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

ABSTRACT

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.

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.

KEYWORDS

Hydrodynamic, Non-Coincident Disks, Porous Medium, Boundary Layer Thickness, Rotation Parameter

Hydrodynamic, Non-Coincident Disks, Porous Medium, Boundary Layer Thickness, Rotation Parameter

Cite this paper

nullR. 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.

nullR. Jana, M. Maji, S. Das, S. Maji and S. Ghosh, "Hydrodynamic Flow between Two Non-Coincident Rotating Disks Embedded in Porous Media,"

References

[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.

[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.