What is the optimal shape of a fin for one dimensional heat conduction?

Abstract : This article is concerned with the shape of small devices used to control the heat flowing between a solid and a fluid phase, usually called \textsl{fin}. The temperature along a fin in stationary regime is modeled by a one-dimensional Sturm-Liouville equation whose coefficients strongly depend on its geometrical features. We are interested in the following issue: is there any optimal shape maximizing the heat flux at the inlet of the fin? Two relevant constraints are examined, by imposing either its volume or its surface, and analytical nonexistence results are proved for both problems. Furthermore, using specific perturbations, we explicitly compute the optimal values and construct maximizing sequences. We show in particular that the optimal heat flux at the inlet is infinite in the first case and finite in the second one. Finally, we provide several extensions of these results for more general models of heat conduction, as well as several numerical illustrations.
Type de document :
Article dans une revue
SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2014, 74 (4), pp.1194--1218. 〈10.1137/130941377〉
Liste complète des métadonnées

Littérature citée [23 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00871135
Contributeur : Yannick Privat <>
Soumis le : mercredi 30 avril 2014 - 15:01:01
Dernière modification le : mercredi 12 octobre 2016 - 01:21:02
Document(s) archivé(s) le : mercredi 30 juillet 2014 - 10:45:40

Fichiers

ailetteNMP_HAL.pdf
Fichiers produits par l'(les) auteur(s)

Licence


Distributed under a Creative Commons Paternité 4.0 International License

Identifiants

Collections

Citation

Gilles Marck, Grégoire Nadin, Yannick Privat. What is the optimal shape of a fin for one dimensional heat conduction?. SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2014, 74 (4), pp.1194--1218. 〈10.1137/130941377〉. 〈hal-00871135v2〉

Partager

Métriques

Consultations de
la notice

611

Téléchargements du document

249