International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 651910, 8 pages
doi:10.1155/2008/651910
Research Article
Stokes Flow past a Swarm of Porous Nanocylindrical Particles Enclosing a Solid Core
Department of Mathematics , University of Allahabad, Allahabad 211002, India
Received 21 May 2007; Revised 12 July 2007; Accepted 5 December 2007
Academic Editor: Manfred Moller
Copyright © 2008 Satya Deo and Pramod Kumar Yadav. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This paper concerns the Stokes flow of an incompressible viscous fluid past a swarm of porous nanocylindrical particles enclosing a solid cylindrical core with Kuwabara boundary condition. An aggregate of porous nanocylindrical particles is considered as a hydro-dynamically equivalent to a solid cylindrical core with concentric porous cylindrical shell. The Brinkman equation inside the porous cylindrical shell and the Stokes equation outside the porous cylindrical shell in their stream function formulations are used. Explicit expressions for the stream functions in both regions have been investigated. The drag force acting at each nanoporous cylindrical particle in a cell is evaluated. Also, we solved the same problem by using Happel boundary condition on the hypothetical cell. In certain limiting cases, drag force converges to pre-existing analytical results, such as the drag on a porous circular cylinder and the drag on a solid cylinder in Kuwabara's cell or Happel's cell. Representative results are then discussed and compared for both cases and presented in graphical form by using Mathematica software.