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Self-similar solutions of the non-linear diffusion equation and application to near-critical fluids

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  • Fröhlich, T.
  • Bouquet, S.
  • Bonetti, M.
  • Garrabos, Y.
  • Beysens, D.

Abstract

We use analytic self-similar solutions of both the linear and non-linear diffusion equation to determine the behavior of a heat conducting system experiencing a time-dependent energy production. Supposing a power law evolution of the system parameters, we calculate the corresponding exponents to describe the temporal behavior of the system. In the non-linear case, we are able to introduce a variation of both the coefficient of diffusion and the amplitude of the heat source. The analytic solutions are checked numerically. These results can be considered, for example, as the basis for further developments on the non-linear behavior of supercritical fluids in a microgravity environment, e.g. the “Piston Effect” (M. Bonetti et al., Phys. Rev. E 49 (1994) 4779) or the “Jet Instability” (D. Beysens et al., Near-critical Fluids in Space, in: Lectures on Thermodynamics and Statistical Mechanics, M. Costas et al., eds. (World Scientific, Singapore, 1994) p. 88).

Suggested Citation

  • Fröhlich, T. & Bouquet, S. & Bonetti, M. & Garrabos, Y. & Beysens, D., 1995. "Self-similar solutions of the non-linear diffusion equation and application to near-critical fluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 218(3), pages 419-436.
    • Handle: RePEc:eee:phsmap:v:218:y:1995:i:3:p:419-436
    DOI: 10.1016/0378-4371(95)00132-Q
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    1. Francke Artillerie-Hauptmann a. D., 1877. "Ueber den Einfluss des Alters der Eltern auf das Geschlecht der Neugeborenen; dargelegt aus der Bevölkerung Norwegens in den Jahren 1870 und 1871," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 29(1), pages 180-190, February.
    2. Siedt Veronika, 1984. "Die Perspektivplanung in der Kaliindustrie der DDR von 1955 bis 1970," Jahrbuch für Wirtschaftsgeschichte / Economic History Yearbook, De Gruyter, vol. 25(1), pages 7-36, January.
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