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Three-dimensional melting of ice around a liquid-carrying tube

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Abstract

Three-dimensional melting of ice around a liquid-carrying tube placed in an adiabatic rectangular cavity is investigated mainly by means of a numerical analysis. Natural convection in the melt layer enhances melting by about 1.2 times compared with the approximate solution of a conduction mode derived from London and Seban and Hausen. The morphology of the melt layer changes in axial direction. Melting is not sensitive to the cavity height and the tube length, but is very responsive to the liquid inlet temperature.

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Abbreviations

c :

Specific heat

C:

Coefficient in flow resistance (=−10−6, Eq. 4)

d i :

Inner diameter of the tube (=17.05 mm)

d o :

Outer diameter of the tube (=19.05 mm)

DTF :

Temperature range (0.2°C) in the mushy zone (0 ≤ f s  ≤ 1)

f :

Mass fraction

F :

Flow resistance (Eq. 4)

FS:

Solid mass fraction (=f s)

h f :

Latent heat of melting

H :

Height/width of the cavity

k :

(effective) thermal conductivity

log:

Logarithmic to natural base

L :

Tube length

Nud :

Nusselt number

Pr:

Prandtl number

r i :

Inner radius of the tube (=d i/2)

r o :

Outer radius of the tube (=d o/2)

Re:

Reynolds number

t :

Time

T :

Temperature

T ph :

Melting temperature (0°C)

T tube :

Fixed tube wall temperature in 2-D calculation

T wℓ :

Temperature of working liquid in the tube

u :

x-Component velocity

v :

y-Component velocity

V :

Velocity vector composed of u, v and w

w :

z-Component velocity

w m :

Mean velocity of the liquid flow in the tube

x :

Horizontal coordinate

y :

Vertical coordinate

z:

Axial coordinate

α m :

Mean heat transfer coefficient of the working liquid

γ :

Volume fraction

δ:

Melt layer thickness from the tube outer surface

δ m :

Mean melt layer thickness on x–y plane

δ mz :

Total mean melt layer thickness (= (δ m,z = 0 + δ m,z = 0.5L + δ m,z = L)/3, corresponding to the melt layer thickness calculated by the approximate solution)

ρ :

Density

Ini:

Initial

Inlt:

Inlet

ℓ:

Liquid (water)

m:

Mean (averaged)

s:

Solid (ice)

wℓ:

Working liquid (flowing liquid in the tube)

x :

x-direction

y :

y-direction

z :

z-direction

References

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Acknowledgments

The authors wish to acknowledge support for this study by the technical official T. Fujita.

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Authors and Affiliations

  1. Mineral Industry Museum, Faculty of Engineering and Resource Science, Akita University, Akita, 010-8502, Japan

    M. Sugawara

  2. Department of Mechanical Engineering, Faculty of Engineering and Resource Science, Akita University, Akita, 010-8502, Japan

    Y. Komatsu

  3. Institut fur Technische Thermodynamik, Technische Universitat Darmstadt, Petersenstrasse 30, 64287, Darmstadt, Germany

    H. Beer

Authors
  1. M. Sugawara
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  2. Y. Komatsu
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  3. H. Beer
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Corresponding author

Correspondence to M. Sugawara.

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Sugawara, M., Komatsu, Y. & Beer, H. Three-dimensional melting of ice around a liquid-carrying tube. Heat Mass Transfer 47, 139–145 (2011). https://doi.org/10.1007/s00231-010-0676-5

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