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Chapter 9
Natural Convection
945
A vertically oriented cylindrical hot water tank is located in a bathroom. The rate of heat loss from the
tank by natural convection and radiation is to be determined.
Assumptions
1
Steady operating conditions exist.
2
Air is an ideal gas with constant properties.
3
The local
atmospheric pressure is 1 atm.
4
The temperature of the outer surface of the tank is constant.
Properties
The properties of air at 1 atm and the film temperature
of (
T
s
+
T
∞
)/2 = (44+20)/2 = 32
°
C are (Table A15)
1

2
5
K
003279
.
0
K
)
273
32
(
1
1
7276
.
0
Pr
/s
m
10
627
.
1
C
W/m.
02603
.
0
=
+
=
=
=
×
=
°
=
−
f
T
k
β
υ
Analysis
The characteristic length in this case is the height of the cylinder,
Air
T
∞
= 20
°
C
Tank
T
s
= 44
°
C
ε
= 0.4
L
= 1.1 m
D
= 0.4 m
m.
1
.
1
=
=
L
L
c
Then,
9
2
2
5
3
1
2
2
3
10
883
.
3
)
/s
m
10
627
.
1
(
)
m
1
.
1
)(
K
20
44
)(
K
003279
.
0
)(
m/s
81
.
9
(
)
(
Gr
×
=
×
−
=
−
=
−
∞
L
T
T
g
s
A vertical cylinder can be treated as a vertical plate when
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Convection, Mass, Heat, Radiation

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