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Inward solidification of a superheated liquid in a cooled horizontal tube

Nach innen gerichtete Erstarrung einer überhitzten Flüssigkeit in einem gekühlten waagerechten Rohr

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Abstract

Inward solidification has been studied experimentally and analytically under conditions where the liquid phase is above the fusion temperature (i.e., superheated). The liquid was housed in a horizontal circular tube in which the surface was maintained at a uniform, time-invariant temperature during test runs. Three phase change materials (n-heptadecane,n-octadecane, and water) were used in the tests. Both analysis and experiments have established that for inward solidification, natural convection in a superheated liquid is not important in controlling the solidliquid interface motion for Stefan numbers less than unity. The interface velocity is determined primarily by the thermal resistance across the solid layer. Good agreement has been obtained between experimentally measured and analytically predicted solid-liquid interface positions when the density differences between the phases were accounted for.

Zusammenfassung

Innere Erstarrung, bei der die Temperatur der flüssigen Phase größer als die Schmelztemperatur ist, wurde experimentell und analytisch untersucht. Die Flüssigkeit war eingeschlossen in einem horizontalen Kreisrohr, dessen Wand während der Versuche auf gleichförmiger, stationärer Temperatur gehalten wurde. Drei Stoffe wurden für die Untersuchungen verwendet:n-Heptadekan,n-Oktadekan und Wasser. Sowohl die Analyse als auch die Versuche zeigten, daß bei nach innen fortschreitender Erstarrung die freie Konvektion in der überhitzten Flüssigkeit nicht wesentlich die Bewegung der fest-flüssigen Grenzfläche beeinflußt, wenn die Stefan-Zahl kleiner als Eins ist. Die Grenzflächengeschwindigkeit wird in erster Linie vom thermischen Widerstand der erstarrten Schicht bestimmt. Gute Übereinstimmung zwischen experimentell gemessener und analytisch bestimmter Lage der fest-flüssigen Grenzschicht wurde erzielt, wenn die Dichteunterschiede der beiden Phasen berücksichtigt wurde.

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Abbreviations

c :

specific heat

Fo:

Fourier number,α 3 t/R 20

Gr :

Grashof number,gβ(T f -T b )(2R)3 /v 2

h :

heat transfer coefficient

Δh f :

latent heat of fusion

k :

thermal conductivity

Nu :

Nusselt number,2Rh/k l

Pr :

Prandtl number,μ l c l /k l

r :

radial distance

R :

radial position of the solid-liquid interface

Ra :

Rayleigh number,Gr·Pr

R 0 :

inside radius of the tube

R * :

dimensionless radial position of the solid-liquid interface,R/R 0

Ste :

Stefan number,c 3(T f -T w )/Δh f

T :

temperature

t :

time

α :

thermal diffusivity

β :

coefficient of thermal expansion

θ :

dimensionless temperature, (T-T w /(T f-T w)

τ :

dimensionless time,Ste Fo

ϱ :

density

μ :

dynamic viscosity

μ :

kinematic viscosity

ξ :

dimensionless radiusr/R o

η :

transformation variable defined by Eq. (12)

b :

refers to bulk

f :

refers to fusion or solid-liquid interface

l :

refers to liquid

0:

refers to initial state

s :

refers to solid

w :

refers to wall

References

  1. London, A. L.; Seban, R. A.: Rates of ice formation. Trans. ASME 65 (1943) 771–778

    Google Scholar 

  2. Megerlin, F.: Geometrisch eindimensionale Wärmeleitung beim Schmelzen und Erstarren. Forsch. Ing.-Wes. 34 (1968) 40–46

    Google Scholar 

  3. Stephan, K.; Holzknecht, B.: Wärmeleitung beim Erstarren geometrisch einfacher Körper. Wärme- Stoffübertrag. 7 (1974) 200–207

    Google Scholar 

  4. Shamsundar, N.; Sparrow, E. M.: Storage of thermal energy by solid-liquid phase change-temperature drop and heat flux. ASME J. Heat Transfer 96 (1974) 541–543

