Wärme - und Stoffübertragung

, Volume 1, Issue 3, pp 190–196 | Cite as

Natural convection heat transfer through an enclosed horizontal layer of supercritical carbon dioxide

  • Erich W. P. Hahne
Article
  • 124 Downloads

Abstract

In natural convection heat transfer through a thin horizontal layer of carbon dioxide, maxima in the equivalent thermal conductivities are obtained in the vicinity of the respective pseudocritical temperatures at pressures of 75.8, 89.6 and 103.4 bar. The maxima are the more pronounced, the closer the critical point is approached.

Comparison of experimental results with Nusselt equations shows good agreement except for the immediate vicinity of the pseudocritical temperature.

In visual observations a distinct change in flow structure appears in the immediate vicinity of the pseudocritical temperature. A steady state polygon pattern and a boiling-like action could not be observed in this geometry.

Keywords

Heat Transfer Steady State Convection Thermal Conductivity Carbon Dioxide 

Nomenclature

A

area of the heating or cooling plate

C

constant in the correlation

g

acceleration of gravity

h

heat transfer coefficient

k

thermal conductivity of fluid in the gap

ke

equivalent thermal conductivity

m, n

exponents of dimensionless numbers

q

heat flux

TC,PC

absolute temperature; critical C, pseudocritical PC

Gr

Grashof number (ϑhϑc)δ3/ν2

Nu

Nusselt numberhδ/k

Pr

Prandtl numberν/α

α

thermal diffusivity

β

coefficient of volume expansion

δ

width of gap

ϑc,h

temperature of cooling (c)-, heating (h)-plate

ϑm

arithmetic mean temperature (ϑc+ϑh)/2

ν

kinematic viscosity

ϱc,h

fluid density at the temperature of the cooling (c)- or heating (h)-plate

φ

heat flow rate through the gap

Zusammenfassung

Beim Wärmetransport durch freie Konvektion in einer dünnen waagerechten Schicht von Kohlendioxid ergaben sich Maxima der scheinbaren Wärmeleitfähigkeit in der Nähe der pseudokritischen Temperaturen bei Drükken von 75,8, 89,6 und 103,4 bar. Die Maxima sind um so ausgeprägter, je mehr man sich dem kritischen Punkt nähert.

