On a family of differential equations for boundary layer approximations in porous media

European Journal of Applied Mathematics

Volumn 12, Issue 4, 2001, Pages 513-528

  Belhachmi, Zakaria ^a   Brighi, Bernard ^b   Taous, Khalid ^a  

^a UNIVERSITÉ DE LORRAINE   (France)

^b UNIVERSITÉ DE HAUTE ALSACE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035596723     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0956792501004582     Document Type: Article

References (25)

1. BANKS, W. H. H. (1983) Similarity solutions of the boundary layer equations for a stretching wall. J. de Mécun. théor. et appl. 2, 375-392.
2. BANKS, W. H. H. & ZATURSKA, M. B. (1986) Eigensolutions in boundary layer flow adjacent to a stretching wall. IMA J. Appl. Math. 36, 263-273.
3. BELHACHMI, Z., BRIGHI, B. & TAOUS, K. (2000a) Solutions similaires pour un problème de couches limites en milieux poreux. C. R. Acad. Sci. Paris, 328(IIb), 407-410.
4. BELHACHMI, Z., BRIGHI, B. & TAOUS, K. (2000b) On the concave solutions of the Blasius equation. Acta Math. Univ. Comenianae, LXIX(2), 199-214.
5. CHAUDARY, M. A., MERKIN, J. H. & POP, I. (1995a) Similarity solutions in free convection boundary layer flows adjacent to vertical permeable surfaces in porous media. I: Prescribed surface temperature. Euro. J. Mech. B-Fluids, 14, 217-237.
6. CHAUDARY, M. A., MERKIN, J. H. & POP, I. (1995b) Similarity solutions in free convection boundary layer flows adjacent to vertical permeable surfaces in porous media. II: Prescribed surface heat flux. Heat and Mass Transfer, 30, 341-347.
7. CHENG, P. & MINKOWYCZ, W. J. (1977) Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from a dike. J. Geophys. Res. 82(14), 2040-2044.
8. COPPEL, W. A. (1960) On a differential equation of boundary layer theory. Phil. Trans. Roy. Soc. London, Ser. A, 253, 101-136.
9. CRANE, L. E. (1970) Flow past a stretching plane. Z. Angew. Math. Phys. 21, 645-647.
10. ENE, H. I. & POLIŠEVSKI, D. (1987) Thermal Flow in Porous Media. Reidel, Dordrecht.
11. FALKNER, V. M. & SKAN, S. W. (1931) Solutions of the boundary layer equations. Phil. Mag. 7(12), 865-896.
12. HARTMAN, P. (1964) Ordinary Differential Equations. Wiley, New York.
13. HASTINGS, S. P. & TROY, W. C. (1987) Oscillating solutions of the Falkner-Skan equations for negative β. SIAM J. Math. Anal. 18(2), 422-429.
14. HASTINGS, S. P. & TROY, W. C. (1988) Oscillating solutions of the Falkner-Skan equations for positive β. J. Diff. Equations, 71(1), 123-144.
15. INGHAM, D. B. & BROWN, S. N. (1986) Flow past a suddenly heated vertical plate in a porous medium. Proc. R. Soc. Lond. A, 403 51-80.
16. KAYS, W. M. & CRAWFORD, M. E. (1993) Convective Heat and Mass Transfer. McGraw-Hill.
17. MAGYARI, E. & KELLER, B. (2000) Exact solutions for self-similar boundary layer flows induced by permeable stretching walls. Euro. J. Mech. B-Fluids, 19, 109-122.
18. MERKIN, J. H. & ZHANG, G. (1990) On the similarity solutions for free convection in a saturated porous medium adjacent to impermeable horizontal surfaces. Wärme-und Stoffübertr, 25, 179-184.
19. PRANDTL L. L. (1904) Über Flüssigkeitsbewegungen bei sehr kleiner Reihung. Verh.d. III. Int. Math.-Kongr., pp. 484-494. Heidelberg. Teubner.
20. PRANDTL, L. L. (1935) Mechanics of viscous fluids. In: W. F. Daniel, editor, Aerodynamics Theory, pp. 34-208.
21. ROSENHEAD L. (1963) Laminar Boundary Layers. Oxford University Press.
22. STUART, J. T. (1966) Double boundary layers in oscillatory viscous flow. J. Fluid Mech. 24, 673-687.
23. UTZ, W. R. (1978) Existence of solutions of a generalized Blasius equation. J. Math. Anal. Appl. 66, 55-59.
24. WALTER, W. (1970) Differential and Integral Inequalities. Springer-Verlag.
25. WEYL, H. (1942) On the differential equations of the simplest boundary-layer problem. Ann. Math. 43, 381-407.