Exact Solutions of Equations for the Strongly-Conductive and Weakly-Conductive Magnetic Fluid Flow in a Horizontal Rectangular Channel
- 1
- 2
- 3
Abstract
This paper presents the results of exact solutions and numerical simulations of strongly-conductive and weakly-conductive magnetic fluid flows. The equations of magnetohydrodynamic (MHD) flows with different conductivity coefficients, which are independent of viscosity of fluids, are investigated in a horizontal rectangular channel under a magnetic field. The exact solutions are derived and the contours of exact solutions of the flow for magnetic induction modes are compared with numerical solutions. Also, two classes of variational functions on the flow and magnetic induction are discussed for different conductivity coefficients through the derived numerical solutions. The known results of the phenomenology of magnetohydrodynamics in a square channel with two perfectly conducting Hartmann-walls are just special cases of our results of magnetic fluid.
- G. W. Sutton and A. Sherman, “Engineering Magneto- hydrodynamics,” McGraw-Hill Book Company, New York, 1965.
- T. C. Papanastasiou, G. C. Georgiou, and A. N. Alexandrou, “Viscous fluid flow,” CRC Press LLC, New York, 2000.
- U. Mueller and L. Buehler, “Magnetofluiddynamics in channel and containers,” Springer-Verlag, Berlin, 2001.
- P. Carletto, G. Bossis, and A. Cebers, “Structures in a magnetic suspension subjected to unidirectional and rotating field,” International Journal of Modern Physics B, Vol. 16, No. 17–18, pp. 2279–2285, 2002.
- E. Blums, A. Cebers, and M. M. Maiorov, “Magnetic fluids,” Walter de G Gruyter, Berlin, 1997.
- C.-Y. Wen and W.-P. Su, “Natural convection of magnetic fluid in a rectangular Hele-Shaw,” Journal of Magnetism and Magnetic Materials, Vol. 289, pp. 299– 302, March 2005.
- C.-Y. Wen, C.-Y. Chen, and S.-F. Yang, “Flow visualization of natural convection of magnetic fluid in a rectangular Hele-Shaw cell,” Journal of Magnetism and Magnetic Materials, Vol. 252, pp. 206–208, November 2002.
- R. E. Rosensweig, “Ferrofluids: Magnetically controllable fluids and its applications,” In: S. Odenbach, Ed., Basic Equations for Magnetic Fluids with Internal Rotations, Springer-Verlag, New York, p. 61, 2002.
- T. H. Kuehn and R. J. Goldstein, “An experimental study of natural convection heat transfer in concentric and eccentric horizontal cylindrical annuli,” ASME Journal of Heat Transfer, Vol. 100, pp. 635–640, 1978.
- H. Yamaguchi, Z. Zhang, S. Shuchi, and K. Shimad, “Heat transfer characteristics of magnetic fluid in a partitioned rectangular box,” Journal of Magnetism and Magnetic Materials, Vol. 252, pp. 203–205, November 2002.
- G. B. Arfken and H. J. Weber, “Mathematical methods for physicists,” 6th Edition, Elsevier Academic Press, New York, p. 1037, 2005.
- H. Yamaguchi, “Engineering fluid mechanics,” Springer- Verlag, New York, 2008.