Abstract
This chapter deals with a theoretical and numerical analysis of similarity solutions of the 2-D boundary-layer flow of a power-law non-Newtonian fluid past a permeable surface in the presence of a magnetic field B(x) applied perpendicular to the surface. The magnetic field B is assumed to be proportional to x (m − 1)/2 , where x is the coordinate along the plate measured from the leading edge and m is a constant. The problem depends on the power-law exponent m, the power-law index n and the magnetic parameter M or the Stewart number. It is shown, under certain circumstance, that the problem has an infinite number of solutions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aly EH, Amkadni M, Guedda M (In preparation) A note on MHD flow over a stretching permeable surface
Aly EH, Elliott L, Ingham DB (2003) Mixed convection boundary-layer flow over a vertical surface embedded in a porous medium. Eur J Mech B Fluids 22:529–543
Andersson HI (1992) MHD flow of a viscous fluid past a stretching surface. Acta Mechanica 95:227–230
Anjali Devi SP, Kandasamy R (2003) Thermal stratification effects on non linear MHD laminar boundary-layer flow over a wedge with suction or injection. Int Comm Heat Mass Transf 30:717–725
Brighi B, Benlahsen M, Guedda M, Peponas S (In preparation) Mixed convection on a wedge embedded in a porous medium
Brighi B, Hoernel D (2006) On the concave and convex solution of mixed convection boundary layer approximation in a porous medium. Appl Math Lett 19:69–74
Callegari AJ, Frieddman MB (1968) An analytical solution of a nonlinear, singular boundary value problem in the theory of viscous fluids. J Math Analy Appl 21:510–529
Chakrabarti A, Gupta AS (1979) Hydromagnetic flow and heat transfer over a stretching sheet. Quart Appl Math 37:73–78
Chaturvedi N (1996) On MHD flow past an infinite porous plate with variable suction. Ener Conv Mgmt 37(5):623–627
Coppel WA (1960) On a differential equation of boundary layer theory. Phil Trans Roy Soc London Ser A 253:101–136
Cortel R (2005) Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to suction and to a transverse magnetic field. Int J Heat Mass Transf (published online)
Guedda M (2006) Multiple solutions of mixed convection boundary-layer approximations in a porous medium. Appl Math Lett 19:63–68
Howell TG, JENG DR, De Witt KJ (1997) Momentum and heat transfer on a continuous moving surface in a power-law fluid. Int J Heat Mass Transfer 40(8):1853–1861
Kumari M, Takhar HS, Nath G (1990) MHD flow and heat transfer over a stretching surface with prescribed wall temperature or heat flux. Warm und Stoffubert 25:331–336
Magyari E, Aly EH (2006) Exact analytical solution for a thermal boundary layer in a saturated porous medium. Appl Math Lett (published online)
Nazar R, Amin N, Pop I (2004) Unsteady mixed convection boundary-layer flow near the stagnation point over a vertical surface in a porous medium. Int J Heat Mass Transfer 47:2681–2688
Pavlov KB (1974) Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a surface. Magnitnaya Gidro-dinamika 4:146–147
Pop I, Na TY (1998) A note on MHD flow over a stretching permeable surface. Mech Res Comm 25(3):263–269
Raptis A, Perdikis C, Takhar H S (2004) Effect of thermal radiation on MDH flow. App Math Comp 153:645–649
Schlichting H, Gersten K (2000) Boundary layer theory. 8th Revised and Enlarged Ed, Springer-Verlag, Berlin, Heidelberg 2000
Takhar HS (1971) hydromagnetic free convection from a flat plate. Indian J Phys 45:289–311
Takhar HS, Ali MA, Gupta AS (1989) Stability of magnetohydrodynamic flow over a stretching sheet. Liquid Metal Hydrodynamics (J. Lielpeteris and R. Moreau eds) Kluwer Academic Publishers, Dordrecht, pp 465–471
Takhar HS, Chamkha AJ, Nath G (2000) Flow and mass transfer on a stretching sheet with a magnetic field and chemically reactive species. Int J Eng Sci 38:1303–1314
Takhar HS, Nath G (1997) Similarity solutions of unsteady boundary layer equations with a magnetic field. Mecanica 32:157–163
Takhar HS, Raptis A, Perdikis C (1987) MHD asymmetric flow past a semi-infinite moving plate. Acta Mechanica 65:287–290
Vajravelu K (1986) Hydromagnetic flow and heat transfer over a continuous moving porous surface. Acta Mechanica 64:179–185
Watanabe T, Pop I (1995) Hall effects on magnetohydrodynamic boundary layer flow over a continuous moving flat plate. Acta Mechanica 108:35–47
Acknowledgments.
The authors wish to thank Robert Kersner for interesting discussion. This work was partially supported by Direction des Affaires Internationals (UPJV) Amiens, France, and by PAI No MA/05/116.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media LLC
About this chapter
Cite this chapter
Guedda, M., Mahani, Z., Benlahcen, M., Hakim, A. (2009). Similarity solutions of an MHD boundary-layer flow of a non-Newtonian fluid past a continuous moving surface. In: Mastorakis, N., Sakellaris, J. (eds) Advances in Numerical Methods. Lecture Notes in Electrical Engineering, vol 11. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-76483-2_1
Download citation
DOI: https://doi.org/10.1007/978-0-387-76483-2_1
Published:
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-76482-5
Online ISBN: 978-0-387-76483-2
eBook Packages: EngineeringEngineering (R0)