[Solution analytique pour la conduction en régime permanent 3D dans un solide soumis à une source de chaleur rectangulaire mobile et à un refroidissement surfacique]
L'échauffement des solides sous l'action du frottement ou du soudage par exemple joue un rôle important dans le comportement thermomécanique des matériaux. Nous proposons dans cet article un modèle analytique pour le calcul de la répartition tridimensionnelle de la température dans un solide soumis à une source de chaleur rectangulaire mobile et à un refroidissement surfacique. On utilise une transformée intégrale fréquentielle et une transformée intégrale de Fourier cosinus finie pour résoudre l'équation d'advection–diffusion associée à ce problème. La solution obtenue est explicite et n'impose aucune restriction en termes de vitesse, de dimensions et de coefficient d'échange. Elle se présente sous la forme de séries qui convergent rapidement.
Heating of solids, e.g. by friction or welding, plays an important role in the thermomechanical behaviour of materials. An analytical model to compute the three-dimensional temperature distribution in a solid, subjected to a moving rectangular heat source with surface cooling is proposed in this article. A frequential integral transform and a finite cosine Fourier integral transform are used to solve the advection–diffusion equation related to this problem. The obtained solution is explicit and does not impose any restriction on the speed, the dimensions and the heat convection coefficient. It is presented in series form which converges rapidly.
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Mot clés : Transferts thermiques, Sources de chaleur mobiles, Problème d'advection–diffusion, Solution analytique
@article{CRMECA_2009__337_2_107_0,
author = {Talaat Osman and Abderrahmane Boucheffa},
title = {Analytical solution for the {3D} steady state conduction in a solid subjected to a moving rectangular heat source and surface cooling},
journal = {Comptes Rendus. M\'ecanique},
pages = {107--111},
publisher = {Elsevier},
volume = {337},
number = {2},
year = {2009},
doi = {10.1016/j.crme.2009.02.003},
language = {en},
}
TY - JOUR AU - Talaat Osman AU - Abderrahmane Boucheffa TI - Analytical solution for the 3D steady state conduction in a solid subjected to a moving rectangular heat source and surface cooling JO - Comptes Rendus. Mécanique PY - 2009 SP - 107 EP - 111 VL - 337 IS - 2 PB - Elsevier DO - 10.1016/j.crme.2009.02.003 LA - en ID - CRMECA_2009__337_2_107_0 ER -
%0 Journal Article %A Talaat Osman %A Abderrahmane Boucheffa %T Analytical solution for the 3D steady state conduction in a solid subjected to a moving rectangular heat source and surface cooling %J Comptes Rendus. Mécanique %D 2009 %P 107-111 %V 337 %N 2 %I Elsevier %R 10.1016/j.crme.2009.02.003 %G en %F CRMECA_2009__337_2_107_0
Talaat Osman; Abderrahmane Boucheffa. Analytical solution for the 3D steady state conduction in a solid subjected to a moving rectangular heat source and surface cooling. Comptes Rendus. Mécanique, Volume 337 (2009) no. 2, pp. 107-111. doi : 10.1016/j.crme.2009.02.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.02.003/
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