Perturbation method for laminar flow of viscous incompressible fluid between two porous boundary walls

  • Authors

    • Samir Chandra Ray Associate Professor, Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University Gopalganj, Dhaka, Bangladesh.
    • Anik Biswas Researcher, Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University Gopalganj, Dhaka, Bangladesh.
    2024-08-19
    https://doi.org/10.14419/h441e002
  • Laminar Flow; Perturbation Method; Reynolds Number; Dimensionless Parameter; Newtonian Fluid.
  • Abstract

    The present study focuses on the investigation of the velocity profile of viscous fluid between two parallel porous walls while fluid is being ejected from both channel walls at the same rate. The distributions of velocity, pressure and shear stress were determined theoretically for incompressible, steady, fully developed laminar flow past a porous boundary wall. Due to the pressure difference across the porous wall, there is ejection or injection into the wall. The velocity specified as the boundary condition at the wall has been used to explore fluid flow phenomena in porous tubes and ducts. The variable wall velocity is based on the pressure differential across the wall, the fluid characteristics, the thickness of the wall, and the permeability of the structure. An appropriate wall condition must take these factors into account. This paper discusses a Reynolds number solution. We seek formulas for the velocity component. The perturbation approach is used to solve the governing differential equation and the general solution of the velocity is obtained for higher terms of Re. Fifth term of perturbation is used in the perturbation method. The velocity of the fluid is analyzed for different values of Re for a boundary condition. Finally, the result is analysis graphically for the range of Re from .1 to 50. In addition, another strategy is used to keep the Reynolds number constant when the diameter of the hole in the porous wall changes, i.e., changing the value of λ.

  • References

    1. R.Yadav(2016); ‘Numerical Analysis of Laminar flow of Viscous Fluid Between Two Porous Bounding walls’ IRJET, Vol. 3 Issue 4 pp.608-615
    2. Kuznetsov., A.V. (1997); ‘Analytical investigation of the fluid flow in the interface region between a porous medium and a clear fluid in channels partially filled with a porous medium.’ Appl. Sci. Res. Vol. 56: pp 53 – 57. https://doi.org/10.1007/BF02282922.
    3. Raptis A and C. Perdikis., (1987); ‘Hydromagnetic free-convective flow through porous media.’ Encyclopedia of Fluid Mechanics and Modeling. (N. P. Cheremisinoff, Editor), Gulf Publishing Co., Houston, Chapter 8, pp 239 – 262.
    4. Beavers G.S. and D.D.Joseph., (1967); ‘Boundary conditions at a naturally permeable wall.’ Jour. Fluid Mech., Vol. 30: pp 197 – 207. https://doi.org/10.1017/S0022112067001375.
    5. L. S. GALOWIN and M.J. DESANTIS,(1971); ‘Theoretical Analysis of Laminar Pipe Flow in a Porous Wall Cylinder.’ Jour. Dyn Sys Meas and Control,pp. 102-108. https://doi.org/10.1115/1.3426467.
    6. S.Krishnambal,(2002); ‘Laminar Flow Between Two Parallel Porous Walls With Variable Permeability and Wall Slip’,ASME 2002 Flu-ids Eng. Div. Summer Metting, FEDSM2002-31291, pp.1-7. https://doi.org/10.1115/FEDSM2002-31291.
    7. S. Chellam and Mark R. Wiesner,(1993); ‘Laminar Flow With Slip in Channels With Uniformly Porous Walls’, J. Hydraul. Eng. 1993.119:126-132. https://doi.org/10.1061/(ASCE)0733-9429(1993)119:1(126).
    8. Beavers, G. S., and Joseph, D. D. (1967). "Boundary conditions at a naturally permeable wall." J. Fluid Mech., 30(1), 197-207. https://doi.org/10.1017/S0022112067001375.
    9. Berman, A. S. (1953). "Laminar flow in channels with porous walls." J. Appl. Physics, 24(9), 1232-1235. https://doi.org/10.1063/1.1721476.
    10. Avramenko, A.A., A.V. Kuznetsov, B.I. Basok and D.G. Blinov., (2005); ‘Investigation of stability of a laminar flow in a parallel-plate channel filled with a saturated porous medium.’ Jour. Physics of Fluids, Vol. 17, pp. 094102-1 – 094102-6 https://doi.org/10.1063/1.2041607.
    11. Kaviany, M. (1991). Principles of heat transfer in porous media. Springer-Verlag, New York, N.Y. https://doi.org/10.1007/978-1-4684-0412-8.
    12. Kohler, J. P. (1973). "An investigation of laminar flow through a porous-walled channel," PhD thesis, University of Massachusetts, Amherst, MA.
    13. Saffman, P. G. (1971). "On the boundary condition at the surface of a porous medium." Studies Appl. Mathematics, 50(2), 93-101. https://doi.org/10.1002/sapm197150293.
    14. J. L. Lage, M. J. S. de Lemos, and D. A. Nield, in Transport Phenomena in Porous Media II, edited by D. B. Ingham and I. Pop (Else-vier, Oxford, 2002), Chap. 8, p. 198. https://doi.org/10.1016/B978-008043965-5/50009-X.
    15. Antohe, B. V. and Lage, J. L. (1997). A general two-equation macroscopic turbulence model for incompressible flow in porous media. Int. J. Heat Mass Transfer 40, 3013-3024 https://doi.org/10.1016/S0017-9310(96)00370-5.
    16. Ochoa-Tapia, J.A. and Whitaker, S., Momentum transfer at the boundary between a porous medium and a homogeneous fluid - I. The-oretical development. Int. I. Heat Mass Transfer 38 (1995) 2635-2646 https://doi.org/10.1016/0017-9310(94)00346-W.
    17. Bear, J. (1972). Dynamics of Fluids in Porous Media. Elsevier, New York
    18. Nield, D. A. (1991). The limitations of the Brinkman-Forchheimer equation in modeling flow in a saturated porous medium and at an interface. Int. J. Heat Fluid Flow 12, 269-272. https://doi.org/10.1016/0142-727X(91)90062-Z.
    19. Nakayama, A. and Kuwahara, F (1999). A macroscopic turbulence model for flow in a porous medium. ASMEJ Fluids Eng. Ill, 427-433. https://doi.org/10.1115/1.2822227.
  • Downloads

  • How to Cite

    Chandra Ray , S., & Biswas, A. (2024). Perturbation method for laminar flow of viscous incompressible fluid between two porous boundary walls. International Journal of Physical Research, 12(2), 62-73. https://doi.org/10.14419/h441e002