3351-4_15
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81597-7
Online ISBN: 978-3-7091-3351-4
eBook Packages: Springer Book Archive