Geodesic
Hyperbolic heat conduction in two semi-infinite bodies in contact
Applications of Mathematics, Tome 50 (2005) no. 1, pp. 27-42.

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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.
DOI : 10.1007/s10492-005-0002-6
Classification : 35L20, 80A20
Keywords: hyperbolic heat conduction; relaxation time 
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López Molina, Juan Antonio; Guillén, Macarena Trujillo. Hyperbolic heat conduction in two semi-infinite bodies in contact. Applications of Mathematics, Tome 50 (2005) no. 1, pp. 27-42. doi : 10.1007/s10492-005-0002-6. http://geodesic.mathdoc.fr/articles/10.1007/s10492-005-0002-6/

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