Skip to main content
SpringerLink
Log in

Transient freezing of liquids in forced laminar flow inside a parallel plate channel

Die zeitliche Entwicklung der Erstarrungsfronten in einem ebenen, gekühlten Kanal mit laminarer Durchströmung

  • Published:
Wärme - und Stoffübertragung Aims and scope Submit manuscript

Abstract

A simple analytical approximative solution was given for calculating the time dependent development of the ice-layers at the cooled walls inside a parallel plate channel. By ignoring the effect of acceleration, resulting from converging ice-layers in the axial direction, an analytical solution for the variation of the ice-layer thickness with time and axial position could be obtained. The approximative solution was checked by numerical calculations and good agreement was found.

Zusammenfassung

Es wurde ein analytisches Näherungsverfahren entwickelt, das es ermöglicht, die zeitliche Entwicklung der Erstarrungsfronten im gekühlten, ebenen Kanal zu bestimmen. Die Methode liefert unter Vernachlässigung der Beschleunigungsterme durch die konvergenten Eisschichten eine exakte Lösung der Phasengrenzbeziehung. Das Näherungsverfahren wurde mittels numerischer Berechnungen überprüft und stimmt bis zu Wandunterkühlungsverhältnissen vonB=10 sehr gut mit der numerischen Lösung überein.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

a :

thermal diffusivity

B :

dimensionless freezing parameter

D :

hydraulic diameter:D=4 h

f :

function according to Eq. (27)

F o :

Fourier number

h :

distance from centerline to the wall

k :

thermal conductivity

P :

pressure

Pr :

Prandtl number

r s :

heat of fusion

Re h :

Reynolds number based onh

Re D :

Reynolds number based on the hydraulic diameter

T :

temperature

T F :

freezing temperature of the liquid

T o :

constant inlet temperature of the liquid

t :

time

u, v :

fluid velocity components

ū :

mean axial velocity

ū o :

mean axial velocity at the entrance

x, y :

coordinates

δ :

distance from centerline to the liquid-solid interface

δ s :

steady state distance from centerline to the liquid-solid interface

ϱ :

density

τ :

dimensionless time

ν :

kinematic viscosity

ξ :

integral coordinate

s :

solid

L :

liquid

w :

at the wall

0:

at the entrance

∼:

dimensionless quantity

References

  1. Zerkle, R. D.; Sunderland, J. E.: The effect of liquid solidification in a tube upon laminar-flow heat transfer and pressure drop. J. Heat Transfer 90 (1968) 183–190

    Google Scholar 

  2. Özisik, M. N.; Mulligan, J. C.: Transient freezing of liquids in forced flow inside circular tubes. J. Heat Transfer 91 (1969) 385–390

    Google Scholar 

  3. Bilenas, J. A.; Jiji, L. M.: Numerical solution of a nonlinear free boundary problem of axisymmetric fluid flow in tubes with surface solidification. Proc. 4th Int. Heat Transfer Conference 1 Paris. Amsterdam: Elsevier 1970 Cu 2.1, 1–11

  4. Chida, K.: Heat Transfer in steady laminar pipe flow with liquid solidification. Heat Transfer: Jap. Res. 81 (1983) 81–94

    Google Scholar 

  5. Hwang, G. J.; Sheu, J. P.: Liquid solidification in combined hydrodynamic and thermal entrance region of a circular tube. Canadian J. Chem. Eng. 54 (1976) 66–71

    Google Scholar 

  6. Lee, D. G.; Zerkle, R. D.: The effect of liquid solidification in a parallel plate channel upon laminar-flow heat transfer and pressure drop. J. Heat Transfer 91 (1969) 583–585

    Google Scholar 

  7. Cheng, K. C.; Wong, L. S.: Liquid solidification in a convectively cooled parallel-plate channel. Canadian J. Chem. Eng. 55 (1977) 149–155

    Google Scholar 

  8. Kikuchi, Y.; Shigemasa, Y., Ogata, T.: Steady-state freezing of liquids in laminar flow between two parallel plates. J. Nucl. Sci. Technol. 23 (1986) 43–55

    Google Scholar 

  9. Weigand, B.; Beer, H.: Liquid solidification in a parallel plate channel upon laminar-flow heat transfer: stationary case. Wärme-Stoffübertrag. 26 (1991) 233–240

    Google Scholar 

  10. Bennon, W. D.; Incropera, F. P.: Developing laminar mixed convection with solidification in a vertical channel. J. Heat Transfer 110 (1988) 410–415

    Google Scholar 

  11. Cebeci, T.; Chang, K. C.: A general method for calculating momentum and heat transfer in laminar and turbulent duct flows. Numerical Heat Transfer 1 (1977) 39–68

    Google Scholar 

  12. Cebeci, T.; Bradshaw, P.: Physical and computational aspects of convective heat transfer. New York: Springer 1984

    Google Scholar 

  13. Shah, R. K.; London, A. L.: Laminar flow forced convection in ducts. Advances in Heat Transfer. New York: Academic Press 1978

    Google Scholar 

  14. Sampson, P.; Gibson, R. D.: A mathematical model of nozzle blockage by freezing. Int. J. Heat Mass Transfer (1981) 231–241

  15. Cebeci, T.; Bradshaw, P.: Momentum transfer in boundary layers. New York: McGraw-Hill 1977

    Google Scholar 

  16. Batchelor, G. K.: An introduction to fluid dynamics. Cambridge: Cambridge University Press 1985

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Technische Thermodynamik, Petersenstraße 30, 6100, Darmstadt

    B. Weigand & H. Beer

Authors
  1. B. Weigand
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Beer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weigand, B., Beer, H. Transient freezing of liquids in forced laminar flow inside a parallel plate channel. Wärme- und Stoffübertragung 27, 77–84 (1992). https://doi.org/10.1007/BF01590122

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01590122

Keywords

Search

Navigation