| 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 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
27-42 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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 |
| . |
| Date available:
|
2009-09-22T18:20:19Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134588 |
| . |
| 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 |
| . |
