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FRICTION FACTORS AND INTERNAL FLOW LENGTH SCALES OF GAS-SOLID MAGNETICALLY STABILIZED BEDS IN AXIAL FIELDS: SCALING AND APPLICATIONS TO BED-TO-SURFACE HEAT TRANSFER

ABSTRACT
Friction factors and internal flow length scales of gas-solid magnetically stabilized beds are discussed. Pressure drop and expansion data of beds stabilized by axial magnetic fields are used. The concept of a variable friction factor of fluid-driven deformable packed bed is discussed. Scaling relationships of the internal flow length scale and the bed overall porosity are developed through three approaches: (1) fluidization approach concerning a length scale proportional to the particle size, (2) packed bed approach based on a hydraulic diameters as a length scale, and (3) porous media approach based on the Forchheimer equation. The main result is that the bed length scale ~e", irrespective of the model used, where n is the exponent of the Richardson-Zaki scaling law. These scaling estimates are used to explain the magnetic field effects on bed-to-surface heat transfer coefficients.
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PAPER SUBMITTED: 2004-03-29
PAPER REVISED: 2005-01-11
PAPER ACCEPTED: 2005-02-15
DOI REFERENCE: https://doi.org/10.2298/TSCI0501073H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2005, VOLUME 9, ISSUE Issue 1, PAGES [73 - 98]
REFERENCES
  1. Hristov, J. Magnetic field assisted fluidization-A unified approach. Part 1. Fundamentals and relevant hydrodynamic of gas-fluidized beds, Reviews in Chemical Engineering, 18 (2002), 4-5, pp. 295-509.
  2. Hristov, J.Y., Expansion Scaling and Elastic moduli of gas-fluidized magnetizable beds, in: Current Issues on Heat and Mass Transfer in Porous Media, NATO ASI "Emerging Technologies and Techniques in Porous Media" (Eds.,D. Ingham, A. Bejan, E.Mamut and I. Pop).,, Kluwer, Dordrecht, 2004, pp. 477-489.
  3. Wentz, C.A. , Thodos, G., Pressure Drop in the Flow of Gases through Packed and Distended Beds of Spherical Particles, AIChE J., 9 (1963),pp. 81-84.
  4. Wentz, C.A. and Thodos, G., Total and Form Drag Friction Factors for the Turbulent Flow of Air through Packed and Distended Beds of Spherical Particles, AIChE J., 9 (1963), pp. 358-361
  5. Merwe D.F. and Gauvin W.H., Pressure Drag Measurements for Turbulent Air Flow through a Packed Bed , AIChE J., 17 (1971),pp. 402-407
  6. Hristov J. Magnetic field assisted fluidization - A unified approach. Part 2. Solids batch gas- fluidized beds: Versions and Rheology, Reviews in Chemical Engineering, 19 (2003), 1, pp.1 -132
  7. Penchev I. and Hristov J., Behaviour of Fluidized Beds of Ferromagnetic Particles in an Axial Magnetic Field, Powder Technology, 61 (1990),pp. 103-118.
  8. Richardson, J.F. and Zaki, W.N. Sedimentation and Fluidization, Part I, Trans. I Chem. Eng., 32 (1954),pp 35-50 ( See also Trans. I Chem. Eng. 75 (1997), S82)
  9. Rosensweig R.E, Fluidization: hydrodynamics stabilization with a magnetic field, Science 204 (1979), pp. 57- 60
  10. Foscolo P.U., Gibilaro, L.G., Di Felice, R. and Waldram,S.PThe effect of the interparticle forces on the stability of fluidized beds, Chem. Eng. Sci. 40 (1985), pp. 2379-2381.
  11. Beek, W.J., Mutzall, K.M.K., Transport Phenomena, Wiley and sons, Bristol, 1975.
  12. Denn M.M, Process Fluid Mechanics, 1st ed., Prentice-Hall, Englewood Cliffs, NJ.USA, 1980
  13. Beavers G.S.. Sparrow, E.M. , Rodenz, D.E., Influence of Bed Size on the Flow Characteristics and Porosity of Randomly Packed Beds of Spheres, J. Appl. Mech, 40 (1973),pp. 655- 660.
  14. Beavers G.S., Wilson, T.A. and Masha B.A., Flow Through a Deformable Porous Material, J. Appl. Mech, 42 (1975), pp. 598 602.
  15. Ward, J.C., Turbulent Flow in Porous Media, J. Hidraul. Div.A. Soc.Civ.Eng., 90, (1964) ,HY5,pp. 1-12
  16. Joseph, D.D., Nield, D.A., Papanicolaou, Non-linear Equation Governing Flow in a Saturated Porous medium, Water Res. Research, 18 (1982),pp 1049-1052
  17. Beavers G.S. , Sparrow, E.M., Compressible Gas Flow through a Porous Material, Int. J. Heat Mass Transfer, 14 (1971), pp. 1855-1899.
  18. Geldart, D. Types of Gas Fluidization, Powder Technology 7 (1973),pp. 285-292
  19. Philippow E., Nichtlineare Electrotechnik, Leipzig, 1971 (there is a Russian translation by Energia publishing, Moscow 1976).
  20. Hristov, J.Y., Comments on Gas-fluidized Magnetizable Beds in a Magnetic field, Part 3: Heat transfer, Thermal Science 4 (2000), 1-2, 3 - 48
  21. Hristov J. Y., Magnetic Field Assisted Fluidization - A unified Approach. Part 3. Heat Transfer- a Critical Re-evaluation of the Results, Reviews in Chemical Engineering, 19 (2003), 3, pp. 229-355.
  22. Hristov J.Y., Fluidization of Ferromagnetic Particles in a Magnetic Field, Part 1: The Effect of the Field Lines Orientation on Bed Stability, Powder Technology, 87 (1996), pp. 59-66.
  23. Beckerman, C. , Viskanta, R. ,Forced Convection Boundary Layer Flow and Heat Transfer along a Plate Embedded in a Porous Medium, Int. J. Heat Mass Transfer 30 (1987), pp. 1547-1551.
  24. M. Kaviany, M. Mittal, Natural Convection Heat Transfer from a Vertical Plate to High Permeability Porous Media: an Experiment and Approximate Solution, Int. J. Heat Mass Transfer 30(5) (1987),pp. 967-977
  25. Arnaldos J, Estudi de l'estabilitzacio dels Llits Fluidizacio Solid-gas Mitjancant l'aplicacio d'un Camp Magnetic, Ph.D. Thesis, Univ. Politechnica de Catalunya, Barcelona, Spain, (1986)
  26. Neff J, Rubinsky B, The Effect of a Magnetic Field on the Heat Transfer Characteristics of an Air Fluidized Bed of Ferromagnetic Particles, Int. J. Heat Mass Transfer, 16 (1983), pp. 1885-1889.
  27. Hristov, J.Y, Heat Transfer between Deformable Magnetic Beds and Immersed Surfaces: Cases of Gas-Fluidized Beds, Thermal Sciences 2004-Proceedings of ASME-ZSIS International Thermal Science Seminar ITSS II, Bled, A.Bergles,
  28. I. Golobic, Cr. Amon and A.Bejan, Eds., Slovenia, June13-16, 2004,pp-267-274.

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