Heat and Mass Transfer

, Volume 45, Issue 9, pp 1223–1231

Numerical analysis for freezing/melting around vertically arranged four cylinders

Original

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

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/m3

c

Specific heat, J/(kg K)

C

Coefficient = −106 (Eq. 4)

ϕC

Temperature 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 < fs < 1)

f

Mass fraction

F

Flow resistance Eq. 4, N

FS

Solid mass fraction in the color figures (=fs)

g

Gravitational acceleration, m/s2

h

The distance of the bottom cylinder center from the cavity bottom, mm

hf

Latent heat of freezing/melting, J/kg

H

Height of the cavity, H = 4a (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

Tph

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/m3

Subscript

c

Cooled

h

Heated

Liquid (water)

s

Solid (ice)

x

x-Direction

y

y-Direction

Copyright information

© Springer-Verlag 2009

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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