Abstract
The combined effects of the magnetic field, permeable walls, Darcy velocity, and slip parameter on the steady flow of a fluid in a channel of uniform width are studied. The fluid flowing in the channel is assumed to be homogeneous, incompressible, and Newtonian. Analytical solutions are constructed for the governing equations using Beavers-Joseph slip boundary conditions. Effects of the magnetic field, permeability, Darcy velocity, and slip parameter on the axial velocity, slip velocity, and shear stress are discussed in detail. It is shown that the Hartmann number, Darcy velocity, porous parameter, and slip parameter play a vital role in altering the flow and in turn the shear stress.
Similar content being viewed by others
References
Makinde, O. D. Magneto-hydrodynamic stability of plane-Poiseuille flow using multideck asymptotic technique. Mathematical and Computer Modelling, 37(3), 251–259 (2003)
Rao, A. R. and Deshikachar, K. S. MHD oscillatory flow of blood through channels of variable cross section. Int. J. Engng. Sci., 24(10), 1615–1628 (1986)
Berman, S. Laminar flow in channels with porous walls. J. Appl. Phys., 24(9), 1232–1235 (1953)
Sellars, J. R. Laminar flow in channels with porous walls at high suction Reynolds number. J. Appl. Phys., 26(4), 489–490 (1955)
Yuan, S. W. Further investigations of laminar flow in channels with porous walls. J. Appl. Phys., 27(3), 267–269 (1956)
Wallace, W. E., Pierce, C. I., and Swayer, W. K. Technical Report TN23, US Bureau of Mines (1969)
Rudraiah, N., Ramaiah, B. K., and Rajasekhar, B. M. Hartmann flow over a permeable bed. Int. J. Engng. Sci., 13(1), 1–24 (1975)
Beavers, G. S. and Joseph, D. D. Boundary conditions at a naturally permeable wall. J. Fluid Mech., 30(1), 197–207 (1967)
Richardson, S. A model for the boundary condition of a porous material-Part 2. J. Fluid Mech., 49(2), 327–336 (1971)
Rajasekhar, B. M. Experimental and Theoretical Study of Flow of Fluids Past Porous Media, Ph. D. dissertation, Banglore University (1974)
Rudraiah, N. and Veerbhadraiah, R. Temperature distribution in Couette flow past a permeable bed. Proceedings Mathematical Sciences, 86(6), 537–547 (1977)
Darcy, H. Les Fountains Publique De La Ville De Dijon, Delmont, Paris (1856)
Van Lankveld, M. A. M. Validation of Boundary Conditions Between a Porous Medium and a Viscous Fluid, Eindhoven University of Technology (1991)
Srivastava, A. C. Flow of a second-order fluid through a circular pipe and its surrounding porous medium. Bulletin Gauhati University Mathematics Association, 3, 1–8 (1996)
Singh, R. and Lawrence, L. Influence of slip velocity at a membrane surface on ultra-filtration performance-II (tube flow system). International Journal of Heat and Mass Transfer, 22(5), 731–737 (1979)
Pal, D., Veerabhadraiah, R., Shivakumar, P. N., and Rudraiah, N. Longitudinal dispersion of tracer particles in a channel bounded by porous media using slip condition. Int. J. Math. Sci., 7(4), 755–764 (1984)
Khan, M., Hayat, T., and Wang, Y. Slip effects on shearing flows in a porous medium. Acta Mechanica Sinica, 24(1), 51–59 (2008)
Makinde, O. D. and Osalusi, E. MHD flow in a channel with slip at the permeable boundaries. Romania Journal of Physics, 51(3), 319–328 (2006)
Ganesh, S. and Krishnambal, S. Magnetohydrodynamic flow of viscous fluid between two parallel porous plates. Journal of Applied Sciences, 6(11), 2420–2425 (2006)
Chandrasekhara, B. D. and Rudraiah, N. MHD flow through a channel of varying gap. Indian Journal of Pure and Applied Mathematics, 11(8), 1105–1123 (1980)
Shivakumar, P. N., Nagaraj, S., Veerabhadraiah, R., and Rudraiah, N. Fluid movement in a channel of varying gap with permeable walls covered by porous media. Int. J. Engng. Sci., 24(4), 479–492 (1986)
Sparrow, E. M. and Cess, R. D. Magnetohydrodynamic flow and heat transfer about a rotating disc. J. Appl. Mech., 29, 181–187 (1962)
Roberts, P. H. An Introduction to Magnetohydrodynamics, Longmans Publications, London (1967)
Langlois, W. F. Creeping viscous flow through a two dimensional channel. Proc. Third U.S. Nat. Cong. Appl. Mech., 777–783 (1958)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ramakrishnan, K., Shailendhra, K. Hydromagnetic flow through uniform channel bounded by porous media. Appl. Math. Mech.-Engl. Ed. 32, 837–846 (2011). https://doi.org/10.1007/s10483-011-1463-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-011-1463-7