Abstract
In papers [1, 2, 3] phenomenological wave equations of heat conduction, thermoelasticity and thermoelectro-magneto-elasticity have been derived. A characteristic property of these equations is their hyperbolic character which means, that disturbations of any field, including the thermal propagate with finite velocity. These equations were obtained on the basis of the generalized Onsager relations by introducing some terms depending on the rate of variability of the stream, which permits the use of these equations not only for stationary dynamical processes but also for the processes of marked nonstationary character. This generalization and its consequences and thermodynamical modifications leads among other things to the elimination of the paradoxical parabolism of the heat equation and the fields coupled with the thermal field.
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References
Kaliski, S: Wave Equation of Heat Conduction. Bull. Acad. Polon. Sci. Ser. Sci. Techn. 4, 13 (1965).
Kaliski, S: Wave Equations of Thermoelasticity. Bull. Adac. Polon. Sci. Ser. Sci. Techn. 5, 13 (1965).
Kaliski, S: Wave Equations of Thermo-electro-magneto-elasticity. Proc. Vibr. Probi. 3, 6 (1965).
Eckart, C.: The Thermodynamics of Irreversible Processes. Phys. Rev. 58 (1940).
Meixner, J., and H. G. Reik: Thermodynamik der irreversiblen Prozesse. Handbuch der Physik, Vol. 1I/3. Berlin-Göttingen-Heidelberg: Springer. 1959.
Hughes, W. F.: Relativistic Magneto-hydrodynamics and Irreversible Thermodynamics. Proc. Cambr. Phil. Soc. 4, 57 (1961).
Cattaneo, C.: Sulla conduzione del calore. Atti de Seminario Math. u Fisico della Univ. di Modena 3 (1948).
Vernotte, P.: Les paradoxes de la théorie continue de l’équation de la chaleur. Comptes Rendus 246, 3154 (1958).
La véritable équation de la chaleur. Comptes Rendus 247, 2103 (1958).
Goldstein, S.: On the Diffusion by Discontinuous Movements and the Telegraph Equation. Q. J. Mech. Appl. Math. 2, 4 (1954).
Sasaki, M.: On the Relativistic Gases. Reprint from the Max-Planck-Festschrift. Berlin: 1958.
Freudenthal, A. M.: One Dimensional Response and Coefficients of Thermal Expansion in Timesensitive Materials. Acta. Techn. Acad. Sci. Hungaricae 3 /4, 41 (1962).
Kaliski, S., and J. Petvkiewioz: Dynamical Equations of Motion Coupled with the Field of Temperatures and Resolving Functions for Elastic and Inelastic Anisotropie Bodies in the Magnetic Field. Proc. Vibr. Probl. 1, 3 (1960).
Groot, S. R., and P. Mazur: Non-Equilibrum Thermodynamics. Amsterdam: North-Holland Publ. Co. 1962.
Mindlin, R.: On the Equations of Motion of Piezoelectric Crystals. In: Problems of Continuum Mechanics. Philadelphia, Penn.: Soc. Ind. Appl. Math. 1961.
Kaliski, S.: Čerenkov Generation of Ultra and Hypersounds. I — Cubic Crystals. II — Piezo-quartz. Proc. Vibr. Probi. 3, 7 (1966).
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Kaliski, S. (1968). Cerenkov Generation of Thermal Waves for the Wave Equations of Thermo—Electro—Magneto—Elasticity. In: Parkus, H., Sedov, L.I. (eds) Irreversible Aspects of Continuum Mechanics and Transfer of Physical Characteristics in Moving Fluids. IUTAM Symposia. Springer, Vienna. https://doi.org/10.1007/978-3-7091-5581-3_10
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DOI: https://doi.org/10.1007/978-3-7091-5581-3_10
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