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He II Heat Transfer

  • Steven W. Van Sciver
Part of the The International Cryogenics Monograph Series book series (ICMS)

Abstract

Chapter 4 emphasized the physical understanding of He II including heat transport in the laminar flow and turbulent mutual friction regimes. These mechanisms are fundamental to the behavior of He II, although they represent rather idealized conditions. Therefore, it is of interest to apply the treatment of He II to practical heat transfer problems. In doing so, the concepts already developed must be extended into regimes that are usable in more practical situations. To be more specific, the emphasis of Chapter 4 has been to understand the interactive mechanisms. Thus, of principal concern are the behavior of the transport properties including mainly the normal fluid viscosity η n and the mutual friction parameter A. Of interest now is to use these concepts in understanding such phenomena as the maximum heat flux q*, the maximum energy deposition ΔE*, and the maximum temperature difference Δ T m , which can be either within the fluid or across a solid—fluid interface. The goal of the present chapter is to establish a connection between the engineering parameters q*, ΔE*, and ΔT m and the physical properties of the fluid and solid—fluid boundaries. In establishing this connection there are a number of subjects of practical interest which must be addressed. These include steady-state heat transport, forced convection, transient heat transport, Kapitza thermal boundary conductance, and film boiling. Some of these phenomena are also important in pool boiling He I heat transfer, which is the subject of Chapter 6.