Ein Vergleich der Versuchsergebnisse mit Nusseltbeziehungen ergibt gute Übereinstimmung außer in unmittelbarer Umgebung der pseudokritischen Temperatur. Direkte Beobachtungen der Konvektionsmuster zeigen in unmittelbarer Umgebung der pseudokritischen Temperatur eine deutliche Strukturänderung. Ein stationäres Zellmuster und siedeähnliche Vorgänge konnten in dieser Anordnung nicht beobachtet werden.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Schmidt, E., E. Eckert u.U. Grigull: Wärmetransport durch Flüssigkeiten in der Nähe ihres kritischen Zustandes. Jahrb. dtsch. Luftfahrtforschung. Bd. 2 (1939), S. 53/58 and AAF Translation Nr. 527 Air Material Command, Wright Field, Dayton, Ohio.Google Scholar
  2. [2]
    Deissler, R. G.: Heat transfer and fluid friction for fully developed turbulent flow of air and supercritical water with variable fluid properties. J. Heat Transfer ASME Vol. 76 (1954) No. 1, p. 73/85.Google Scholar
  3. [3]
    Goldmann, K.: Heat transfer to supercritical water and other fluids with temperature dependent properties. Chem. Engng. Progr. Sympos. Ser. Nuclear Eng. Vol. 50 (1954) No. 11, p. 105/113.Google Scholar
  4. [4]
    Doughty, D. L., andR. M. Drake Jr.: Free convection heat transfer from a horizontal right circular cylinder to Freon 12 near the critical state. J. Heat Transfer ASME Vol. 78 (1956) No. 4, p. 1843/1850.Google Scholar
  5. [5]
    Goldmann, K.: Special heat transfer phenomena for supercritical fluids. Nuclear Development Associates Inc. Report NDA-2-31 (1956).Google Scholar
  6. [6]
    Bringer, R. P., andJ. M. Smith: Heat transfer in the critical region. J. Americ. Inst. Chem. Engrs. Vol. 3 (1957) No. 1, p. 49/55.Google Scholar
  7. [7]
    Powell, W. B.: Heat transfer to fluids in the region of the critical temperature. Jet Propulsion Vol. 27 (1957) No. 7, p. 776/783.Google Scholar
  8. [8]
    Dickinson, N. L., andC. P. Welch: Heat transfer to supercritical water. J. Heat Transfer ASME Vol. 80 (1958) No. 2, p. 746/752.Google Scholar
  9. [9]
    Del Bene, J. V., andJ. P. Barger: Heat transfer to supercritical Freon 12. Massachusetts Inst. Technology Contr. Nonr 1841 — (14) DSR Proj. Nr. 7484. Techn. Rep. to Office of Naval Research 1959.Google Scholar
  10. [10]
    Holman, J. P., andJ. H. Boggs: Heat transfer to Freon 12 near the criticla state in a natural-circulation loop. J. Heat Transfer ASME Vol. 81 (1959) No. 3, p. 221/226.Google Scholar
  11. [11]
    Schitzmann, M. E.: Heat transfer to water, oxygen and carbon dioxide in the approximately critical range. Teploenergetika Tom. 1 (1959) No. 1, S. 68/72, transl. Eng. RTS 1229.Google Scholar
  12. [12]
    Griffith, J. D., andR. H. Sabersky: Convection in a fluid at supercritical pressures. ARS J. Vol. 30 (1960) No. 3, p. 289/290.Google Scholar
  13. [13]
    Bonilla, C. F., andA. Sigel: High intensity natural convection heat transfer near the critical point. Chem. Engng. Progr. Sympos. Ser. Vol. 57 (1961) No. 32, p. 87/95.Google Scholar
  14. [14]
    Hsu, Y., andJ. M. Smith: The effect of density variation on heat transfer in the critical region. J. Heat Transfer ASME Vol. 83 (1961) No. 2, p. 176/182.Google Scholar
  15. [15]
    Fritsch, C. A., andR. J. Grosh: Free convective heat transfer to a supercritical fluid. Int'l. Developments in Heat Transfer. 1961 ASME Conference Part V, p. 1010/1016.Google Scholar
  16. [16]
    Goldmann, K.: Heat transfer to supercritical water at 5000 psi flowing at high mass flow rates through round tubes. Int'l. Developments in Heat Transfer. 1961 ASME Conference Part III, p. 561/568.Google Scholar
  17. [17]
    Koppel, L. B., andJ. M. Smith: Turbulent heat transfer in the critical region. Int'l. Developments in Heat Transfer. 1961 ASME Conference, Part III, p. 585/590.Google Scholar
  18. [18]
    Hendricks, R. C., et al.: Correlation of hydrogen heat transfer in boiling and supercritical pressure states. ARS J. Vol. 32 (1962) No. 2, p. 244/250.Google Scholar
  19. [19]
    Fritsch, C. A., andR. J. Grosh: Free convective heat transfer to supercritical water, experimental measurements. J. Heat Transfer ASME Vol. 85 (1963) No. 4, p. 289/294.Google Scholar
  20. [20]
    Simon, H. A., andE. R. G. Eckert: Laminar free convection in carbon dioxide near its critical point. Int. J. Heat and Mass Transfer Vol. 6 (1963) No. 8, p. 681/690.Google Scholar
  21. [21]
    Harden, D. G., andJ. H. Boggs: Transient flow characteristics of a natural circulation loop operated in the critical region. Proc. Heat Transfer and Fluid Mech. Inst. 1964, p. 38/50.Google Scholar
  22. [22]
    Hahne, E.: Wärmetransport durch natürliche Konvektion in Medien nahe ihrem kritischen Zustand. Int. J. Heat and Mass Transfer Vol. 8 (1965) No. 3, p. 481/497.Google Scholar
  23. [23]
    Larson, J. R., andR. J. Schoenhals: Turbulent free convection in near critical water. ASME Publication 65-H-57 (1965).Google Scholar
