Abstract
We study the evolution of a thermal perturbation in a nonlinear medium whose thermal conductivity depends on the temperature and the temperature gradient according to a power law.
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Abbreviations
- u:
-
temperature
- k:
-
coefficient of thermal conductivity
- t:
-
time
- x:
-
spatial variable
- x+ :
-
a point on the thermal wave front
- a 2 :
-
generalized coefficient of thermal diffusivity
- σ, α, ν, and s:
-
parameters of the process
- δ(xs):
-
Dirac delta-function
- B[ξ, η]:
-
a beta function
- v(τ, x), τ(t):
-
auxiliary functions
- A, C, To, Tm, T*, R, r, p, and τm :
-
constants and parameters
Literature cited
Ya. B. Zel'dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Academic Press (1966).
B. M. Berkovsky and V. G. Bashtovoi, “The finite velocity of heat propagation from the viewpoint of the kinetic theory,” Int. J. Heat Mass Transfer,20, No. 6, 621–626 (1977).
G. I. Barenblatt, “Self-similar motions of a compressible liquid in a porous medium,” Prikl. Mat. Mekh.,16, No. 6, 679–698 (1952).
M. S. Chu, “Thermonuclear reaction waves at high densities,” Phys. Fluids,15, No. 3, 413–422 (1972).
L. K. Martinson and K. B. Pavlov, “Spatial localization of thermal perturbations in the theory of nonlinear heat conduction,” Zh. Vychisl. Mat. Mat. Fiz.,12, No. 4, 1048–1053 (1972).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 728–731, October, 1980.
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Granik, I.S., Martinson, L.K. Motion of a thermal wave front in a nonlinear medium with absorption. Journal of Engineering Physics 39, 1143–1145 (1980). https://doi.org/10.1007/BF00822153
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DOI: https://doi.org/10.1007/BF00822153