Keywords

Heat Transfer Heat Flux Heat Transport Critical Heat Flux Vapor Film 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    W. F. Viner, Mutual Friction in a Heat Current in Liquid Helium II. I. Experiments on Steady State Heat Currents, Proc. R. Soc. London A240, 114 (1957).ADSCrossRefGoogle Scholar
  2. 2.
    V. Arp, Heat Transport Through Helium II, Cryogenics 10, 96 (1970).CrossRefGoogle Scholar
  3. 3.
    S. W. Van Sciver, Kapitza Conductance of Aluminum and Heat Transport Through Sub-cooled He II, Cryogenics 18, 521 (1978).CrossRefGoogle Scholar
  4. 4.
    W. F. Vinen, Mutual Friction in a Heat Current in Liquid Helium II. III. Theory of Mutual Friction, Proc. R Soc. London A242, 493 (1957).ADSCrossRefGoogle Scholar
  5. 5.
    R. Srinivasan and A. Hofmann, Investigations on Cooling with Forced Flow of He II, Cryogenics 25, 641 (1985).CrossRefGoogle Scholar
  6. 6.
    C. Linnet and T. H. K. Frederking, Thermal Conditions at the Gorter—Mellink Counter-flow Limit between 0.01 and 3 Bar, J. Low Temp. Phys. 21, 447 (1975).ADSCrossRefGoogle Scholar
  7. 7.
    A. C. Leonard and M. A. Clermont, Correlation of the Vaporization Onset Heat Flux for Cylinders in Saturated Liquid Helium II, in Proceedings of the 4th International Cryogenics Engineering Conference, pp. 301–306, IPC Science and Technology Press, London, 1972.Google Scholar
  8. 8.
    J. S. Goodling and R. K. Irey, Nonboiling and Film Boiling Heat Transfer to a Saturated Bath of Liquid Helium, Adv. Cryog. Eng. 14, 159 (1969).Google Scholar
  9. 9.
    T. H. K. Frederking and R. L Haben, Maximum Low Temperature Dissipation Rates of Single Horizontal Cylinders in Liquid Helium II, Cryogenics 8, 32 (1968).ADSCrossRefGoogle Scholar
  10. 10.
    S. W. Van Sciver and R. L Lee, Heat Transfer to He II in Cylindrical Geometries, Adv. Cryog. Eng. 25, 363 (1980).Google Scholar
  11. 11.
    S. W. Van Sciver and R. L Lee, Heat Transfer from Circular Cylinders in He II, in Cryogenic Processes and Equipment in Energy Systems, ASME Publication No. H00164, 1981, pp. 147–154.Google Scholar
  12. 12.
    H. Van Dijk, M. Durieux, J. R. Clement, and J. K. Logan, The 1958 `He Scale of Temperatures, National Bureau of Standards Monograph 10, U.S. Government Printing Office, Washington, DC, June 17, 1960.Google Scholar
  13. 13.
    G. Krafft, Superheating and Bubble Formation in Helium II, J. Low Temp. Phys. 31, 441 (1978).ADSCrossRefGoogle Scholar
  14. 14.
    L. J. Rybarcyk and J. T. Tough, Superheating in He II and the Extension of the Lambda Line, J. Low Temp. Phys. 43, 197 (1981).ADSCrossRefGoogle Scholar
  15. 15.
    S. W. Van Sciver and O. Christianson, Heat Transport in a Long Tube of He II, in Proceedings of the 7th International Cryogenics Engineering Conference, pp. 228–234, IPC Science and Technology Press, London, 1978.Google Scholar
  16. 16.
    S. Breon, Boiling Phenomena in Saturated and Subcooled He II, Ph.D. thesis, University of Wisconsin-Madison (1986).Google Scholar
  17. 17.
    S. W. Van Sciver, Heat Transport in Forced Flow He II: Analytic Solution, Ada. Cryog. Eng. 29, 315 (1984).CrossRefGoogle Scholar
  18. 18.
    A. Kashani and S. W. Van Sciver, Steady State Forced Convection Heat Transfer in He II, Adv. Cryog. Eng. 31, 489 (1986).CrossRefGoogle Scholar
  19. 19.
    W. W. Johnson and M. C. Jones, Measurements of Axial Heat Transport in Helium II with Forced Convection, Adv. Cryog. Eng. 23, 363 (1978).CrossRefGoogle Scholar
  20. 20.
    F. P. Incropera and D. P. Dewitt, Fundamentals of Heat Transfer, Chap. 5, Wiley, New York, 1981.Google Scholar
  21. 21.
    G. E. Myers, Analytical Methods in Conduction Heat Transfer, McGraw-Hill, New York, 1971.Google Scholar
  22. 22.
    L. Dresner, Transient Heat Transfer in Superfluid Helium, Adv. Cryog. Eng. 27, 411 (1982).Google Scholar
  23. 23.
    L. Dresner, Transient Heat Transfer in Superfluid Helium-Part II, Adv. Cryog. Eng. 29, 323 (1984).CrossRefGoogle Scholar
  24. 24.
    L. Dresner, Similarity Solution of Non-Linear Partial Differential Equations, Pitman Publishing, Boston, MA, 1983.Google Scholar
  25. 25.
    S. W. Van Sciver, Transient Heat Transport in He II, Cryogenics 19, 385 (1979).CrossRefGoogle Scholar
  26. 26.
    P. Seyfert, J. Lafferranderie, and G. Claudet, Time Dependent Heat Transport in Sub-cooled Superfluid Helium, Cryogenics 22, 401 (1982).CrossRefGoogle Scholar
  27. 27.
    P. L. Kapitza, The Study of Heat Transfer on Helium II, J. Phys. (USSR) 4, 181 (1941).Google Scholar
  28. 28.
    O. V. Lounasmaa, Experimental Principles and Method Below I K Academic Press, London, 1974.Google Scholar
  29. 29.
    T. H. K. Frederking, Thermal Transport Phenomena at Liquid Helium II Temperatures, Adv. Cryog. Heat Transfer 64, 21 (1968).Google Scholar
  30. 30.
    L. J. Challis, Kapitza Resistance and Acoustic Transmission Across Boundaries at High Frequencies, J. Phys. C. Solid State Phys. 7, 481 (1974).ADSCrossRefGoogle Scholar
  31. 31.
    N. S. Snyder, Thermal Conductance at the Interface of a Solid and Helium II (Kapitza Conductance). NBS Technical Note 385, U.S. Government Printing Office, Washington, DC, 1969; Heat Transport through Helium II: Kapitza Conductance, Cryogenics 10, 89 (1970).CrossRefGoogle Scholar
  32. 32.
    L. J. Challis, Experimental Evidence for a Dependence of the Kapitza Conductance on the Debye Temperature of a Solid, Phys. Lett. 26A, 105 (1968).CrossRefGoogle Scholar
