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

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 OberbeckBoussinesq 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.

authors

• Rajagopal, Kumbakonam

published proceedings

• PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

author list (cited authors)

• Rajagopal, K. R., Saccomandi, G., & Vergori, L.

citation count

• 10

complete list of authors

• Rajagopal, KR||Saccomandi, G||Vergori, L

publication date

• August 2015

publisher

• The Royal Society  Publisher

published in

• Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences  Journal

keywords

• Oberbeck-boussinesq Approximation
• Perturbation Theory
• Pressure- And Temperature-dependent Viscosity

Digital Object Identifier (DOI)

• 10.1098/rspa.2015.0159

start page

• 20150159

end page

• 20150159

volume

• 471

issue

• 2180

URL

• http%3A%2F%2Fdx.doi.org%2F10.1098%2Frspa.2015.0159