Abstract
Chapter 6 emphasized the physics of He II including heat transport in the laminar flow and the turbulent mutual friction regimes. These mechanisms are fundamental to the behavior of He II, although that discussion mostly described idealized behavior. In the present chapter we will build on the fundamental understanding of He II to treat practical heat and mass transfer problems that may occur in He II systems. In doing so, the concepts already developed must be extended into regimes that are more usable in engineering calculations. To be more specific, the emphasis of Chap. 6 has been to understand the interactive mechanisms and the two fluid nature of He II.
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W. F. Vinen, Mutual Friction in a Heat Current in Liquid Helium II. I. Experiments on Steady State Heat Currents, Proc. R. Soc. London A240, 114 (1957).
V. Arp, Heat Transport through Helium II, Cryogenics 10, 96 (1970).
C. E. Chase, Thermal Conduction in Liquid Helium II I: Temperature Dependence, Phys. Rev. Vol. 127, 361 (1962).
S. W. Van Sciver, Kapitza Conductance of Aluminum and Heat Transport through Sub-cooled He II, Cryogenics 18, 521 (1978).
G. Bon Mardion, et al, Steady State Heat Transport in Superfluid Helium at 1 Bar, Proc. 20th Intern. Cryog. Engn. Conf., IPC Technology Press, London (1978) pp. 214–222.
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).
A. Sato, et al, Normalized Representation for Steady State Heat Transport in a Channel Containing He II Covering Pressure Range up to 1.5 MPa, Proc. 7th Intern. Cryog. Engn. Conf., Beijing, China (2004) pp. 849–52.
A. Sato, et al, Steady State Heat Transport in a Channel Containing He II at High Pressures up to 1.5 MPa, Adv. Cryog. Engn. Vol. 49, 999 (2004).
A. Sato, et al, Temperature Dependence of the Gorter-Mellink Exponent m Measured in a Channel Containing He II, Adv. Cryog. Engn. Vol. 51A, 387 (2006).
M. Maeda, et al, Heat Transport Near the Lambda Line in a Channel Containing He II, Adv. Cryog. Engn. Vol. 51A, 379 (2006).
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.
C. Linnet and T. H. K. Frederking, Thermal Conditions at the Gorter-Mellink Counterflow Limit between 0.01 and 3 Bar, J. Low Temp. Phys. Vol. 21, 447 (1975).
S. R. Breon and S. W. Van Sciver, Boiling in Subcooled and Saturated He II, Advances in Cryogenic Engineering 31, 465 (1986) and Boiling Phenomena in Pressurized He II Confined to a Channel, Cryogenics 26, 682 (1986).
A. C. Leonard and M. A. Clermont, Correlation of the Vaporization Onset Heat Flux for Cylinders in Saturated Liquid Helium II, in Proc. 4th Intern. Cryog. Engn. Conf., IPC Science and Technology Press, London, 1972, pp. 301–306.
J. S. Goodlang and R. K. Irey, Nonboiling and Film Boiling Heat Transfer to a Saturated Bath of Liquid Helium, Adv. Cryog. Eng. 14, 159 (1969).
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).
S. W. Van Sciver and R. L. Lee, Heat Transfer to He II in Cylindrical Geometries, Adv. Cryog. Eng. 25, 363 (1980).
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.
S.W. Van Sciver, Heat Transfer through Extended Surfaces Containing He II, ASME Journal of Heat Transfer Vol. 121, 142 (1999).
A. Bezaguet, J. Casas-Cubillos, P. Lebrun, M. Marquet, L. Tavian, and R. van Weelderen, The superfluid helium model cryoloop for the CERN Large Hadron Collider, Adv. Cryog. Engr. Vol. 39, 649 (1994).
G. Horlitz, T. Peterson and D. Trines, A 2 Kelvin Helium II Distributed Cooling System for the 2x250 Gev e + e- Linear Collider TESLA, Cryogenics Vol. 34 (Supplement), 131 (1994).
