Freezing enhancement around a horizontal tube using copper foil disks

Abstract

Freezing of water saturated in circumferentially arranged copper foils around a cooling tube is studied experimentally and numerically. The copper foils need not to be welded to the cooling tube but are merely placed around the tube so that the freezing system is easily arranged. Copper foils greatly enhance freezing compared with that of a bare tube, even with a small copper volume fraction in the freezing system. Numerical calculations by means of a continuum model predict well freezing enhancement. The effect of the copper foils is also considered numerically for the melting process in order to compare with freezing. It is seen that copper foils contribute more to the melting enhancement than to the increase of the freezing rate.

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Abbreviations

A :

Cross sectional area of a manometer to measure freezing mass

d :

Outer diameter of the cooling/heating tube, 19.05 mm

d h :

Hydraulic diameter, Eq. 6

D :

Outer diameter of the copper foil disk, 94 mm

f :

Mass fraction

h :

Water rise in a manometer due to freezing

h f :

Latent heat of freezing/melting

H :

Cavity width and height

k :

(Effective) thermal conductivity

L :

Longitudinal length of the cooling tube in the cavity

M :

Transient mean phase change mass per unit outer surface area of the cooling/heating tube

R :

Flow resistance in the momentum equation (Eq. 4)

t :

Time

T :

Temperature

T c :

Cooling tube surface temperature

T h :

Heating tube surface temperature

u :

x-component velocity

v :

y-component velocity

V :

Volume

w :

Distance between copper foils facing each other

x, y:

Coordinates

ε:

Porosity (=1−γ c  = γ s  + γ )

γ:

Volume fraction

υ :

Kinematic viscosity

ρ:

Density

c:

Copper

f:

Freezing

ini:

Initial

ℓ:

Liquid (water)

m:

Melting

s:

Solid (ice)

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Acknowledgment

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

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Correspondence to M. Sugawara.

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Sugawara, M., Komatsu, Y., Takahashi, Y. et al. Freezing enhancement around a horizontal tube using copper foil disks. Heat Mass Transfer 47, 1691–1698 (2011). https://doi.org/10.1007/s00231-011-0839-z

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Keywords

  • Effective Thermal Conductivity
  • Phase Change Material
  • Copper Foil
  • Cooling Tube
  • Freezing Front