  33. 33.
    I. M. Khalatnikov, Introduction to the Theory of Superfluidity, Chap. III, W. A. Benjamin, New York, 1965.Google Scholar
  34. 34.
    R. E. Peterson and A. C. Anderson, The Kapitza Thermal Boundary Resistance, J. Low Temp. Phys. 11, 639 (1973).ADSCrossRefGoogle Scholar
  35. 35.
    L. J. Challis, K. Dransfeld, and J. Wilks, Heat Transfer Between Solids and Liquid Helium II, Proc. R. Soc. London A260, 31 (1961).ADSCrossRefGoogle Scholar
  36. 36.
    D. Cheeke and H. Ettinger, Macroscopic Calculation of the Kapitza Resistance Between Solids and Liquid ‘He, Phys. Rev. Lett. 37, 1625 (1976).ADSCrossRefGoogle Scholar
  37. 37.
    P. H. E. Meijer and J. S. R. Peri, New Kapitza Heat Transfer Model for Liquid ‘He, Phys. Rev. B 22, 195 (1980).ADSCrossRefGoogle Scholar
  38. 38.
    J. G. Dash, Films on Solid Surfaces, Academic Press, New York, 1974.Google Scholar
  39. 39.
    J. Wilks, The Properties of Liquid and Solid Helium, Chap. 14, Clarendon Press, Oxford, 1967.Google Scholar
  40. 40.
    B. W. Clement and T. H. K. Frederking, Thermal Boundary Resistance and Related Peak Flux During Supercritical Heat Transport from a Horizontal Surface Through a Short Tube to a Saturated Bath of Liquid Helium II, Liquid Helium Technology, Proceedings of the International Institute of Refrigeration,Commission I, Boulder, CO, Pergamon Press, Oxford, 1966, pp.49–59 (see also Ref. 29).Google Scholar
  41. 41.
    K. Mittag, Kapitza Conductance and Thermal Conductivity of Copper, Niobium, and Aluminum in the Range from 1.3 to 2.1 K, Cryogenics 13, 94 (1973).Google Scholar
  42. 42.
    S. W. Van Sciver, Kapitza Conductance of Aluminum and Heat Transport from a Flat Surface through a Large Diameter Tube to Saturated He II, Adv. Cryog. Eng. 23, 340 (1977).Google Scholar
  43. 43.
    G. Claudet and P. Seyfert, Bath Cooling with Subcooled Superfluid Helium, Adv. Cryog. Eng. 27, 441 (1981).Google Scholar
  44. 44.
    S. W. Van Sciver, Developments in He II Heat Transfer and Applications to Superconducting Magnets, Adv. Cryog. Eng. 27, 375 (1981).Google Scholar
  45. 45.
    A. Kashani and S. W. Van Sciver, Kapitza Conductance of Technical Copper with Several Different Surface Preparations, Cryogenics 25, 238 (1985).CrossRefGoogle Scholar
  46. 46.
    R. K. Irey, Heat Transport in Liquid Helium II, in Heat Transfer at Low Temperatures, W. Frost (Ed.), Plenum Press, New York, 1975.Google Scholar
  47. 47.
    D. Gentile and M. X. Francois, Heat Transfer Properties in a Vertical Channel Filled with Saturated and Pressurized Helium II, Cryogenics 21, 234 (1981).CrossRefGoogle Scholar
  48. 48.
    S. W. Van Sciver, Heat Transfer in Superfluid Helium II, in Proceedings of the 8th International Cryogenics Engineering Conference, pp. 228–237, Butterworth Scientific, London, 1980.Google Scholar
  49. 49.
    K. R. Betts and A. C. Leonard, Free Convection Film Boiling from a Flat, Horizontal Surface in Saturated He II, Adv. Cryog. Eng. 21, 282 (1975).Google Scholar
  50. 50.
    A. C. Leonard, Helium II Noisey Film Boiling and Silent Film Boiling Heat Transfer Coefficient Values, in Proceedings of the 3rd International Cryogenics Engineering Conference, pp. 109–114, ILIFFE Science and Tech. Publications, Guildford, Surrey, U.K., 1970.Google Scholar
  51. 51.
    J. S. Goodling and R. K. Irey, Non-Boiling and Film Boiling Heat Transfer to a Saturated Bath of Liquid Helium, Adv. Cryog. Eng. 14, 159 (1969).Google Scholar
  52. 52.
    R. C. Steed and R. K. Irey, Correlation of the Depth Effect on Film Boiling Heat Transfer in Liquid Helium II, Adv. Cryog. Eng. 15, 299 (1970).Google Scholar
  53. 53.
    R. M. Holdredge and P. W. McFadden, Boiling Heat Transfer from Cylinders in Super-fluid Liquid Helium II Bath, Adv. Cryog. Eng. 11, 507 (1966).CrossRefGoogle Scholar
  54. 54.
    W. J. Rivers and P. W. McFadden, Film-Free Convection in Helium II, Trans. ASME, J. Heat Transfer, 88C, 343 (1966).CrossRefGoogle Scholar
  55. 55.
    D. A. Labuntzov and Ye. V. Ametistov, Analysis of Helium II Film Boiling, Cryogenics 19, 401 (1979).CrossRefGoogle Scholar
  56. 56.
    P. L. Bhatnager, E. P. Gross, and M. Krook, A Model for Collision Processes in Gases. L Small-Amplitude Processes in Charged and Neutral One-Component Systems, Phys. Rev. 94, 511 (1954).ADSCrossRefGoogle Scholar
  57. 57.
    A. P. Kryukov and S. W. Van Sciver, Calculation of the Recovery Heat Flux from Film Boiling in Superfluid Helium, Cryogenics 21, 525 (1981).CrossRefGoogle Scholar
  58. 58.
    G. D. Lemieux and A. C. Leonard, Maximum and Minimum Heat Flux in Helium II for a 76.2 inn Diameter Horizontal Wire at Depths of Immersion Up to 70 cm, Adv. Cryog. Eng. 13, 624 (1968).Google Scholar
  59. 59.
    S. W. Van Sciver, Correlation of Time Dependent Recovery from Film Boiling Heat Transfer in He II, Cryogenics 21, 529 (1981).CrossRefGoogle Scholar
  60. 60.
    P. Seyfert, Practical Results on Heat Transfer to Superfluid Helium, in Stability of Superconductors, pp. 53–62, International Institute of Refrigeration Commission A 1/2, Saclay, France, 1981.Google Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Steven W. Van Sciver
    • 1
  1. 1.University of Wisconsin-MadisonMadisonUSA

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