Hyperbolic heat conduction in two semi-infinite bodies in contact

J. A. López Molina; Macarena Trujillo Guillén

Applications of Mathematics (2005)

  • Volume: 50, Issue: 1, page 27-42
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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López Molina, J. A., and Guillén, Macarena Trujillo. "Hyperbolic heat conduction in two semi-infinite bodies in contact." Applications of Mathematics 50.1 (2005): 27-42. <http://eudml.org/doc/33203>.

@article{LópezMolina2005,
abstract = {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.},
author = {López Molina, J. A., Guillén, Macarena Trujillo},
journal = {Applications of Mathematics},
keywords = {hyperbolic heat conduction; relaxation time; hyperbolic heat conduction; relaxation time},
language = {eng},
number = {1},
pages = {27-42},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Hyperbolic heat conduction in two semi-infinite bodies in contact},
url = {http://eudml.org/doc/33203},
volume = {50},
year = {2005},
}

TY - JOUR
AU - López Molina, J. A.
AU - Guillén, Macarena Trujillo
TI - Hyperbolic heat conduction in two semi-infinite bodies in contact
JO - Applications of Mathematics
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 1
SP - 27
EP - 42
AB - 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.
LA - eng
KW - hyperbolic heat conduction; relaxation time; hyperbolic heat conduction; relaxation time
UR - http://eudml.org/doc/33203
ER -

References

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  1. 10.1115/1.3580239, Journal of Heat Transfer, Ser. C 91 (1969), 543–548. (1969) DOI10.1115/1.3580239
  2. Conduction of Heat in Solids. Oxford Science Publications, Clarendon Press, Oxford, 1990. (1990) MR0959730
  3. 10.1115/1.3143705, Appl. Mech. Rev. 39 (1986), 355–376. (1986) DOI10.1115/1.3143705
  4. 10.1115/1.3450441, Journal of Heat Transfer, Ser. C 97 (1975), 615–617. (1975) DOI10.1115/1.3450441
  5. Méthodes de la théorie des fonctions d’une variable complexe, Mir, Moscow, 1977. (1977) 
  6. 10.1115/1.2910903, Journal of Heat Transfer 116 (1994), 526–535. (1994) DOI10.1115/1.2910903
  7. 10.1115/1.3450651, Journal of Heat Transfer 99 (1977), 35–40. (1977) DOI10.1115/1.3450651
  8. 10.1115/1.2910860, Journal of Heat Transfer 116 (1994), 224–228. (1994) DOI10.1115/1.2910860

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