# Numerical analysis for freezing/melting around vertically arranged four cylinders

- First Online:

- Received:
- Accepted:

DOI: 10.1007/s00231-009-0492-y

- Cite this article as:
- Sugawara, M. & Beer, H. Heat Mass Transfer (2009) 45: 1223. doi:10.1007/s00231-009-0492-y

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## Abstract

Freezing/melting of water/ice around vertically arranged four horizontal cylinders placed in a rectangular cavity is investigated numerically by using a commercial software package. Freezing/melting is affected by the bottom cylinder distance *h* from the cavity bottom and by a complicated natural convection as well as the interaction with the flow around each cylinder.

### List of symbols

*a*Width of the cavity (50 mm)

*B*Body force (Eq. 5), N/m

^{3}*c*Specific heat, J/(kg K)

*C*Coefficient = −10

^{6}(Eq. 4)*ϕ*CTemperature in the color figures (=°C)

*d*Outer diameter of the cooled/heated cylinder (=19.05 mm)

- DTF
Temperature range in the mushy zone of the freezing front (0.1°C, 0 <

*f*_{s}< 1)*f*Mass fraction

*F*Flow resistance Eq. 4, N

- FS
Solid mass fraction in the color figures (=

*f*_{s})*g*Gravitational acceleration, m/s

^{2}*h*The distance of the bottom cylinder center from the cavity bottom, mm

*h*_{f}Latent heat of freezing/melting, J/kg

*H*Height of the cavity,

*H*= 4*a*(for four cylinders),*H*=*a*(for one cylinder), mm*k*(effective) Thermal conductivity, J/(m s K) or W/(m K)

*t*Time, s

*T*Temperature, °C

*T*_{ph}Freezing/melting temperature (0°C)

*u**x*-Component velocity, m/s*v**y*-Component velocity, m/s**V**Velocity vector composed of

*u*and*v*, m/s*x*Horizontal coordinate, m

*y*Vertical coordinate, m

### Greek letters

*γ*Volume fraction

*η*Viscosity, kg/(m s)

*ρ*Density, kg/m

^{3}

### Subscript

- c
Cooled

- h
Heated

- ℓ
Liquid (water)

- s
Solid (ice)

*x**x*-Direction*y**y*-Direction