Effects of strong convection on the cooling process for a long or thin pipe

Sanja Marušić; Eduard Marušić-Paloka; Igor Pažanin

doi:10.1016/j.crme.2008.03.003

Effects of strong convection on the cooling process for a long or thin pipe

Presented by: Évariste Sanchez-Palencia

Sanja Marušić ¹; Eduard Marušić-Paloka ² ; Igor Pažanin ²

¹ Faculty of Transport and Traffic Engineering, University of Zagreb, Vukelićeva 4, 10000 Zagreb, Croatia
² Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

Comptes Rendus. Mécanique, Volume 336 (2008) no. 6, pp. 493-499.

Abstract
Résumé

In this Note a heat flow through a thin pipe filled with fluid is studied. The pipe is cooled by the exterior medium. Depending on the ratio between the pipe's thickness ε and the Reynolds number ${Re}^{ε}$ , we obtain three different macroscopic models via rigorous asymptotic analysis. For small ${Re}^{ε}$ the fluid in the pipe is perfectly cooled, i.e. it assumes the temperature of the surrounding medium. For large ${Re}^{ε}$ , the fluid is not cooled at all, i.e. it maintains the same temperature as it had when it entered the pipe. Between those two cases there is a critical value of ${Re}^{ε}$ when the macroscopic model is described by an ODE keeping the effects of the surrounding medium as well as the entering temperature.

Dans cette Note, nous étudions la conduction thermique dans un tube mince rempli par un fluide. Le tube est refroidi par le milieu extérieur. Suivant le rapport entre l'épaisseur du tube ε et le nombre de Reynolds ${Re}^{ε}$ , on obtient, via une analyse asymptotique rigoureuse, trois modèles différents. Pour ${Re}^{ε}$ assez petit, le fluide est parfaitement refroidi, c'est-à-dire qu'il prend la température du milieu extérieur au tube. Pour ${Re}^{ε}$ grand, le fluide n'est pas du tout refroidi, c'est-à-dire qu'il reste à la température qu'il avait à l'entrée du tube. Entre ce deux cas existe un cas critique où le modèle macroscopique est donné par une EDO où cohabitent les effets du milieu extérieur au tube ainsi que ceux de la température à l'entrée de celui-ci.

Received: 2007-04-01
Accepted: 2008-03-11
Published online: 2008-04-28

DOI: 10.1016/j.crme.2008.03.003

Keywords: Heat transfer, Heat conduction, Asymptotic analysis, High convection
Mots-clés : Transferts thermiques, Conduction thermique, Analyse asymptotique, Convection forte

Author's affiliations:

Sanja Marušić ¹; Eduard Marušić-Paloka ²; Igor Pažanin ²

¹ Faculty of Transport and Traffic Engineering, University of Zagreb, Vukelićeva 4, 10000 Zagreb, Croatia
² Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

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     title = {Effects of strong convection on the cooling process for a long or thin pipe},
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Sanja Marušić; Eduard Marušić-Paloka; Igor Pažanin. Effects of strong convection on the cooling process for a long or thin pipe. Comptes Rendus. Mécanique, Volume 336 (2008) no. 6, pp. 493-499. doi : 10.1016/j.crme.2008.03.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2008.03.003/

References
Cited by

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[2] A. Sili Heat propagation in a thin rod, Rend. di Mathematica, Serie VII, Volume 13 (1993), pp. 149-166

[3] E. Marušić-Paloka, I. Pažanin, Non-isothermal fluid flow through a thin pipe with cooling, submitted for publication

[4] G.P. Panasenko Multi-Scale Modelling for Structures and Composites, Springer, 2004

[5] R.E. O'Malley Introduction to Singular Perturbations, Applied Mathematics and Mechanics, vol. 14, Academic Press, 1974

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