  24. [24]
    Nishikawa, K., andK. Miyabe: On the boiling-like phenomena at supercritical pressures. Memoirs of the Faculty of Eng. Kyushu University Vol. 25 (1965) No. 1, p. 1/25.Google Scholar
  25. [25]
    Swenson, H. S., J. R. Carver, andC. R. Kakarola: Heat transfer to supercritical water in smooth-bore tubes. J. Heat Transfer ASME Vol. 87 (1965) No. 4, p. 477/484.Google Scholar
  26. [26]
    Knapp, K. K., andR. H. Sabersky: Free convection heat transfer to carbon dioxide near the critical point. Int. J. Heat and Mass Transfer Vol. 9 (1966) No. 1, p. 41/51.Google Scholar
  27. [27]
    Sabersky, R. H.: Recent developments in convective heat transfer. ARS J. Vol. 29 (1959) No. 5, p. 325/331.Google Scholar
  28. [28]
    Gröber, Erk, andGrigull: Fundamentals of heat transfer. pp. 313, 3rd edition rev. byU. Grigull. McGraw Hill Book Co., Inc. New York 1961.Google Scholar
  29. [29]
    Mull, W., andH. Reiher: Der Wärmeschutz von Luftschichten. Beihefte zum Gesundheitsingenieur, Reihe 1, Heft 28 (1930).Google Scholar
  30. [30]
    Schmidt, R. J., andO. A. Saunders: On the motion of a fluid heated from below. Proc. Roy. Soc. Vol. A 165 (1938), No. A 921, p. 216/228.Google Scholar
  31. [31]
    Jakob, M., andP. C. Gupta: Heat transfer by free convection through liquid between two horizontal surfaces. Chem. Engng. Progr. Sympos. Ser. Vol. 50 (1954) No. 9, p. 15.Google Scholar
  32. [32]
    Silveston, P. L.: Wärmedurchgang in waagerechten Flüssigkeitsschichten. Forsch. Ing. Wes. Bd. 24 (1958) Nr. 1 u. Nr. 2, S. 29/32 u. S. 59/69.Google Scholar
  33. [33]
    Globe, S., andD. Dropkin: Natural-convection heat transfer in liquids confined by two horizontal plates and heated from below. J. Heat Transfer ASME Vol. 81 (1959) No. 1, p. 24/28.Google Scholar
  34. [34]
    Dropkin, D., andE. Somerscales: Heat transfer by natural convection in liquids confined by two parallel plates which are inclined at various angles with respect to the horizontal. J. Heat Transfer ASME Vol. 87 (1965) No. 1, p. 77/84.Google Scholar
  35. [35]
    Sengers, J. V.: Behaviour of viscosity and thermal conductivity of fluids near the critical point. Preprint of a paper to be published in Proc. Conf. Phenomena in the Neighborhood of the critical point, NBS Wash. 1965.Google Scholar
  36. [36]
    Sengers, J. V.: Thermal conductivity and viscosity of simple fluids. Int. J. Heat and Mass Transfer Vol. 8 (1965) No. 8, p. 1103/1116.Google Scholar
  37. [37]
    Thomson, J.: On a changing tessellated structure in certain liquids. Proc. Glasgow Philos. Soc. Vol. 13 (1882), p. 464/470.Google Scholar
  38. [38]
    Bénard, H.: Les turbillons cellaires dans une nappe liquide transportant de la chaleur par convection en regime permanent. Ann. Chim. et Phys. Tom. 23 (1901) No. 7, p. 62/144.Google Scholar
  39. [39]
    Walker, G. T., andA. C. Philips: The forms of stratified clouds. Quart. J. Roy. Meteorological Soc. Vol. 58 (1932) No. 243, p. 23/30.Google Scholar
  40. [40]
    Mal, S.: Forms of stratified clouds. Beitr. z. Physik d. freien Atmosphäre Bd. 17 (1930) Nr. 1, S. 40/68.Google Scholar
  41. [41]
    Graham, A.: Shear Patterns in an unstable layer of air. Philos. Trans. Roy. Soc. Vol. A 232 (1933) No. A 714, p. 285/296.Google Scholar
  42. [42]
    Chandra, K.: Instability of fluids heated from below. Proc. Roy. Soc. Vol. A 164 (1938) No. A 917, p. 231/242.Google Scholar
  43. [43]
    De Graaf, J. G. A., andE. F. M. van der Held: The relation between the heat transfer and the convection phenomena in enclosed plane air layers. Appl. sci. Res. Hague Vol. A 3 (1953), p. 393/409.Google Scholar
  44. [44]
    v. Tippelskirch, H.: Über Konvektionszellen, insbesondere im flüssigen Schwefel. Beitr. z. Physik d. Atmosphäre Bd. 29 (1956) Nr. 1, S. 37/54.Google Scholar
  45. [45]
    Linde, H., andK. Loeschke: Rollzellen und Oszillation beim Wärmeübergang zwischen Gas und Flüssigkeit. Chemie Ing. Techn. Bd. 39 (1967) Nr. 2, S. 65/74.Google Scholar
  46. [46]
    Federico, I. di, andF. P. Foraboschi: A contribution to the study of free convection in a fluid layer heated from below. Int. J. Heat and Mass Transfer Vol. 9 (1966) No. 12, p. 1351/1360.Google Scholar
  47. [47]
    Mori, Y., andY. Uchida: Forced convective heat transfer between horizontal flat plates. Int. J. Heat and Mass Transfer Vol. 9 (1966) No. 8, p. 803/817.Google Scholar
  48. [48]
    Ostrach, S.: Convection phenomena in fluids heated from below. J. Heat Transfer ASME Vol. 79 (1957) No. 1, p. 299/305.Google Scholar
  49. [49]
    Sobermann, R. K.: Effects of lateral boundaries on natural convection. J. Appl. Physics Vol. 29 (1958), p. 872/873.Google Scholar

Copyright information

© Springer-Verlag 1968

Authors and Affiliations

  • Erich W. P. Hahne
    • 1
  1. 1.München

Personalised recommendations