Skip to main content
SpringerLink
Log in

Combined free and forced convection flow in a cooled vertical duct with internal solidification

Gemischte Konvektion in einem gekühlten, vertikalen Kanal mit Eisschichtbildung

  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

The effect of mixed convection flow on the shape of the frozen crust in a cooled vertical channel was investigated numerically. For the prediction of the ice-layer thickness a simple numerical model which is based on the boundary layer equations was used. It can be seen that in case of assisting mixed convection flow the heat transfer at the solid crust increases because of inreasing velocity near the solid-liquid interface. On the other hand this increase of the velocity near the solid-liquid interface can lead to flow separation in the core region of the channel because of continuity of mass. By comparing the numerically obtained results for aiding mixed flow with measurements of Campbell and Incropera [10] good agreement can be observed.

In case of opposing mixed flow it can be shown that flow separation might occur near the solid-liquid interface. This can result in a wave-like structure of the ice-layer.

Zusammenfassung

Überlagerte freie und aufgezwungene Konvektionsströmung in einem gekühlten vertikalen Kanal mit Eisschichtbildung an den Wänden ist numerisch untersucht worden. Grundlage der Eisschichtberechnung ist das einfache numerische Modell der Grenzschichtgleichungen. Für den Fall der dem Gravitationsvektor gleichgerichteten, gemischten Konvektion wird eine Verstärkung des Wärmeübergangs beobachtet, da die Strömungsgeschwindigkeit in der Nähe der Phasengrenze zunimmt. Aufgrund der Massenerhaltung kann es bei einer ausgeprägten Geschwindigkeitszunahme in der Nähe der Phasengrenze zu Rückströmungen in der Kanalmitte kommen. Die numerischen Ergebnisse zeigen gute Übereinstimmung mit Messungen von Campbell und Incropera [10].

Für den Fall der dem Gravitationsvektor entgegengerichteten Strömung kann es zur Strömungsablösung nahe der Phasengrenze kommen, die eine wellenartige Eisschicht bewirkt.

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 (T W −T F )/(T F −T 0)k s /k

F :

modified stream function

Gr 4h :

Grashof number based on 4h, [∣ρ(T F )−ρ(T 0)∣/ρ(T 0)]g(4h)3/v 2

Gr h :

Grashof number based onh, [∣ρ(T F )−ρ(T 0)∣/ρ(T 0)]gh 3/v 2

H :

temperature function, defined by Eq. (14)

h :

distance from centerline to wall

k :

thermal conductivity

Nu :

Nusselt number based on 4δ

P :

pressure

Pr :

prandtl number

Re 4h :

Reynolds number based on 4h, ū 04h/v

Re h :

Reynolds number based onh, ū 0 h/v

Ri 4h :

Richardson number based on 4h,Gr 4th /Re 24h

Ri h :

Richardson number based onh,Gr h /Re 2 th

T :

temperature

T b :

bulk temperature,\(\int\limits_0^\delta {Tudy/} \int\limits_0^\delta {udy} \)

T F :

freezing temperature of the liquid

T 0 :

constant inlet temperature of the liquid

T W :

wall temperature

u, v :

velocity components

ū0 :

mean axial velocity at the inlet

x, y :

coordinates

β i :

constants for the density-temperature relationship for water

δ:

distance between centerline and solid-liquid interface

θ:

dimensionless temperature, (T−T F )/(T 0−T F )

θ s :

dimensionless temperature in the solid,(T s −T F )/(T W −T F )

ν:

kinematic viscosity

ρ:

density

ψ:

stream function

0:

at the entrance

d :

dynamic

s :

solid

w :

at the wall

*, ∼:

dimensionless quantity

−:

mean 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) 233–240

    Google Scholar 

  3. Bilenas, J. A.;Jiji, L. M.: Numerical solution of a non-linear free boundary problem of axisymmetric fluid flow in tubes with surface solidification. Proc. 4th Int. Heat Transfer Conf. 1, Paris, Amsterdam: Elsevier Publishing Company, Cu 2. 1 (1970) 1–11

    Google Scholar 

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

    Google Scholar 

  5. 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 

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

    Google Scholar 

  7. Weigand, B.;Beer, H.: Heat transfer and solidification of a laminar liquid flow in a cooled parallel plate channel. Wärme- und Stoffübertragung 26 (1991) 233–240

    Google Scholar 

  8. Weigand, B.;Höhn, W.;Beer, H.: A perturbation analysis of transient freezing of a laminar liquid flow in a cooled two-dimensional channel. J. Heat Transfer 115 (1993) 294–301

    Google Scholar 

  9. 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 

  10. Campbell, J. S.;Incropera, F. P.: Mixed convection solidification in a vertical channel. proc. 9th Int. Heat Transfer Conf. 4, Jerusalem, 12PC17 (1990) 311–316

    Google Scholar 

  11. Cebeci, T.;Bradshaw, P.: Physical and Computational Aspects of Convective Heat Transfer, Springer, New York (1984)

    Google Scholar 

  12. Fujii, T.: Fundamentals of Free Convection Heat Transfer (in Japanese) Progress in Heat Transfer Engineering 3 (1974) 66

    Google Scholar 

  13. Cheng, K. C.;Takeuchi, M.: Transient natural convection of water in a horizontal pipe with constant cooling rate through 4°C. J. Heat Transfer 98 (1976) 581–587

    Google Scholar 

  14. Landolt-Börnstein, Zahlenwerte und Funktionen. Band II, Teil 1, Springer (1971) 36–37

  15. Reyhner, T. A.;Flügge-Lotz, I.: The interaction of a shock wave with a laminar boundary layer. Int. J. Nonlinear Mech. 3 (1968) 173–199

    Article  Google Scholar 

  16. Cebeci, T.;Lee, K. H.;Wang, S.;Chang, K. C.: Heat Transfer in vertical duct flows. Math. Eng. Ind. 1 (1987) 67–81

    Google Scholar 

  17. Kwon, O. K.;Pletcher, R. H.;Lewis, J. P.: Prediction of sudden expansion flows using the boundary-layer equations. J. Fluid Engng. 106 (1984) 285–291

    Google Scholar 

  18. Aung, W.;Worku, G.: Developing flow and flow reversal in a vertical channel with asymmetric wall temperature. J. Heat Transfer 108 (1986) 299–304

    Google Scholar 

  19. Morton, B.;Ingham, D. B.;Keen, D. J.;Heggs, P. J.: Recirculating combined convection in laminar pipe flow. J. Heat Transfer 111 (1989) 106–113

    Google Scholar 

  20. Gilpin, R. R.: Ice formation in a pipe containing flows in the transition and turbulent regimes. J. Heat Transfer 103 (1981) 363–369

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ABB Power Generation Ltd, CH-5041, Baden, Switzerland

    B. Weigand

  2. Institut für Technische Thermodynamik, Technische Hochschule Darmstadt, Petersen Str. 30, D-64287, Darmstadt, Germany

    O. Neumann,  T. Strohmayer &  H. Beer

Authors
  1. B. Weigand
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. Neumann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. Strohmayer
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. 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., Neumann, O., Strohmayer, T. et al. Combined free and forced convection flow in a cooled vertical duct with internal solidification. Heat and Mass Transfer 30, 349–359 (1995). https://doi.org/10.1007/BF01463926

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01463926

Keywords

Search

Navigation