    Google Scholar 

  5. Riley, D. S.; Smith, F. T.; Foots, G.: The inward solidification of spheres and circular cylinders. Int. J. Heat Mass Transfer 17 (1974) 1507–1515

    Google Scholar 

  6. Huang, C.-L.; Shih, Y.-P.: A perturbation method for spherical and cylindrical solidification. Chem. Eng. Sci. 30 (1975) 876–906

    Google Scholar 

  7. Duda, J. L.; Malone, M. F.; Notter, R. H.: Analysis of twodimensional diffusion-controlled moving boundary problems. Int. J. Heat Mass Transfer 18 (1975) 901–910

    Google Scholar 

  8. Goodling, J. S.; Khader, M. S.: Results of the numerical solution for outward solidification with flux boundary conditions. ASME J. Heat Transfer 97 (1975) 307–309

    Google Scholar 

  9. Horsthemke, A.; Marshall, E.: Speicherung von thermischer Energie in Salz- und Metallschmelzen. Brennst.-Wärme-Kraft 28 (1) (1976) 18–22

    Google Scholar 

  10. Patel, G. S.; Goodling, J. S.; Khader, M. S.: Experimental results of two-dimensional inward solidification. Heat Transfer 3 (1978) 313–317

    Google Scholar 

  11. Ito, S.; Miura, N.; Watanbe, F.: An experimental study on a capsule-type thermal energy storage. Proceedings of the 17th Japanese Heat Transfer Conference 1980

  12. Deaver, F. K.; Eckert, E. R. G.: An interferometric investigation of convective heat transfer in a horizontal cylinder with wall temperature increasing at a uniform rate. Heat Transfer, Vol. 4, Paper NC 1.1. Amsterdam: Elsevier Publishing 1970

    Google Scholar 

  13. Hauf, W.; Grigull, U.: Instationärer Wärmeübergang durch freie Konvektion in horizontalen zylindrischen Behältern. Heat Transfer Vol. 4, Paper NC1. 3, Amsterdam: Elsevier Publishing 1970

    Google Scholar 

  14. Hauf, W.; Grigull, U.: Instationärer Wärmeübergang in horizontalen zylindrischen Behältern. Wärme- Stoffübertrag. 8 (1975) 57–68

    Google Scholar 

  15. Sparrow, W. M.; Ramsey, J. W.; Kemink, R. G.: Freezing controlled by natural convection. ASME J. Heat Transfer 101 (1979) 578–584

    Google Scholar 

  16. Takeuchi, M.; Cheng, K. C.: Transient natural convection in horizontal cylinders with constant cooling rate. Wärme- Stoffübertrag. 9 (1976) 215–225

    Google Scholar 

  17. Bathelt, A. G.; van Buren, P. D.; Viskanta, R.: Heat transfer during solidification around a cooled horizontal cylinder. AIChE Symp. Ser. 75 (1979) 103 -111

    Google Scholar 

  18. Goodman, T. R.: Application of integral methods to transient nonlinear heat transfer. In: T. F. Irvine, Jr. and J. P. Hartnett, (eds.): Advances in Heat Transfer. Vol. 1, pp. 51–122. New York: Academic Press 1964

    Google Scholar 

  19. Saitoh, T.: Numerical method for multi-dimensional freezing problems in arbitrary domains. ASME J. Heat Transfer 100 (1978) 294–299

    Google Scholar 

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Authors and Affiliations

  1. Heat Transfer Laboratory School of Mechanical Engineering, Purdue University, 47907, West Lafayette, Indiana, USA

    R. Viskanta & C. Gau

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  1. R. Viskanta
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  2. C. Gau
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Viskanta, R., Gau, C. Inward solidification of a superheated liquid in a cooled horizontal tube. Wärme- und Stoffübertragung 17, 39–46 (1982). https://doi.org/10.1007/BF01686964

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