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Melting and freezing around a horizontal cylinder placed in a square cavity

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Abstract

Freezing/melting of water/ice around a horizontal cylinder placed in a square cavity of the inner side length H is investigated numerically. The cylinder is fixed at the centerline of the cavity and placed at various vertical distances of h = H/3, H/2 and 2H/3 from the bottom. Melting decreases considerably with increasing cylinder distance h. Freezing shows the utmost effect at h = H/2, other locations h = H/3 and h = 2H/3 will considerably retard freezing.

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Abbreviations

B :

body force (Eqs. 3 and 12)

c :

specific heat

d :

outer diameter of the cooling/heating cylinder (=19.05 mm)

d p :

diameter of a sphere particle in the porous bed

f :

mass fraction

g :

gravitational acceleration

h :

the distance of the cooling/heating cylinder center from the cavity bottom

h f :

latent heat of freezing/melting

H :

inner side length of the square cavity

k :

thermal conductivity

K :

permeability

K 0 :

permeability coefficient

L :

length of the cooling/heating cylinder in the experiment (see Fig. 2)

M :

transient mean freezing/melting mass per unit outer surface area of the cooling/heating cylinder

p :

pressure

S :

equivalent freezing/melting front distance from the cooling/heating cylinder center

t :

time

T :

temperature

T ph :

freezing/melting temperature (0°C)

u :

x-component velocity

v :

y-component velocity

V:

velocity vector composed of u and v

x :

horizontal coordinate

Δx :

mesh sizes of x-coordinate

y :

vertical coordinate

Δy :

mesh sizes of y-coordinate

ε :

porosity (=1 − γ p = γ s + \(\gamma_{\rm \ell}\))

γ :

volume fraction

\(\rm \upsilon \) :

kinematic viscosity

ρ :

density

c:

cooling

f:

freezing

h:

heating

k:

phase k (p, s and \( \rm{\ell} \))

\( \rm{\ell} \) :

liquid (water)

m:

melting

p:

particle

s:

solid (ice)

References

  1. Viskanta R (1991) Phase change heat transfer in porous media. In: Proceedings in third international symposium on cold regions heat transfer, Fairbanks, Alaska, pp 1–24

  2. Fukai J, Hamada Y, Morozumi Y, Miyatake O (2003) Improvement of the thermal characteristics of latent heat thermal energy storage units using carbon–fiber brushes. Int J Heat Mass Transf 46:4513–4525

    Article  Google Scholar 

  3. Krishnan S, Murthy JY, Garimella SV (2005) A two-temperature model for solid-liquid phase change in metal foams. ASME J Heat Transf 127:995–1004

    Article  Google Scholar 

  4. Sugawara M, Onodera T, Komatsu Y, Tago M, Beer H (2007) Freezing of water saturated in aluminum wool mats. Heat Mass Transf 44(7):835–843

    Article  Google Scholar 

  5. Bathelt AG, Viskanta R (1981) Heat transfer and interface motion during melting and solidification around a finned heat source/sink. ASME J Heat Transf 103:720–726

    Google Scholar 

  6. Padmanabhan PV, Murthy MVK (1986) Outward Phase Change in a Cylindrical Annulus with Axial Fins on the Inner Tube. Int J Heat Mass Transf 29(12):1855–1868

    Article  Google Scholar 

  7. 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):159–166

    Google Scholar 

  8. Sasaguchi K, Imura H, Furusho H (1986) Heat transfer characteristics for latent heat storage system with finned tube (2nd report: comparison of numerical ad experiment for solidification processes) (in Japanese). Trans Jpn Soc Mech Eng (Ser B) 52(473):167–173

    Google Scholar 

  9. Sugawara M, Kamada H, Fujita T (1990) A study of the fin size ratio for freezing of water on an upper coolong wall with fins (in Japanese). Trans Jpn Soc Mech Eng (Ser B) 56(532):3835–3840

    Google Scholar 

  10. 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):13–26

    Article  Google Scholar 

  11. Zhang Y, Faghri A (1995) Heat transfer enhancement in latent heat thermal energy storage system by using the internally finned tube. Int J Heat Mass Transf 39(15):3165–3173

