Hydrodynamic Flow between Two Non-Coincident Rotating Disks Embedded in Porous Media

Hydrodynamic viscous incompressible fluid flow through a porous medium between two disks rotating with same angular velocity about two non-coincident axes has been studied. An exact solution of the govern-ing equations has been obtained in a closed form. It is found that the primary velocity decreases and the sec-ondary velocity increases with increase in porosity parameter to the left of the z-axis and the result is re-versed to the right of the z-axis. It is also found that the torque on the disks increases with increase in either rotation parameter or porosity parameter. For large rotation, there exist a thin boundary layer near the disks and the thickness of this boundary layer decreases with increase in porosity parameter.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

R. Jana, M. Maji, S. Das, S. Maji and S. Ghosh, "Hydrodynamic Flow between Two Non-Coincident Rotating Disks Embedded in Porous Media," World Journal of Mechanics, Vol. 1 No. 2, 2011, pp. 50-56. doi: 10.4236/wjm.2011.12007.

 [1] R. Berker, “Hand Book of Fluid Dynamics,” Vol. VIII/3, Springer, Berlin, 1963. [2] T. N. G. Abbott and K. Walters, “Rheometrical Flow Systems, Part-2. Theory for Orthogonal Rheometer, Including an Exact Solution of the Navier-Stokes Equations,” Journal of Fluid Mechanics, Vol. 40, 1970, pp. 205-213.doi:10.1017/S0022112070000125 [3] M. E. Erdogan, “Unsteady Flow between Eccentric Rotating Disks Executing Non-Torsional Oscollations,” International Journal of Non-Linear Mechanics, Vol. 35, No. 4, 2000, pp. 691-699. doi:10.1016/S0020-7462(99)00051-7 [4] M. E. Erdogan, “Unsteady Viscous Flow between Eccentric Rotating Disks,” International Journal of Non-Linear Mechanics, Vol. 30, No. 5, 1995, pp. 711-717. doi:10.1016/0020-7462(95)00030-R [5] H. V. Ersoy, “Unsteady Flow Due to Sudden Pull of Eccentric Rotating Disks,” International Journal of Engineering Science, Vol. 39, No. 3, 2001, pp. 343-354. doi:10.1016/S0020-7225(00)00040-9 [6] H. V. Ersoy, “Unsteady Flow Due to Concentric Rotation of Eccentric Rotating Disks,” Meccanica, Vol. 38, No. 3, 2003, pp. 325-334. doi:10.1023/A:1023374214783 [7] H. V. Ersoy, “MHD Flow of an Oldroyd-B Fluid between Eccentric Rotating Disks,” International Journal of Engineering Science, Vol. 37, No. 15, 1999, pp. 1973-1984. doi:10.1016/S0020-7225(99)00010-5 [8] K. R. Rajagopal, “Flow of Viscoelastic Fluids between Rotating Disks,” Theoretical and Computational Fluid Dynamics, Vol. 3, No. 4, 1992, pp. 185-206. doi:10.1007/BF00417912 [9] H. K. Mohanty, “Hydromagnetic Flow between Two Rotating Disks with Non-Coincident Parallel Axes of Rotation,” Physics of Fluids, Vol. 15, No. 8, 1972, pp. 1456-1458. doi:10.1063/1.1694107 [10] A. K. Kanch and R. N. Jana, “Hall Effects on Hydromag- netic Flow Between Two Disks with Non-Coincident Parallel Axes of Rotation,” Revue Roumaine des Sciences Techniques-Série de Mécanique Appliquée, Vol. 37, No. 4, 1992, pp. 379- 385. [11] M. Guria, R. N. Jana and S. K. Ghosh, “Unsteady MHD Flow Between Two Disks with Non-Coincident Parallel Axes of Rotation,” International Journal of Fluid Mechanics Research, Vol. 34, No. 5, 2007, pp. 425-433. doi:10.1615/InterJFluidMechRes.v34.i5.30 [12] S. L. Maji, N. Ghara, R. N. Jana and S. Das, “Unsteady MHD Flow Between two Eccentric Rotating Disks,” Journal of Physical Sciences, Vol. 13, 2009, pp. 87-96. [13] M. Guria, B. K. Das, R. N. Jana and S. K. Ghosh, “Magnetohydrodynamic Flow With Reference to Non-Coaxial Rotation of a Porous Disk and a Fluid at Infinity,” International Journal of Dynamics of Fluids, Vol. 7, No. 1, 2011, pp. 25-34. [14] S. Das, S. L. Maji, M. Guria and R. N. Jana, “Hall Effects on Unsteady MHD Flow Between two Disks with Non-Coincident Parallel Axes of Rotation,” International Journal of Applied Mechanics and Engineering, Vol. 15, No. 1, 2010, pp. 5-18.