THERMAL SCIENCE

International Scientific Journal

Iftikhar Ahmad

,

Aziz Khan

,

Kamal Shah

,

Thabet Abdeljawad

,

Saeed Islam

ANALYTICAL AND COMPUTATIONAL RESULTS FOR BOUNDARY-LAYER EQUATIONS IN POROUS MEDIUM

ABSTRACT
The aim of this paper is to determine analytic solutions to the steady/unsteady 2-D flows of a Newtonian fluid passing through a porous media. Using the stream function, the analytical general solutions of the non-linear equations corresponding to boundary-layer flows are determined by employing the extended approach of variable separation. Some specific flow problems, described by given initial and boundary conditions, are investigated using the obtained general analytic solutions.
KEYWORDS
boundary-layer, exact solution, porous medium, inverse method
PAPER SUBMITTED: 2022-06-11
PAPER REVISED: 2022-06-24
PAPER ACCEPTED: 2022-07-14
PUBLISHED ONLINE: 2023-04-08
DOI REFERENCE: https://doi.org/10.2298/TSCI23S1163A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Special issue 1, PAGES [163 - 172]
REFERENCES
  1. Andreev, V. K., et al., Applications of Group-Theoretical Methods in Hydrodynamic, Kluwer, Dordrecht, The Netherlands, 1998
  2. Burde, G. I., The Construction of Special Explicit Solutions of the Boundary-Layer Equations, Unsteady Flows, Q. J. Mech. Appl. Math., 48 (1995), 4, pp. 611-633
  3. Burde, G. I., New Similarity Reductions of the Steady-State Boundary-Layer Equations, Journal Phys. A: Math. Gen., 29 (1996), 8, pp. 1665-1683
  4. Ludlow, D. K., et al., New Similarity Solutions of the Unsteady Incompressible Boundary-Layer Equations, Q. J. Mech. Appl. Math., 53 (2000), 2, pp. 175-206
  5. Polyanin, A. D., Exact Solutions and Transformations of the Equations of a Stationary Laminar Boundary-layer, Theo. Foun. Chem. Engg., 35 (2001), July, pp. 319-328
  6. Ludlow, D. K., et al., Non-Classical Symmetry Reductions of the 3-D Incompressible Navier' Stokes Equations, Journal Phys. A: Math. Gen., 31 (1998), 39, pp. 7965-7980
  7. Ludlow, D. K., et al., Non-Classical Symmetry Reductions of the 2-D Incompressible Navieras Stokes Equations, Stud. Appl. Math., 103 (1999), 3, pp. 183-240
  8. Saccomandi, G., A Remarkable Class of Non-Classical Symmetries of the Steady 2-D Boundary-Layer Equations, Journal Phys. A: Math. Gen., 37 (2004), 27, pp. 7005-7017
  9. Polyanin, A. D, Zaitsev, V. F., Transformations and Exact Solutions Containing Arbitrary Functions for Boundary-Layer Equations, Dok. Phy., 46 (2001), 7, pp. 526-531
  10. Polyanin, A. D., Zaitsev, V. F., Equations of an Unsteady-State Laminar Boundary-Layer: General Transformation and Exact Solutions, Theo. Foun. Chem. Engg., 35 (2001), Nov., pp. 529-539
  11. Papanastasiou, T. C., et al., Viscous Fluid-Flow, CRC Press, Boca Raton, Fla., USA, 2000
  12. Polyanin, A. D., Zhurov, A. I., Methods of Generalized and Functional Separation of Variables in Hydrodynamics and Heat and Mass Transfer Equations, Theo. Foun. Chem. Engg., 36 (2002), May, pp. 201-213
  13. Labropulu, F., A Few More Exact Solutions of a Second Grade Fluid via Inverse Method, Mech. Res. Comm., 27 (2000), 6, pp. 713-720
  14. Loitsyanskiy, L.G., Mechanics of Liquids and Gases, Begell House, New York, USA, 1996
  15. Schlichting, H., Boundary-Layer Theory, McGraw-Hill, New York, USA, 1981
  16. Kamel, M. T., Hamdan, M. H., Riabounchisky Flow through Porous Media, Int. J. Pure. Appl. Math., 27 (2005), 1, pp. 113-125
  17. Merabet, N., et al., Analytical Approach to the Darcy-Lapwood-Brinkman Equation, Appl. Math. and Comput., 195 (2008), 2-1, pp. 579-585
  18. Vafai, K., Tien, C. L., Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media, Int. J. Heat Mass Trans., 24 (1981), 2, pp. 211-220
  19. Vafai, K., Kim, S. J., On the Limitations of Brinkman-Forchheimer-Extended Darcy Equation, Int. J. Heat Fluid-Flow, 16 (1995), 1, pp. 11-15
  20. Kaviany, M., Laminar Flow Through a Porous Channel Bounded by Isothermal Parallel Plates, Int. J. Heat Mass Trans., 28 (1985), 4, pp. 851-858
  21. Polyanin, A. D., et al., Exact Solutions of Navier' Stokes, Boundary-Layer, and Heat-Conduction Equations, Theo. Foun. Chem. Engg., 36 (2002), July, pp. 346-352
  22. Polyanin, A. D., Zaitsev, V. F., Handbook of Exact Solutions for Ordinary Differential Equations, CRC Press, New York, USA, 2002
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Analytical and computational results for boundary-layer equations in porous medium

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