    Article  Google Scholar 

  12. Lamberg P, Siren K (2003) Analytical model for melting in a semi-infinite PCM storage with an internal fin. Heat Mass Transf 39:167–176

    Google Scholar 

  13. Inaba H, Matsuo K, Horibe A (2003) Numerical simulation for fin effect of a rectangular latent heat storage vessel packed with molten salt under heat release process. Heat Mass Transf 39:231–237

    Google Scholar 

  14. Stritih U (2004) An experimental study of enhanced heat transfer in rectangular PCM thermal storage. Int J Heat Mass Transf 47:2841–2847

    Article  Google Scholar 

  15. Shatikian V, Ziskind G, Letan R (2005) Numerical investigation of a PCM-based heat sink with internal fins. Int J Heat Mass Transf 48:3689–3706

    Article  Google Scholar 

  16. Bathelt AG, Van Buren PD, Viskanta R (1981) Heat transfer during solidification around a cooled horizontal cylinder. AIChE Symp Ser 75(189):103–111

    Google Scholar 

  17. Prusa J, Yao LS (1984a) Melting around a horizontal heated cylinder: part I—Perturbation and numerical solution for constant heat flux boundary condition. ASME J Heat Transf 106:376–384

    Google Scholar 

  18. Prusa J, Yao LS (1984b) Melting around a horizontal heated cylinder: part II—numerical solution for isothermal boundary condition. ASME J Heat Transf 106:469–474

    Google Scholar 

  19. Bareiss M, Beer H (1984) An analytical solution of the heat transfer process during melting of an unfixed solid phase change material inside a horizontal tube. Int J Heat Mass Transf 27(5):739–746

    Article  Google Scholar 

  20. Zhang GP, Jiji LM, Weinbaum S (1985) Quasi-three-dimensional steady-state analytic solution for melting or freezing around a buried pipe in a semi-infinite medium. ASME J Heat Transf 107:245–247

    Google Scholar 

  21. Rieger H, Beer H (1986) The melting process of ice inside a horizontal cylinder: effects of density anomaly. ASME J Heat Transf 108:166–173

    Article  Google Scholar 

  22. Chung JD, Lee JS, Yoo H (1997) Thermal instability during the melting process in an isothermally heated horizontal cylinder. Int J Heat Mass Transf 40(16):3899–3907

    Article  MATH  Google Scholar 

  23. Sasaguti K, Kusano K, Viskanta R (1997) A numerical analysis of solid–liquid phase change heat transfer around a single and two horizontal, vertically spaced cylinders in a rectangular cavity. Int J Heat Mass Transf 40(6):1343–1354

    Article  Google Scholar 

  24. 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 30:2161–2170

    Article  MATH  Google Scholar 

  25. Kaviany M (1995) Principles of heat transfer in porous media, 2nd edn. Springer, Berlin

    MATH  Google Scholar 

  26. Sasaguchi K (1994) Heat and flow analysis accompanied with solid–liquid phase change (Kikai no Kenkyu, in Japanese). Mech Res 46-9:931–936

    Google Scholar 

  27. Bennon WD, Incropera FP (1987) A continuum model for momentum, heat and species transport in binary solid–liquid phase change systems–II. Application to solidification in a rectangular cavity. Int J Heat Mass Transf 30:2171–2187

    Article  Google Scholar 

  28. Patankar SV (1980) Numerical heat transfer and fluid flow, Hemisphere Publishing Company, NY

    MATH  Google Scholar 

  29. Prakash C, Voller V (1989) On the numerical solution of continuum mixture model equations describing binary solid-liquid phase change. Numer Heat Transf B 15:171–189

    Article  MATH  Google Scholar 

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Acknowledgment

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

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Authors and Affiliations

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

    M. Sugawara & Y. Komatsu

  2. 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. Melting and freezing around a horizontal cylinder placed in a square cavity. Heat Mass Transfer 45, 83–92 (2008). https://doi.org/10.1007/s00231-008-0403-7

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  • DOI: https://doi.org/10.1007/s00231-008-0403-7

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