Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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HYDROMAGNETIC ROTATING DISK FLOW OF A NON-NEWTONIAN FLUID WITH HEAT TRANSFER AND OHMIC HEATING

  • Attia, Hazem A. (Department of Engineering Mathematics and Physics, Faculty of Engineering, Fayoum University) ;
  • Ewis, Karem M. (Department of Engineering Mathematics and Physics, Faculty of Engineering, Fayoum University) ;
  • Abd Elmaksoud, Ibrahim H. (Department of Engineering Mathematics and Physics, Faculty of Engineering, Fayoum University) ;
  • Awad-Allah, Nabil A. (Department of Civil Engineering, Faculty of Engineering, Fayoum University)
  • Received : 2011.09.12
  • Accepted : 2012.09.13
  • Published : 2012.09.25
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Abstract

The steady hydromagnetic flow of an electrically conducting non-Newtonian fluid due to the rotation of an infinite disk is studied with heat transfer with the inclusion of the ion slip as well as Ohmic heating. The governing nonlinear momentum equations and energy equations are solved using the finite difference method. The numerical results indicate the important effect of the ion slip and the non-Newtonian fluid characteristics on the velocity and temperature distributions.

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References

  1. Von Karman, T., "Uber laminare und turbulente reibung", ZAMM, vol. 1, No. 4, pp. 233-235, 1921. https://doi.org/10.1002/zamm.19210010401
  2. Cochran, W.G., "The flow due to a rotating disk", Proc. Cambridge Philos. Soc. 30 (3), pp. 365-375, 1934. https://doi.org/10.1017/S0305004100012561
  3. 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. 1211-1222, Jan. 2-4, 1990.
  4. 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. 69-82, Nov. 5-7, 1991.
  5. Sutton, G.W. and Sherman, A., Engineering magneto hydrodynamics, McGraw-Hill, New York, 1965.
  6. Crammer, K.R. and Pai, S.-I., Magnetofluid dynamic for engineers and applied physicists, New York, McGraw-Hill, 1973.
  7. Aboul-Hassan, A.L. and Attia, H.A., "The flow due to a rotating disk with Hall effect", Physics Letters A, 228, pp. 286-290, 1997. https://doi.org/10.1016/S0375-9601(97)00086-8
  8. Attia, H.A., "On the effectiveness of ion slip on steady MHD flow and heat transfer above a rotating disk with Ohmic heating", Journal of Fluids Engineering, Vol. 128, Issue 5, 2006.
  9. 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 Modeling, Vol. 25, No. 12, pp. 1089-1098, 2001. https://doi.org/10.1016/S0307-904X(01)00033-6
  10. Attia, H.A., "On the effectiveness of ion slip and uniform suction or injection on steady MHD flow due to a rotating disk with heat transfer and ohmic heating", Chemical Engineering Communications (CEC), Vol. 194, Issue 10, pp. 1396-1407, 2007. https://doi.org/10.1080/00986440701401545
  11. Millsaps, K. and Pohlhausen, K., "Heat transfer by laminar flow from a rotating disk", J. of the Aeronautical Sciences, Vol. 19, pp. 120-126, 1952. https://doi.org/10.2514/8.2175
  12. Sparrow, E.M. and Gregg, J.L., "Mass transfer, flow, and heat transfer about a rotating disk", ASME J. of Heat Transfer, pp. 294-302, 1960.
  13. Attia, H.A., "Unsteady MHD flow near a rotating porous disk with uniform suction or injection", Fluid Dynamics Research 23, pp. 283-290, 1998. https://doi.org/10.1016/S0169-5983(98)80011-7
  14. Mithal, K.G., "On the effects of uniform high suction on the steady flow of a non-Newtonian liquid due to a rotating disk", Quart. J. Mech. Appl. Math., Vol. XIV, pp. 401-410, 1961.
  15. Attia, H.A., "Unsteady flow of a non-Newtonian fluid above a rotating disk with heat transfer", Int. J. of Heat and Mass Transfer, Vol. 46, No. 41, pp. 2695-2700, 2003. https://doi.org/10.1016/S0017-9310(03)00029-2
  16. Ames, W.F., Numerical methods in partial differential equations, 2nd ed., Academic Press, New York, 1977.