Chapter 1
Basics of Heat Transfer
187E
A 200ft long section of a steam pipe passes through an open space at a specified temperature. The
rate of heat loss from the steam pipe and the annual cost of this energy lost are to be determined.
Assumptions
1
Steady operating conditions exist.
2
Heat transfer by radiation is disregarded.
3
The
convection heat transfer coefficient is constant and uniform over the surface.
Analysis
(
a
) The rate of heat loss from the steam pipe is
2
ft
4
.
209
ft)
200
(
ft)
12
/
4
(
=
=
=
π
DL
A
s
Btu/h
289,000
=
F
)
50
280
)(
ft
4
.
209
(
F)
.
Btu/h.ft
6
(
)
(
2
2
pipe
°

°
=

=
air
s
s
T
T
hA
Q
(
b
) The amount of heat loss per year is
Q
Q t
=
=
×
=
×
(
,
.
∆
289 000
2 532
10
9
Btu / h)(365
24 h / yr)
Btu / yr
The amount of gas consumption per year in the furnace that has an efficiency of 86% is
therms/yr
438
,
29
Btu
100,000
therm
1
86
.
0
Btu/yr
10
532
.
2
Loss
Energy
Annual
9
=
×
=
Then the annual cost of the energy lost becomes
Energy cost
Annual energy loss)(Unit cost of energy)
= (29,438 therms / yr)
therm)
=
=
(
($0.
/
58
$17,074 / yr
188
A 4m diameter spherical tank filled with liquid nitrogen at 1 atm and 196
°
C is exposed to
convection with ambient air. The rate of evaporation of liquid nitrogen in the tank as a result of the heat
transfer from the ambient air is to be determined.
Assumptions
1
Steady operating conditions exist.
2
Heat transfer by radiation is disregarded.
3
The
convection heat transfer coefficient is constant and uniform over the surface.
4
The temperature of the
thinshelled spherical tank is nearly equal to the temperature of the nitrogen inside.
Properties
The heat of vaporization and density of liquid nitrogen at 1 atm are given to be 198 kJ/kg and
810 kg/m
3
, respectively.
Analysis
The rate of heat transfer to the nitrogen tank is
2
2
2
m
27
.
50
m)
4
(
=
=
=
D
A
s
W
271,430
=
°


°
=

=
C
)]
196
(
20
)[
m
27
.
50
(
C)
.
W/m
25
(
)
(
2
2
air
T
T
hA
Q
s
s
Then the rate of evaporation of liquid nitrogen in the tank is determined to be
kg/s
1.37
=
=
=
→
=
kJ/kg
198
kJ/s
430
.
271
fg
fg
h
Q
m
h
m
Q
143
D =4 in
280
°
F
L=200 ft
Q
Air,50
°
F
1 atm
Liquid N
2
196
°
C
Q
Vapor
Air
20
°
C
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Basics of Heat Transfer
189
A 4m diameter spherical tank filled with liquid oxygen at 1 atm and 183
°
C is exposed to
convection with ambient air. The rate of evaporation of liquid oxygen in the tank as a result of the heat
transfer from the ambient air is to be determined.
Assumptions
1
Steady operating conditions exist.
2
Heat transfer by radiation is disregarded.
3
The
convection heat transfer coefficient is constant and uniform over the surface.
4
The temperature of the
thinshelled spherical tank is nearly equal to the temperature of the oxygen inside.
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 Spring '11
 ENgel
 Heat Transfer, qtotal, qconv

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