Flow of a Pressure-Dependent Viscosity Fluid in Porous Media
Keywords:Porous media, pressure-dependent viscosity, variable permeability
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.
S. O. Alharbi, T. L. Alderson and M. H. Hamdan, â€œFlow of a Fluid with Pressure-Dependent Viscosity through
Porous Mediaâ€, Advances in Theoretical and Applied Mechanics, vol. 9, no. 1, pp. 1 â€“ 9, 2016.
W.S. Almalki and M.H. Hamdan, â€œInvestigations 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, â€œMathematical 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, â€œComparison of measurement techniques for
evaluating the pressure dependence of the viscosityâ€, Applied Rheology, vol. 11, pp. 26â€“37, 2001.
J. Hron, J. Malek and K. R. Rajagopal, â€œSimple flows of fluids with pressure-dependent viscositiesâ€, Proc. R. Soc.
Lond A, vol. 457, pp. 1-20, 2001.
K. Kannan and K.R. Rajagopal, â€œFlow through porous media due to high pressure gradientsâ€, Applied
Mathematics and Computation, vol. 199, pp. 748â€“759, 2008.
K.D. Housiadas, G.C. Georgiou and R.I. Tanner, â€œA note on the unbounded creeping flow past a sphere for
Newtonian fluids with pressure-dependent viscosityâ€, International Journal of Engineering Science, vol. 86, pp. 1â€“
L. Fusi, A. Farina and F. Rosso, â€œMathematical models for fluids with pressure-dependent viscosity flowing in
porous mediaâ€, International Journal of Engineering Science, vol. 87, pp. 110â€“118, 2015.
M.J. Martin-Alfonso, F.J. Martinez-Boza, F.J. Navarro, M. Fernandez and C. Gallegos, â€œPressure-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, â€œInfluence of pressure and temperature on the
flow behaviour of heavy fluid oilsâ€, Rheol. Acta, vol. 45, pp. 357-365, 2006.
R. K. Naeem, â€œRiabouchinsky 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, â€œOn implicit constitutive theories for fluidsâ€, J. Fluid Mech., vol. 550, 243-249, 2006.
K.R. Rajagopal, â€œOn 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, â€œUnsteady 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, â€œParallel shear flows of fluids with a pressure-dependent viscosityâ€, Journal of Non-Newtonian Fluid
Mechanics, vol. 114, pp. 229-236, 2003.
How to Cite
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.