Generalized models of flow of a fluid with pressure-dependent viscosity through porous channels: channel entry conditions

  • Authors

    • M. .S.Abu Zaytoon University of New Brunswick
    • M. H.Hamdan On Leave, University of New Brunswick
    • Yiyun (Lisa) Xiao University of New Brunswick
    2021-10-16
    https://doi.org/10.14419/ijpr.v9i2.31744
  • Channel Entry Conditions, Generalized Models, Porous Media.
  • The flow of fluids with pressure-dependent viscosity in free-space and in porous media is considered in this study. The interest is to employ the physical model of flow through a porous layer down an inclined plane in order to derive velocity expressions that can be used as entry conditions in the study of two-dimensional flows through free-space and through porous channels. The generalized equations of Darcy, Forchheimer and Brinkman are used in this work.

     

     

  • References

    1. [1] G.G. Stokes, On the theories of the internal friction of fluids in motion, and of the equilibrium and motion of elastic solids, Trans. Camb. Philos. Soc. 8 (1845) 287-305.

      [2] C.J. Barus, Note on dependence of viscosity on pressure and temperature, Proceedings of the American Academy 27 (1891) 13-19. https://doi.org/10.2307/20020462.

      [3] C.J. Barus, Isothermals, isopiestics and isometrics relative to viscosity, American Journal of Science 45 (1893) 87–96. https://doi.org/10.2475/ajs.s3-45.266.87.

      [4] S. Srinivasan, K.R. Rajagopal, A thermodynamic basis for the derivation of the Darcy, Forchheimer and Brinkman models for flows through porous media and their generalizations, International Journal of Non-Linear Mechanics 58 (2014)162-166. https://doi.org/10.1016/j.ijnonlinmec.2013.09.004.

      [5] K.R. Rajagopal, G. Saccomandi, L. Vergori, Flow of fluids with pressure- and shear-dependent viscosity down an inclined plane, Journal of Fluid Mechanics 706 (2012) 173-189. https://doi.org/10.1017/jfm.2012.244.

      [6] V.L. Savatorova, K.R. Rajagopal, Homogenization of a generalization of Brinkman’s equation for the flow of a fluid with pressure dependent viscosity through a rigid porous solid, ZAMM 91#8 (2011) 630-648. https://doi.org/10.1002/zamm.201000141.

      [7] K. Kannan, K.R, Rajagopal, Flow through porous media due to high pressure gradients, Applied Mathematics and Computation 199 (2008) 748-759. https://doi.org/10.1016/j.amc.2007.10.038.

      [8] P.W. Bridgman, The Physics of High Pressure, MacMillan, New York, 1931.

      [9] A.Z. Szeri, Fluid Film Lubrication: Theory and Design, Cambridge University Press, 1998. https://doi.org/10.1017/CBO9780511626401.

      [10] P.H. Vergne, Pressure-viscosity behavior of various fluids, High Press. Res. 8 (1991) 451–454. https://doi.org/10.1080/08957959108260704.

      [11] F.J. Martinez-Boza, M.J. Martin-Alfonso, C. Callegos, M. Fernandez, High-pressure behavior of intermediate fuel oils, Energy Fuels 25 (2011) 5138-5144. https://doi.org/10.1021/ef200958v.

      [12] K.B. Nakshatrala, K.R. Rajagopal, A numerical study of fluids with pressure-dependent viscosity flowing through a rigid porous medium, Int. J. Numer. Meth. Fluids 67 (2011) 342-368. https://doi.org/10.1002/fld.2358.

      [13] L. Fusi, A. Farina, F. Rosso, Mathematical models for fluids with pressure-dependent viscosity flowing in porous media, Int. J. Engineering Science 87 (2015) 110-118. https://doi.org/10.1016/j.ijengsci.2014.11.007.

      [14] K.D. Housiadas, G.C. Georgiou, R.I. Tanner, A note on the unbounded creeping flow past a sphere for Newtonian fluids with pressure-dependent viscosity, International Journal of Engineering Science 86 (2015) 1–9. https://doi.org/10.1016/j.ijengsci.2014.09.004.

      [15] M.H. Hamdan, Single-phase flow through porous channels: A review. Flow models and channel entry conditions, Applied Mathematics and Computations 62 #2&3 (1994) 203-222. https://doi.org/10.1016/0096-3003(94)90083-3.

      [16] S.C. Subramanian, K.R. Rajagopal, A note on the flow through porous solids at high pressures, Computers and Mathematics with Applications 53 (2007) 260–275. https://doi.org/10.1016/j.camwa.2006.02.023.

      [17] S. Srinivasan, A. Bonito, K.R. Rajagopal, Flow of a fluid through a porous solid due to high pressure gradient, J. Porous Media 16 (2013) 193-203. https://doi.org/10.1615/JPorMedia.v16.i3.20.

      [18] J. Hron, J. Málek, K.R. Rajagopal, Simple flows of fluids with pressure-dependent viscosities, Proceedings of the Royal Society 457 (2001) 1603-1622. https://doi.org/10.1098/rspa.2000.0723.

      [19] J. Málek, K.R. Rajagopal, Mathematical properties of the solutions to the equations governing the flow of fluids with pressure and shear rate dependent viscosities, in: Handbook of Mathematical Fluid Dynamics, Elsevier, 2007.

      [20] J. Chang, K.B. Nakashatrala, J.N. Reddy, Modification to Darcy-Forchheimer model due to pressure-dependent viscosity: consequences and numerical solutions, J. Porous Media 20#3 (2017) 263-285. https://doi.org/10.1615/JPorMedia.v20.i3.60.

      [21] I. Pažanin, M. C. Pereira, F. J. Suárez-Grau, Asymptotic approach to the generalized Brinkman’s equation with pressure-dependent viscosity and drag coefficient, J. Applied Fluid Mechanics 9#6 (2016) 3101-3107. https://doi.org/10.29252/jafm.09.06.25756.

      [22] M.H. Hamdan, M.T. Kamel, Flow through Variable Permeability Porous Layers, Adv. Theor. Appl. Mech. 4#3 (2011) 135-145. https://doi.org/10.1615/SpecialTopicsRevPorousMedia.v2.i2.80.

      [23] S.M. Alzahrani, I. Gadoura, M.H. Hamdan, A Note on the flow of a fluid with pressure-dependent viscosity through a porous medium with variable permeability, J. Modern Technology and Engineering, 2#1 (2017) 21-33.

  • Downloads

    Additional Files

  • How to Cite

    .S.Abu Zaytoon, M., H.Hamdan, M., & (Lisa) Xiao, Y. (2021). Generalized models of flow of a fluid with pressure-dependent viscosity through porous channels: channel entry conditions. International Journal of Physical Research, 9(2), 84-91. https://doi.org/10.14419/ijpr.v9i2.31744