S. W. Van Sciver, Heat and Mass Transfer Processes in Two Phase He II/Vapor, Cryogenics Vol. 39, 1039 (1999).
Y. Xiang, B. Peterson, S. Wolff, S. W. Van Sciver, and J. G. Weisend II, Numerical Study of Two-Phase Helium II Stratified Channel Flow with Inclination, IEEE Trans. On Applied Superconductivity Vol. 10, 1530 (2000) and Y. Xiang, N. N. Filina, S. W. Van Sciver, J. G. Weisend II and S. Wolff, Numerical Study of Two-Phase He II Stratified Channel Flow, Adv. Cryog. Engn. Vol. 45B, 1001 (2000).
Ph. Lebrun, L. Serio, L. Tavian and R. van Weelderen, Cooling Strings of Superconducting Devices Below 2 K: the Helium II Bayonet Heat Exchanger, Adv. Cryog. Engn. Vol. 43A, 419 (1998).
B. Rousset, L. Grimaud, A. Gauthier, Stratified Two-Phase Superfluid Helium Flow: ICryogenics Vol. 37, 733 (1997) and L. Grimaud, A. Gauthier, B. Rousset, J. M. Delhaye, Stratified Two-Phase Superfluid Helium Flow: II, Cryogenics Vol. 37, 739 (1997).
L. Dresner, Transient Heat Transfer in Superfluid Helium, Adv. Cryog. Eng. 27, 411 (1982).
L. Dresner, Transient Heat Transfer in Superfluid Helium-Part II, Adv. Cryog. Eng. 29, 323 (1984).
L. Dresner, Similarity Solution of Non-Linear Partial Differential Equations, Pitman Publishing, Boston, MA, 1983.
S. W. Van Sciver, Transient Heat Transport in He II, Cryogenics 19, 385 (1979).
P. Seyfert, J. Lafferranderie, and G. Claudet, Time Dependent Heat Transport in Subcooled Superfluid Helium, Cryogenics 22, 401 (1982).
S. W. Van Sciver, Heat Transport in Forced Flow He II: Analytic Solution, Adv. Cryog. Eng. 29, 315 (1984).
R. Srinvasan and A. Hofmann, Investigations on Cooling with Forced Flow of He II, Cryogenics 25, 641 (1985).
A. Kashani and S. W. Van Sciver, Steady State Forced Convection Heat Transfer in He II, Adv. Cryog. Eng. 31, (1986).
W. W. Johnson and M. C. Jones, Measurements of Axial Heat Transport in Helium II with Forced Convection, Adv. Cryog. Eng. 23, 363 (1978).
S. Fuzier and S. W. Van Sciver, Steady-State Pressure Drop and Heat Transfer in He II Forced Flow at High Reynolds Number, Cryogenics 41, 453 (2001) and S. Fuzier, S. Maier and S. W. Van Sciver, Pressure Drop in Forced Flow He II at High Reynolds Numbers, in Proc. 19th Intern. Cryog. Engn. Conf., Grenoble, France July, 15, 2002, pp. 755–8.
P.L. Walstrom, J.G. Weisend II, J.R. Maddocks, and S.W. Van Sciver, Turbulent Flow Pressure Drop in Various He II Transfer System Components, Cryogenics Vol. 28, 101 (1988).
M.A. Daughterty and S.W. Van Sciver, Pressure Drop Measurements on Cable-in-Conduit Conductors of Various Geometries, IEEE Trans. on Magnetics 27, 2108 (1991).
A. Hofmann, A. Khalil and H.P. Kramer, Operational Characteristics of Loops, Adv. Cryog. Engn. 33, 471 (1988).
B. Rousset, G. Claudet, A. Gauthier, P. Seyfert, P. Lebrun, M. Marquet, R. Van Weelderen and J. Duchateau, Operation of a Forced Flow Superfluid Helium Test Facility and First Results, Cryogenics (Supplement) Vol. 3, 134 (1992).
P. L. Walstrom, Joule-Thomson Effect and Internal Convection Heat Transfer in Turbulent He II Flow, Cryogenics Vol. 28, 151 (1988).
