On the approximation of isochoric motions of fluids under different flow conditions

Rajagopal, K.R., Saccomandi, G. and Vergori, L. (2015) On the approximation of isochoric motions of fluids under different flow conditions. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 471(2180), 20150159. (doi: 10.1098/rspa.2015.0159)

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Abstract

There has been considerable interest, ever since the development of the approximation by Oberbeck and Boussinesq concerning fluids that are mechanically incompressible but thermally compressible, in giving a rigorous justification for the same. For such fluids, it would be natural to assume that the determinant of the deformation gradient (which is a measure of the volume change of the body) depends on the temperature. However, such an assumption has the attendant drawbacks of the specific heat of the fluid at constant volume being zero and the speed of sound in the fluid being complex. In this paper, we consider a generalization of the Oberbeck-Boussinesq approximation wherein the volume change depends both on the temperature and on the pressure that the fluid is subject to. We show that within the context of this generalization, the specific heat at constant volume can be definedmeaningfully, and it is not zero.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Vergori, Dr Luigi
Authors: Rajagopal, K.R., Saccomandi, G., and Vergori, L.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences
Publisher:The Royal Society
ISSN:1364-5021
ISSN (Online):1471-2946
Copyright Holders:Copyright © 2015 The Authors
First Published:First published in Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences 471:2180
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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