Heat and Mass Transfer

, Volume 30, Issue 5, pp 349–359 | Cite as

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

  • B. Weigand
  • O. Neumann
  • T. Strohmayer
  • H. Beer


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.


Heat Transfer Flow Separation Forced Convection Mixed Convection Boundary Layer Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



thermal diffusivity


dimensionless freezing parameter (T W T F )/(T F T0)k s /k


modified stream function


Grashof number based on 4h, [∣ρ(T F )−ρ(T0)∣/ρ(T0)]g(4h)3/v2


Grashof number based onh, [∣ρ(T F )−ρ(T0)∣/ρ(T0)]gh3/v2


temperature function, defined by Eq. (14)


distance from centerline to wall


thermal conductivity


Nusselt number based on 4δ




prandtl number


Reynolds number based on 4h, ū04h/v


Reynolds number based onh, ū0h/v


Richardson number based on 4h,Gr4th/Re 4h 2


Richardson number based onh,Gr h /Re th 2




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


freezing temperature of the liquid


constant inlet temperature of the liquid


wall temperature

u, v

velocity components


mean axial velocity at the inlet

x, y


Greek symbols


constants for the density-temperature relationship for water


distance between centerline and solid-liquid interface


dimensionless temperature, (T−T F )/(T0T F )


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


kinematic viscosity




stream function



at the entrance






at the wall


*, ∼

dimensionless quantity

mean quantity

Gemischte Konvektion in einem gekühlten, vertikalen Kanal mit Eisschichtbildung


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.


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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • B. Weigand
    • 1
  • O. Neumann
    • 2
  • T. Strohmayer
    • 2
  • H. Beer
    • 2
  1. 1.ABB Power Generation LtdBadenSwitzerland
  2. 2.Institut für Technische ThermodynamikTechnische Hochschule DarmstadtDarmstadtGermany

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