A. Kashani, S.W. Van Sciver, and J.C. Strikwerda, Numerical Solution of Forced Convection Heat Transfer in He II, J. Num Heat Transfer, Part A, Vol. 16, 213 (1989).
L. Bottura and C. Rosso, Finite Element Simulation of Steady-State and Transient Forced Convection in Superfluid Helium, Intern. J. Numerical Methods in Fluids, Vol. 30, 1091 (1999).
Rousset B., Claudet G., Gauthier A., Seyfert P., Martinez A., Lebrun P., Marquet M. and Van Weelderen R., Pressure Drop and Transient Heat Transport in Forced Flow Single Phase Helium II at High Reynolds Numbers, Cryogenics (Supplement) Vol. 34, 317 (1994).
S. Fuzier and S. W. Van Sciver, Experimental Measurements and Modeling of Transient Heat Transfer in Forced Flow He II at High Velocities, Cryogenics Vol. 48, 130 (2008).
R. Maekawa and B. Baudouy, Heat Transfer through Porous Media in the Counterflow Regime, Adv. Cryog. Engn. Vol. 41, 983 (2004).
M. Dalban-Canassy and S. W. Van Sciver, Steady Counterflow He II Heat Transfer Through Porous Media, Adv. Cryog. Engn. Vol. 55, 1327 (2010).
B. Baudouy, et al, Heat Transfer through Porous Media in Static Superfluid Helium, Adv. Cryog. Engn. Vol. 51, 409 (2006).
B. Maytal, J. A. Nissen and S. W. Van Sciver, Iso-chemical Trajectories in the P-T Plane for He II, Cryogenics Vol. 30, 730 (1990).
P. Kittel, Losses in Fountain Effect Pumps, in Proc. 11th Intern. Cryog. Engn. Conf., Butterworth, UK (1986) pp. 317–322.
A.R. Urbach, J. Vorreiter and P. Mason, Design of a Superfluid Helium Dewar for the IRAS Telescope, in Proc. 7th Intern. Cryog. Engn. Conf., IPC Science and Technology Press, UK (1978) pp. 126–133.
D. Petrac and P. V. Mason, Evaluation of Porous-Plug Liquid Separators for Space Helium Systems, in Proc. 7th Intern. Cryog. Engn. Conf., IPC Science and Technology Press, UK (1978) pp. 120–5.
P. L. Kapitza, The Study of Heat Transfer on Helium II, J. Phys. (USSR) 4, 181 (1941).
T. H. K. Frederking, Thermal Transport Phenomena at Liquid Helium II Temperatures, Adv. Cryog. Heat Transfer 64, 21 (1968).
N. S. Snyder, Heat Transport through Helium II: Kapitza Conductance, Cryogenics Vol. 10, 89 (1970).
L. J. Challis, Experimental Evidence for a Dependence of the Kapitza Conductance on the Debye Temperature of a Solid, Phys. Lett. 26A, 105 (1968).
M. Khalatnikov, Introduction to the Theory of Superfluidity, Chap. 111, W. A. Benjamin, New York, 1965.
R. E. Peterson and A. C. Anderson, The Kapitza Thermal Boundary Resistance, J. Low Temp. Phys. 11, 639 (1973).
L. J. Challis, K. Dransfeld, and J. Wilks, Heat Transfer Between Solids and Liquid Helium II, Proc. R. Soc. London A260, 31 (1961).
D. Cheeke and H. Ettinger, Macroscopic Calculation of the Kapitza Resistance Between Solids and Liquid 4He, Phys. Rev. Lett. 37, 1625 (1976).
P. H. E. Meijer and J. S. R. Pert, New Kapitza Heat Transfer Model for Liquid 4He, Phys. Rev. B 22, 195 (1980).
J. Wilks, The Properties of Liquid and Solid Helium, Chap. 14, Clarendon Press, Oxford, 1967.
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).
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).
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).
