Hazem A. Attia This email address is being protected from spambots. You need JavaScript enabled to view it.1

1Department of Mathematics, College of Science, Al-Qasseem University Buraidah 81999, Kingdom of Saudi Arabia


 

Received: October 15, 2004
Accepted: March 14, 2005
Publication Date: September 1, 2006

Download Citation: ||https://doi.org/10.6180/jase.2006.9.3.01  


ABSTRACT


The steady flow and heat transfer of a conducting fluid due to the rotation of an infinite, non-conducting, porous disk in the presence of an axial uniform steady magnetic field are studied considering the ion slip. A uniform injection or suction is applied through the surface of the disk. The relevant equations are solved numerically using finite differences and the solution shows that the inclusion of the ion slip and the injection or suction through the surface of the disk gives some interesting results.


Keywords: Rotating Disk Flow, Hydromagnetic Flow, Heat Transfer, Numerical Solution, Finite Differences


REFERENCES


  1. [1] Von Karman, T., “Uber Laminare Und Turbulente Reibung,” ZAMM, Vol. 1, pp. 233235 (1921).
  2. [2] Cochran, W. G., “The Flow Due to a Rotating Disk,” Proc. Cambridge Philos. Soc. Vol. 30, pp. 365375 (1934).
  3. [3] Benton, E. R., “On the Flow Due to a Rotating Disk,” J. Fluid Mech. Vol. 24, pp. 781800 (1966).
  4. [4] El-Mistikawy, T. M. A. and Attia, H. A., “The Rotating Disk Flow in the Presence of Strong Magnetic Field,” Proc. 3rd Int. Congress of Fluid Mechanics, Cairo, Egypt, Vol. 3, pp. 12111222 (1990).
  5. [5] El-Mistikawy, T. M. A., Attia, H. A., and Megahed, A. A., “The Rotating Disk Flow in the Presence of Weak Magnetic Field,” Proc. 4th Conference on Theoretical and Applied Mechanics,Cairo, Egypt, pp. 6982 (1991).
  6. [6] Aboul-Hassan, A. L. and Attia, H. A., “The Flow Due to a Rotating Disk with Hall Effect,” Physics Letters A, Vol. 228, pp. 286290 (1997).
  7. [7] Millsaps, K. and Pohlhausen, K., “Heat Transfer by Laminar Flow from a Rotating Disk,” J. of the Aeronautical Sciences, Vol. 19, pp. 120126 (1952).
  8. [8] Sparrow, E. M. and Gregg, J. L., “Mass Transfer, Flow, And Heat Transfer About a Rotating Disk,” ASME J. of Heat Transfer, pp. 294302 (1960).
  9. [9] Attia, H. A., “On the Effectiveness of Uniform Suction-injection on the Unsteady Flow Due to a Rotating Disk with Heat Transfer,” Vol. 29, pp. 653661 (2002).
  10. [10] Stuart, J. T., “On the Effects of Uniform Suction on the Steady Flow Due to a Rotating Disk,” Quart. J. Mech. Appl. Math. Vol. 7, pp. 446457 (1954).
  11. [11] Kuiken, H. K., “The Effect of Normal Blowing on the Flow Near a Rotating Disk of Infinite Extent,” J. Fluid Mech. Vol. 47(4), pp. 789798 (1971).
  12. [12] Ockendon, H., “An Asymptotic Solution for Steady Flow Above an Infinite Rotating Disk with Suction,” Quart. J. Fluid Mech. Appl. Math. Vol. XXV, pp. 291301 (1972).
  13. [13] Attia, H. A., “Unsteady MHD Flow Near a Rotating Porous Disk with Uniform Suction Or Injection,” Fluid Dynamics Research, Vol. 23, pp. 283290 (1998).
  14. [14] Attia, H. A. and Aboul-Hassan, A. L., “Effect of Hall Current on the Unsteady MHD Flow Due to a Rotating Disk with Uniform Suction or Injection,” Applied Mathematical Modelling, Vol. 25, pp. 10891098 (2001).
  15. [15] Sutton, G. W. and Sherman, A., Engineering Magnetohydrodynamics, McGraw-Hill, New York, NY, U.S.A. (1965).
  16. [16] Ames, W. F., Numerical Methods in Partial Differential Equations, 2nd ed., Academic Press, New York, NY, U.S.A. (1977).