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

Rajagopal, K. R.
; 
Saccomandi, G.
; 
Vergori, L.
Identifiers
http://hdl.handle.net/10379/13579
 https://doi.org/10.13025/28703
Publication Date
2015-07-22
Keywords
pressure- and temperature-dependent viscosity, oberbeck-boussinesq approximation, perturbation theory, oberbeck-boussinesq approximation, pressure-dependent viscosity, compressible fluid, temperature, convection, turbulence, layer
Type
Article
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Citation
Rajagopal, K. R. Saccomandi, G.; Vergori, L. (2015). On the approximation of isochoric motions of fluids under different flow conditions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 471 (2180),
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 defined meaningfully, and it is not zero.
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Publisher
The Royal Society
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)