G. Claudet and P. Seyfert, Bath Cooling with Subcooled Superfluid Helium, Adv. Cryog. Eng. 27, 441 (1981).
S. W. Van Sciver, Developments in He II Heat Transfer and Applications to Superconducting Magnets, Adv. Cryog. Eng. 27, 375 (1981).
A. Kashani and S. W. Van Sciver, Kapitza Conductance of Technical Copper with Several Different Surface Preparations, Cryogenics 25, 238 (1985).
H. P. Kramer, Heat Transfer to Forced Flow Helium II, in Proc. 12 th Intern. Cryog. Engn. Conf., Southampton, UK, Butterworth, UK, 1988, pp. 299–304.
J. G. Weisend II and S. W. Van Sciver, Surface Heat Transfer Measurements in Forced Flow He II, in Superfluid Helium Heat Transfer, ASME HTD-Vol. 134 ed. J. P. Kelly and W. J Schneider, 1990, pp 1–7.
A. C. Leonard, Helium I Noise Film Boiling and Silent Film Boiling Heat Transfer Coefficient Values, in Proc. 3rd Intern. Cryog. Engn. Conf., pp. 109–114, ILIFFE Science and Tech. Publications, Guilderford, Surrey, U.K., 1970.
R. K. Irey, Heat Transport in Liquid Helium II, in Heat Transfer at Low Temperatures, W. Frost (Ed.), Plenum Press, New York, 1975.
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).
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).
R. C. Steed and R. K. Irey, Correlation of the Depth Effect on Film Boiling Heat Transfer in Liquid Helium I, Adv. Cryog. Eng. 15, 299 (1970).
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).
M. Nozawa, N. Kimura, M. Murakami and S. Takada, Thermo-fluid Dynamics of Several Film Boiling Modes in He II in the Pressure Range between Atmospheric Pressure and Saturated Vapor Pressure, Cryogenics Vol. 49, 583 (209).
S. Takada, M. Murakami, and N. Kimura, Heat Transfer Characteristics of Four Film Boiling Modes Around a Horizontal Cylindrical Heater in He II, Adv. Cryog. Engn. Vol. 55A, 1355 (2010).
W. J. Rivers and P. W. McFadden, Film-Free Convection in Helium II, Trans. ASME, J. Heat Transfer, 88C, 343 (1966).
D. A. Labuntzov and Ye. V. Ametistov, Analysis of Helium II Film Boiling, Cryogenics 19, 401 (1979).
P. L. Bhatnager, E. P. Gross, and M. Krook, A Model for Collision Processes in Gases. I. Small-Amplitude Processes in Charged and Neutral One-Component Systems, Phys. Rev. 94, 511 (1954).
A. P. Kryukov and S. W. Van Sciver, Calculation of the Recovery Heat Flux from Film Boiling in Superfluid Helium, Cryogenics 21, 525 (1981).
G. D. Lemieux and A. C. Leonard, Maximum and Minimum Heat Flux in Helium II for a 76.2 μm Diameter Horizontal Wire at Depths of Immersion Up to 70 cm, Adv. Cryog. Eng. 13, 624 (1968).
S. W. Van Sciver, Correlation of Time Dependent Recovery from Film Boiling Heat Transfer in He II, Cryogenics 21, 529 (1981).
Further Readings
F. P. Incropera and D. P. Dewitt, Fundamentals of Heat Transfer, Wiley, New York, 1981.
G. E. Myers, Analytical Methods in Conduction Heat Transfer, McGraw-Hill, New York, 1971.
S. W. Van Sciver, He II (Superfluid Helium), Chapter 10 in Handbook of Cryogenic Engineering, ed. J. G. Weisend II, Taylor & Francis, Washington, DC (1998), pp. 445–483.
J. Wilks, The Properties of Liquid and Solid Helium, Chap. 14, Clarendon Press, Oxford, 1967.
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Van Sciver, S.W. (2012). He II Heat and Mass Transfer. In: Helium Cryogenics. International Cryogenics Monograph Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9979-5_7
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