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Heat and Mass Transfer

, Volume 46, Issue 11–12, pp 1307–1314 | Cite as

Three dimensional freezing around a coolant-carrying tube

  • M. SugawaraEmail author
  • Y. Komatsu
  • T. Makabe
  • H. Beer
Original

Abstract

The 3-D freezing of water around a coolant carrying horizontal tube placed in an adiabatic rectangular cavity is investigated mainly by means of a numerical analysis. The results are not sensitive to the coolant flow velocity and the tube length, but are very responsive to the coolant inlet temperature and the initial water temperature. The numerical analysis predicts fairly experimental results without introducing a heat transfer coefficient.

Keywords

Heat Transfer Coefficient Natural Convection Phase Change Material Thermal Boundary Layer Thickness Stanton Number 
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.

List of symbols

Bi

Biot number, α(d i /2)/k s

c

Specific heat

C

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

di

Inner diameter of the tube (=17.05 mm)

d0

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 )

hf

Latent heat of freezing

H

Height/width of the rectangular cavity

k

(Effective) thermal conductivity

L

Tube length

ri

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

St

Stanton number, α/w m () c

Ste

Stefan number, c s (T ph  − T inlt)/h f

t

Time

T

Temperature

Tph

Freezing temperature (=0°C)

u

X-component velocity

v

Y-component velocity

V

Velocity vector composed of u, v and w

w

Z-component velocity

wm

Mean velocity of the coolant in the tube

x

Horizontal coordinate

y

Vertical coordinate

z

Axial coordinate

Greek symbols

α

Heat transfer coefficient of the coolant

γ

Volume fraction

δ

Local frozen layer thickness from the tube outer surface

δm

Mean frozen layer thickness on xy cross section

δmz

Total mean frozen layer thickness (=(δ m,z=0 + δ m,z=0.5L + δ m,z=L)/3, corresponding to the frozen layer thickness measured by experiment)

ρ

Density

Subscripts

c

Coolant

ini

Initial

inlt

Inlet

Liquid (water)

s

Solid (ice)

x

x-direction

y

y-direction

z

z-direction

Notes

Acknowledgments

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

References

  1. 1.
    Sparrow EM, Hsu CF (1981) Analysis of two-dimensional freezing on the outside of a coolant-carrying tube. Int J Heat Mass Transf 24(8):1345–1357CrossRefGoogle Scholar
  2. 2.
    Shamsundar N (1982) Formulae for freezing outside a circular tube with axial variation of coolant temperature. Int J Heat Mass Transf 25(10):1614–1616CrossRefGoogle Scholar
  3. 3.
    Shamsundar N, Srinivasan R (1980) Effectiveness-NTU charts for heat recovery from latent heat storage units. ASME J Heat Transf 102:263–271Google Scholar
  4. 4.
    Sasaguchi K, Imura H, Furusho H (1986) Heat transfer characteristics for latent heat storage system with finned tube (1st Report: experimental study for solidification and melting processes) (in Japanese). Trans Jpn Soc Mech Eng (Ser B) 52(473):159–166Google Scholar
  5. 5.
    Sasaguchi K, Imura H, Furusho H (1986) Heat transfer characteristics for latent heat storage system with finned tube (2nd Report: comparison of numerical and experiment for solidification processes) (in Japanese). Trans Jpn Soc Mech Eng (Ser B) 52(473):167–173Google Scholar
  6. 6.
    Esen M, Ayhan T (1996) Development of a model compatible with solar assisted cylindrical energy storage tank and variation of stored energy with time for different phase-change materials. Energy Convers Manag 37(12):1775–1785CrossRefGoogle Scholar
  7. 7.
    Esen M, Durmus A, Durmus A (1998) Geometric design of solar-aided latent heat store depending on various parameters and phase change materials. Sol Energy 62(1):19–28CrossRefGoogle Scholar
  8. 8.
    Esen M (2000) Thermal performance of a solar-aided latent heat store used for space heating by heat pump. Sol Energy 69(1):15–25CrossRefGoogle Scholar
  9. 9.
    Erek A, Ilken Z, Acar MA (2005) Experimental and numerical investigation of thermal energy storage with a finned tube. Int J Energy Res 29:283–301CrossRefGoogle Scholar
  10. 10.
    Kayansayan N, Acar MA (2006) Ice formation around a finned-tube heat exchanger for cold thermal energy storage. Int J Therm Sci 45:405–418CrossRefGoogle Scholar
  11. 11.
    Ermis K, Erek A, Dincer I (2007) Heat Transfer analysis of phase change process in a finned-tube thermal energy storage system using artificial neural network. Int J Heat Mass Tranf 50:3163–3175zbMATHCrossRefGoogle Scholar
  12. 12.
    Fukai J, Hamada Y, Morozumi Y, Miyatake O (2003) Improvement of thermal characteristics of latent heat thermal energy storage units using carbon-fiber brushes: experiments and modeling. Int J Heat Mass Transf 46:4513–4525CrossRefGoogle Scholar
  13. 13.
    Sari A, Kaygusuz K (2001) Thermal energy storage system using stearic acid as a phase change material. Sol Energy 71:365–376CrossRefGoogle Scholar
  14. 14.
    Sari A, Kaygusuz K (2002) Thermal performance of a eutectic mixture of lauric and stearic acids as PCM encapsulated in the annulus of two concentric pipes. Sol Energy 72:493–504CrossRefGoogle Scholar
  15. 15.
    Trp A (2005) An experimental and numerical investigation of heat transfer during technical grade paraffin melting and solidification in a shell-and-tube latent thermal energy storage unit. Sol Energy 79:648–660CrossRefGoogle Scholar
  16. 16.
    Agyenim F, Eames P, Smyth M (2009) A comparison of heat transfer enhancement in a medium temperature thermal energy storage heat exchanger using fins. Sol Energy 83:1509–1520CrossRefGoogle Scholar
  17. 17.
    Bennon WD, Incropera FP (1987) A continuum model for momentum, heat and species transport in binary solid-liquid phase change systems—I. Model formation. Int J Heat Mass Transf 30:2161–2170zbMATHCrossRefGoogle Scholar
  18. 18.
    Sasaguti K, Takeo H (1994) Effect of the orientation of a finned surface on the melting of frozen porous media. Int J Heat Mass Transf 37(1):13–26CrossRefGoogle Scholar
  19. 19.
    Sugawara M, Beer H (2009) Numerical analysis for freezing/melting around vertically arranged four cylinders. Heat Mass Transf 45:1223–1231CrossRefGoogle Scholar
  20. 20.
    Sugawara M, Onodera T, Komatsu Y, Tago M, Beer H (2008) Freezing of water saturated in aluminum wool mats. Heat Mass Transf 44:835–843CrossRefGoogle Scholar
  21. 21.
    Hand book of air conditioning system design, part 4 (1965) McGraw Hill Book Company, USA, pp 32–35Google Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Faculty of Engineering and Resource ScienceAkita UniversityAkitaJapan
  2. 2.Institut fur Technische ThermodynamikTechnische Universitat DarmstadtDarmstadtGermany

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