GAS FLOWS WITH HEAT TRANSFER IN MICRO CHANNELS: CLARIFICATIONS ABOUT THE NUSSELT NUMBER

Abstract : This paper deals with the modelling of weakly rarefied and dilute gas flows in heated micro channels by the continuum approach, valid for Knudsen numbers smaller than about 0.1. The first order slip and thermal jump model usually used for the forced convection of gas flows in long micro channels between two infinite plates is discussed. Indeed, in the huge literature related to this subject, it appears that simplified models are often used without justifying them and recurrent errors propagate from one paper to the other. The erroneous models particularly concern the heat transfer analysis and the energy equation. The compatibility of the pressure work and viscous dissipation in the energy equation with the power of the viscous forces at the walls and the choice of an appropriate Nusselt number are particularly discussed. Our aim is to provide a consistent model for gaseous micro-flows and the linked heat transfer. Then, a dimensional and asymptotic analysis is performed in the context of long micro channels. An analytical solution for the temperature field and the Nusselt number is proposed in the case of a compressible gas flow in a long micro-channel maintained at a constant wall temperature. This solution is compared with the numerical solution of the full model taking into account the first order slip and thermal jump conditions at the walls, the power of the viscous forces in the wall heat flux, the thermal creep term, the pressure work and the viscous dissipation in the bulk. The vanishing values of the Nusselt number measured in the experiments by Demsis et al. (2009, 2010) are explained for the first time.
Type de document :
Communication dans un congrès
CHT17 - ICHMT International Symposium on Advances in Computational Heat Transfer, May 2017, Napoli, Italy. Proceedings of CHT-17, 2017
Liste complète des métadonnées

Littérature citée [18 références]  Voir  Masquer  Télécharger

https://hal-upec-upem.archives-ouvertes.fr/hal-01544307
Contributeur : Xavier Nicolas <>
Soumis le : mercredi 21 juin 2017 - 15:40:20
Dernière modification le : jeudi 11 janvier 2018 - 06:22:28
Document(s) archivé(s) le : samedi 16 décembre 2017 - 02:44:39

Fichier

paper_CHT-17_Nicolas_et_al_fin...
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01544307, version 1

Collections

Citation

Xavier Nicolas, Eric Chénier, Chahinez Tchekiken, Guy Lauriat. GAS FLOWS WITH HEAT TRANSFER IN MICRO CHANNELS: CLARIFICATIONS ABOUT THE NUSSELT NUMBER. CHT17 - ICHMT International Symposium on Advances in Computational Heat Transfer, May 2017, Napoli, Italy. Proceedings of CHT-17, 2017. 〈hal-01544307〉

Partager

Métriques

Consultations de la notice

125

Téléchargements de fichiers

194