Abstract
This note is concerned with the historical background to the Beavers–Joseph boundary condition at the interface of a porous medium and a clear fluid. Relevant papers published prior to 1975 are discussed. The merits of the alternative methodology utilizing the Brinkman equation are also discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Beavers G.S., Joseph D.D.: Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207 (1967). doi:10.1017/S0022112067001375
Beavers G.S., Sparrow E.M., Magnuson R.A.: Experiments on coupled parallel flows in a channel and a bounding medium. ASME J. Basic Eng. 92, 843–848 (1970)
Beavers G.S., Sparrow E.M., Masha B.A.: Boundary conditions at a porous surface which bounds a fluid flow. AIChE J. 20, 596–597 (1974). doi:10.1002/aic.690200323
Brinkman H.C.: A calculation of the viscous force exerted by flowing fluid on a dense swarm of particles. Appl. Sci. Res. A 1, 27–34 (1947). doi:10.1007/BF02120313
Jones I.P.: Low Reynolds number flow past a porous spherical shell. Proc. Camb. Philos. Soc. 73, 231–238 (1973)
Joseph D.D., Tao L.N.: Lubrication of a porous bearing—Stokes solution. J. Appl. Mech. 33, 753–760 (1966)
Larson R.E., Higdon J.L.L.: Microscopic flow near the surface of two-dimensional porous media. 1. Axial flow. J. Fluid Mech. 166, 449–472 (1986). doi:10.1017/S0022112086000228
Larson R.E., Higdon J.L.L.: Microscopic flow near the surface of two-dimensional porous media. 2. Transverse flow. J. Fluid Mech. 178, 119–136 (1987). doi:10.1017/S0022112087001149
Lundgren T.S.: Slow flow through stationary random beds and suspensions of spheres. J. Fluid Mech. 51, 273–299 (1972). doi:10.1017/S002211207200120X
Neale G., Nader W.: Practical significance of Brinkman’s extension of Darcy’s law: coupled parallel flows within a channel and a bounding porous medium. Can. J. Chem. Eng. 52, 475–478 (1974)
Nield D.A.: Onset of convection in a fluid layer overlying a layer of porous medium. J. Fluid Mech. 81, 513–522 (1977). doi:10.1017/S0022112077002195
Nield D.A.: Modeling the effect of surface tension on the onset of natural convection in a saturated porous medium. Transp. Porous Media 31, 365–368 (1998). doi:10.1023/A:1006598423126
Nield D.A., Bejan A.: Convection in porous media. Springer, New York (2006)
Rhodes C.A., Rouleau W.T.: Hydrodynamic lubrication of partial porous metal bearings. ASME J. Basic Eng. 88, 53–60 (1966)
Richardson S.: A model for the boundary condition of a porous material, Part 2. J. Fluid Mech. 49, 327–336 (1971). doi:10.1017/S002211207100209X
Saffman P.: On the boundary condition at the surface of a porous medium. Stud. Appl. Math. 50, 93–101 (1971)
Sahraoui M., Kaviany M.: Slip and no-slip velocity boundary conditions at the surface of porous, plain media. Int. J. Heat Mass Transf. 35, 927–943 (1992). doi:10.1016/0017-9310(92)90258-T
Shir C.C., Joseph D.D.: Lubrication of a porous bearing—Reynolds solution. J. Appl. Mech. 33, 761–767 (1966)
Tao L.N., Joseph D.D.: Fluid flow between porous rollers. J. Appl. Mech. 29, 429–433 (1962)
Taylor G.I.: A model for the boundary condition of a porous material, Part 1. J. Fluid Mech. 49, 319–326 (1971). doi:10.1017/S0022112071002088
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nield, D.A. The Beavers–Joseph Boundary Condition and Related Matters: A Historical and Critical Note. Transp Porous Med 78, 537–540 (2009). https://doi.org/10.1007/s11242-009-9344-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-009-9344-y