Abstract
Alternative analytical solutions of the diffusion (or thermal conductivity) equation are presented, which ensure rapid convergence even for small values of Dt/l 2 (αt/l 2), where D is the diffusion coefficient, α is the thermal diffusivity, t is the time, and l is the characteristic size. The solutions possess a general character and are valid for an arbitrary initial distribution of the concentration (temperature).
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References
J. Crank, The Mathematics of Diffusion (Clarendon, Oxford, 1956).
H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids (Clarendon Press, Oxford, 1956; Nauka, Moscow, 1964).
R. Sh. Malkovich, The Mathematics of Diffusion in Semiconductors (Nauka, St. Petersburg, 1999).
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Translated from Pis’ma v Zhurnal Tekhnichesko\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} \) Fiziki, Vol. 28, No. 21, 2002, pp. 91–94.
Original Russian Text Copyright © 2002 by Malkovich.
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Malkovich, R.S. Alternative analytical solutions of the diffusion (thermal conductivity) equation for an arbitrary initial concentration (temperature) distribution. Tech. Phys. Lett. 28, 923–924 (2002). https://doi.org/10.1134/1.1526884
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DOI: https://doi.org/10.1134/1.1526884