Flow of a Pressure-Dependent Viscosity Fluid in Porous Media
Keywords:
Porous media, pressure-dependent viscosity, variable permeabilityAbstract
Two-dimensional flow of a fluid with pressure-dependent viscosity through a variable permeability porous structure is considered. Exact solutions are obtained for a Riabouchinsky type flow using a procedure that is based on a method implemented by the late Professor Dr. R.K. Naeem of Karachi University in his study of Navier-Stokes flow with pressure-dependent viscosity.
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References
S. O. Alharbi, T. L. Alderson and M. H. Hamdan, “Flow of a Fluid with Pressure-Dependent Viscosity through
Porous Mediaâ€, Advances in Theoretical and Applied Mechanics, vol. 9, no. 1, pp. 1 – 9, 2016.
W.S. Almalki and M.H. Hamdan, “Investigations in effective viscosity of fluid in a porous mediumâ€, Int. Journal
of Engineering Research and Applications, vol. 6, issue 4, no. 4, pp. 41-51, 2016.
M.M. Denn, Polymer Melt Processing, Cambridge University Press, Cambridge, 2008.
J.P. Du Plessis and J.H. Masliyah, “Mathematical modeling of flow through consolidated isotropic porous mediaâ€,
Transport in Porous Media, vol. 3, pp. 145-161, 1998.
A. Goubert, J. Vermant, P. Moldenaers, A. Gottfert and B. Ernst, “Comparison of measurement techniques for
evaluating the pressure dependence of the viscosityâ€, Applied Rheology, vol. 11, pp. 26–37, 2001.
J. Hron, J. Malek and K. R. Rajagopal, “Simple flows of fluids with pressure-dependent viscositiesâ€, Proc. R. Soc.
Lond A, vol. 457, pp. 1-20, 2001.
K. Kannan and K.R. Rajagopal, “Flow through porous media due to high pressure gradientsâ€, Applied
Mathematics and Computation, vol. 199, pp. 748–759, 2008.
K.D. Housiadas, G.C. Georgiou and R.I. Tanner, “A note on the unbounded creeping flow past a sphere for
Newtonian fluids with pressure-dependent viscosityâ€, International Journal of Engineering Science, vol. 86, pp. 1–
, 2015.
L. Fusi, A. Farina and F. Rosso, “Mathematical models for fluids with pressure-dependent viscosity flowing in
porous mediaâ€, International Journal of Engineering Science, vol. 87, pp. 110–118, 2015.
M.J. Martin-Alfonso, F.J. Martinez-Boza, F.J. Navarro, M. Fernandez and C. Gallegos, “Pressure-temperature-
viscosity relationship for heavy petroleum fractionsâ€, Fuel, vol. 86, 227-233, 2007.
M.J. Martin-Alfonso, F.J. Martinez-Boza, P. Partal and C. Gallegos, “Influence of pressure and temperature on the
flow behaviour of heavy fluid oilsâ€, Rheol. Acta, vol. 45, pp. 357-365, 2006.
R. K. Naeem, “Riabouchinsky type steady flows of an incompressible fluid of pressure-dependent viscosityâ€,
Journal of Basic and Applied Sciences, vol. 6, no. 2, pp. 99-105, 2010.
K.R. Rajagopal, “On implicit constitutive theories for fluidsâ€, J. Fluid Mech., vol. 550, 243-249, 2006.
K.R. Rajagopal, “On a hierarchy of approximate models for flows of incompressible fluids through porous solidsâ€,
Mathematical Models and Methods in Applied Sciences; vol. 17, no. 2, pp. 215-252, 2007.
K.R. Rajagopal and G. Saccomandi, “Unsteady exact solutions for flows of fluids with pressure-dependent
viscositiesâ€, Mathematical Proceedings of the Royal Irish Academy, vol. 106A, no. 2, pp. 115-130, 2006.
M. Renardy, “Parallel shear flows of fluids with a pressure-dependent viscosityâ€, Journal of Non-Newtonian Fluid
Mechanics, vol. 114, pp. 229-236, 2003.
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