Comptes Rendus
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.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2009.02.003
Keywords: Heat transfer, Moving heat sources, Advection–diffusion problem, Analytical solution
Mot clés : Transferts thermiques, Sources de chaleur mobiles, Problème d'advection–diffusion, Solution analytique

Talaat Osman 1; Abderrahmane Boucheffa 1

1 Université Paris 11, IUT d'Orsay, Département mesures physiques, plateau du Moulon, 91400 Orsay, France
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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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