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Title: Hyperbolic heat conduction in two semi-infinite bodies in contact (English)
Author: López Molina, Juan Antonio
Author: Guillén, Macarena Trujillo
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940
Volume: 50
Issue: 1
Year: 2005
Pages: 27-42
Summary lang: English
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Category: math
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Summary: We find, under the viewpoint of the hyperbolic model of heat conduction, the exact analytical solution for the temperature distribution in all points of two semi-infinite homogeneous isotropic bodies that initially are at uniform temperatures $T_0^1$ and $T_0^2$, respectively, suddenly placed together at time $t=0$ and assuming that the contact between the bodies is perfect. We make graphics of the obtained temperature profiles of two bodies at different times and points. And finally, we compare the temperature solution obtained from hyperbolic model to the parabolic or classical solution, for the same problem of heat conduction. (English)
Keyword: hyperbolic heat conduction
Keyword: relaxation time
MSC: 35L20
MSC: 80A20
idZBL: Zbl 1099.80005
idMR: MR2117694
DOI: 10.1007/s10492-005-0002-6
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Date available: 2009-09-22T18:20:19Z
Last updated: 2015-05-17
Stable URL: http://hdl.handle.net/10338.dmlcz/134588
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Reference: [1] J. K.  Baumeister, T. D.  Hamill: Hyperbolic heat-conduction equation—a solution for the semi-infinite body problem.Journal of Heat Transfer, Ser. C 91 (1969), 543–548. 10.1115/1.3580239
Reference: [2] H. S. Carslaw, J. C.  Jaeger: Conduction of Heat in Solids. Oxford Science Publications.Clarendon Press, Oxford, 1990. MR 0959730
Reference: [3] D. S.  Chandrasekharaiah: Thermoelasticity with a second sound: A review.Appl. Mech. Rev. 39 (1986), 355–376. 10.1115/1.3143705
Reference: [4] M. S. Kazimi, C. A.  Erdman: On the interface temperature of two suddenly contacting materials.Journal of Heat Transfer, Ser. C 97 (1975), 615–617. 10.1115/1.3450441
Reference: [5] M. Lavrentiev, E. T.  Chabat: Méthodes de la théorie des fonctions d’une variable complexe.Mir, Moscow, 1977.
Reference: [6] M. N. Özisik, D. Y.  Tzou: On the wave theory in heat conduction.Journal of Heat Transfer 116 (1994), 526–535. 10.1115/1.2910903
Reference: [7] D. C.  Wiggert: Analysis of early-time transient heat conduction by method of characteristics.Journal of Heat Transfer 99 (1977), 35–40. 10.1115/1.3450651
Reference: [8] R. C.  Xin, W. Q. Tao: Analytical solution for transient heat conduction in two semi-infinite bodies in contact.Journal of Heat Transfer 116 (1994), 224–228. 10.1115/1.2910860
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