APPENDIX B: DETERMINATION OF CONVECTION COEFFICIENT
FOR COLDROOM 165
5118ε
hc =
According to Vesilind (1990), the rate of freez-
(B5)
.
(
)
tf -T af
ing (dy/dt) for a thin layer of sludge can be pre-
dicted by the equation
To calculate hc we had to determine Taf, tf, and
(
)
ε. Taf was determined by setting coldroom 165 at
dy hc Tf - T af
14C. The values for tf, and ε were determined
=
(B1)
ρf L
dt
by freezing a tray of distilled water. Both the tray
and the distilled water were precooled to 0C.
The tray was removed at various time intervals
(W/m2-C )
and the depth of the ice layer was measured with
ρf = the density of ice (917 kg/m3)
calipers. The data from this analysis are shown in
L = the latent heat of fusion (93 W-h/kg)
the table below. Based on these data the average
Tf = the freezing point of sludge (0C)
convection coefficient was calculated to be 23.1
Taf = the average air temperature in the
W/m2-C. This was the value used in eq B1 to
coldroom (C).
predict the freezing times.
By separating variables eq B1 becomes
(
)
ρf Ldy = hc Tf - T f dt.
(B2)
Table B1. Laboratory data
on freezing distilled water
At t = 0, y = 0, and when t = the freezing time
at 14C.
tf, y = the depth of frozen sludge, ε. Integrating
eq B2 between these limits yields
Freezing
Ice
Conv.
depth (ε) coefficient
time
ρf Lε = hc Tf - T af tf .
(W/m2-C)
(min)
(mm)
(B3)
15
1.01
24.6
By rearranging terms and solving for hc , the
20
1.13
20.6
above equation becomes
30
1.95
23.8
40
2.63
24.0
ρf Lε
hc =
45
2.50
20.3
(B4)
.
(
)
tf Tf - T af
60
4.43
27.0
60
2.98
18.2
80
5.72
26.1
Substituting the values for each constant and
changing ii to minutes and ε to millimeters, eq 4
Avg.
23.1
s.d.
3.1
becomes:
19
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