Explicit solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity

María F. Natale; Domingo A. Tarzia

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 1, page 79-99
  • ISSN: 0392-4033

Abstract

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We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity with a constant temperature or a heat flux condition of the type - q 0 / t ( q 0 > 0 ) at the fixed face x = 0 . We obtain in both cases sufficient conditions for data in order to have a parametric representation of the solution of the similarity type for t t 0 > 0 with t 0 an arbitrary positive time. These explicit solutions are obtained through the unique solution of an integral equation with the time as a parameter.

How to cite

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Natale, María F., and Tarzia, Domingo A.. "Explicit solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity." Bollettino dell'Unione Matematica Italiana 9-B.1 (2006): 79-99. <http://eudml.org/doc/289613>.

@article{Natale2006,
abstract = {We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity with a constant temperature or a heat flux condition of the type $-q_0/\sqrt\{t\}$ ($q_0 > 0$) at the fixed face $x=0$. We obtain in both cases sufficient conditions for data in order to have a parametric representation of the solution of the similarity type for $t\geq t_0>0$ with $t_0$ an arbitrary positive time. These explicit solutions are obtained through the unique solution of an integral equation with the time as a parameter.},
author = {Natale, María F., Tarzia, Domingo A.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {79-99},
publisher = {Unione Matematica Italiana},
title = {Explicit solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity},
url = {http://eudml.org/doc/289613},
volume = {9-B},
year = {2006},
}

TY - JOUR
AU - Natale, María F.
AU - Tarzia, Domingo A.
TI - Explicit solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity
JO - Bollettino dell'Unione Matematica Italiana
DA - 2006/2//
PB - Unione Matematica Italiana
VL - 9-B
IS - 1
SP - 79
EP - 99
AB - We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity with a constant temperature or a heat flux condition of the type $-q_0/\sqrt{t}$ ($q_0 > 0$) at the fixed face $x=0$. We obtain in both cases sufficient conditions for data in order to have a parametric representation of the solution of the similarity type for $t\geq t_0>0$ with $t_0$ an arbitrary positive time. These explicit solutions are obtained through the unique solution of an integral equation with the time as a parameter.
LA - eng
UR - http://eudml.org/doc/289613
ER -

References

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