Chapter 5
The First Law of Thermodynamics
Pipe and duct Flow
5125
A desktop computer is to be cooled safely by a fan in hot environments and high elevations. The air
flow rate of the fan and the diameter of the casing are to be determined.
Assumptions
1
Steady operation under worst conditions is considered.
2
Air is an ideal gas with constant
specific heats.
3
Kinetic and potential energy changes are negligible.
Properties
The specific heat of air at the average temperature of
T
ave
=
(45+60)/2 = 52.5
°
C = 325.5 K is C
p
= 1.0065 kJ/kg.
°
C (Table A2b)
Analysis
The fan selected must be able to meet the cooling requirements of the computer at worst
conditions. Therefore, we assume air to enter the computer at 66.63 kPa and 45
°
C, and leave at 60
°
C.
We take the air space in the computer as the system, which is a control volume. The energy
balance for this steadyflow system can be expressed in the rate form as
&&
&
&
&
&
()
EE
E
Qm
hm
h
C
T
T
in
out
in
out
in
in
p
−=
=
+=
≅≅
=−
Rate of net energy transfer
by heat, work, and mass
system
(steady)
Rate of change in internal, kinetic,
potential, etc. energies
(since
ke
pe
0)
12
43
4
44
444
Δ
ΔΔ
Ê
0
21
0
=
Then the required mass flow rate of air to absorb heat at a rate of 60 W is
determined to be
kg/min
0.238
=
kg/s
00397
.
0
C
45)

C)(60
J/kg.
(1006.5
W
60
)
(
)
(
=
°
°
=
−
=
→
−
=
in
out
p
in
out
p
T
T
C
Q
m
T
T
C
m
Q
&
&
&
&
The density of air entering the fan at the exit and its volume flow rate are
/min
m
0.341
3
=
=
=
=
=
=
3
3
3
kg/m
6972
.
0
kg/min
238
.
0
kg/m
6972
.
0
273)K
+
/kg.K)(60
kPa.m
287
.
0
(
kPa
63
.
66
ρ
m
V
RT
P
&
&
For an average exit velocity of 110 m/min, the diameter of the casing of the fan is determined from
cm
6.3
V
V
V
=
m
063
.
0
m/min)
110
(
/min)
m
341
.
0
)(
4
(
4
4
3
2
=
=
=
→
=
=
ππ
π
V
D
D
A
V
c
&
&
5114
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View Full DocumentChapter 5
The First Law of Thermodynamics
5126
A desktop computer is to be cooled safely by a fan in hot environments and high elevations. The air
flow rate of the fan and the diameter of the casing are to be determined.
Assumptions
1
Steady operation under worst conditions is considered.
2
Air is an ideal gas with constant
specific heats.
3
Kinetic and potential energy changes are negligible.
Properties
The specific heat of air at the average temperature of
T
ave
=
(45+60)/2 = 52.5
°
C is C
p
= 1.0065
kJ/kg.
°
C (Table A3).
Analysis
The fan selected must be able to meet the cooling requirements of the computer at worst
conditions. Therefore, we assume air to enter the computer at 66.63 kPa and 45
°
C, and leave at 60
°
C.
We take the air space in the computer as the system, which is a control volume. The energy
balance for this steadyflow system can be expressed in the rate form as
&&
&
&
&
&
()
EE
E
Qm
hm
h
C
T
T
in
out
in
out
in
in
p
−=
=
+=
≅≅
=−
Rate of net energy transfer
by heat, work, and mass
system
(steady)
Rate of change in internal, kinetic,
potential, etc. energies
(since
ke
pe
0)
12
43
4
44
444
Δ
ΔΔ
Ê
0
21
0
=
Then the required mass flow rate of air to absorb heat at a rate of 100 W is
determined to be
kg/min
0.397
=
kg/s
006624
.
0
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 Spring '07
 Dr.Kinne
 Thermodynamics, Energy, Heat, net energy transfer, The First Law of Thermodynamics

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