9-121
9-143 An electronic box is cooled internally by a fan blowing air into the enclosure. The fraction of the heat lost from the
outer surfaces of the electronic box is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 Heat transfer from the base
surface is disregarded. 4 The pressure of air inside the enclosure is 1 atm.
Properties The properties of air at 1 atm and the film temperature of (Ts+T)/2 = (32+15)/2 = 28.5C are (Table A-15)
1–
25
K 003317.0
K)2735.28(
11
7286.0Pr
/sm 10594.1
C W/m.02577.0
=
+
==
=
=
=
−
f
T
k
Analysis Heat loss from the horizontal top surface:
The characteristic length in this case is
m 125.0
)]m 5.0()m 5.0[(2
)m 5.0( 2
=
+
== P
A
Lc
.
Then,
6
225
3-12
2
3
10275.1)7286.0(
)/sm 10594.1(
)m 125.0)(K 2532)(K 003317.0)(m/s 81.9(
Pr
)( =
−
=
−
=−
cs LTTg
Ra
15.18)10275.1(54.054.0 4/164/1 === RaNu
22
2
m 25.0)m 5.0(
C.W/m741.3)15.18(
m 125.0
C W/m.02577.0
==
=
==
top
c
A
Nu
L
k
h
and
W55.6C)2532)(m 25.0)(C. W/m741.3()( 22 =−=−=
TThAQstoptop
Heat loss from vertical side surfaces:
The characteristic length in this case is the height of the box Lc = L =0.15 m. Then,
Air
T =25C
15 cm
200 W
= 0.75
Ts = 32C
50 cm
50 cm
9-123
)10379.6(387.0
Ra387.0
2
6/16
2
6/1
9-124
9-145E The components of an electronic system located in a horizontal duct of rectangular cross section is cooled by natural
convection. The heat transfer from the outer surfaces of the duct by natural convection and the average temperature of the
duct are 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 Radiation effects are negligible. 5 The thermal resistance of the duct is negligible.
Properties Based on the problem statement, the properties of air at 1 atm and the anticipated film temperature of (Ts+T)/2 =
(160+80)/2 = 120F are (Table A-15E)
1–
23
R 001724.0R) 460120/(1/1
723.0Pr
/sft 101923.0
FBtu/h.ft. 01576.0
=+==
=
=
=
−
f
T
k
Analysis (a) Noting that radiation heat transfer is negligible and no heat is
removed by forced convection because of the failure of the fan, the entire
180 W heat generated must be dissipated by natural convection,
150 W
L = 5 ft
Air duct
6 in 6 in
Air
80F
9-125
3.41214 Btu/h
æö
÷
-1
Pr 0.7245
1/ 1/(110 460 R) 0.001754 R
f
T
b
=
= = + =
Horizontal top surface:
32 –1 3
6
() (32.2 ft/s )(0.001754 R )(140 80 R)(0.2273 ft)
sc
g T T L
¥
––
9-126
9-146E The components of an electronic system located in a horizontal duct of circular cross section is cooled by forced air.
The heat transfer from the outer surfaces of the duct by natural convection and the average temperature of the duct are 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 Radiation effects are negligible. 5 The thermal resistance of
the duct is negligible.
Properties Based on the problem statement, the properties of air at
1 atm and the anticipated film temperature of (Ts+T)/2 =
(150+80)/2 = 115F are (Table A-15E)
1–
23
R 001739.0
R )460115(
11
7238.0Pr
/sft 101895.0
FBtu/h.ft. 01564.0
=
+
==
=
=
=
−
f
T
k
Analysis (a) Using air density at the inlet temperature of 85F and the specific heat at the average temperature of (85+100))/2
= 92.5F and 1 atm for the forced air, the mass flow rate of air and the heat transfer rate by forced convection are determined
1–
R 001786.0R)460100/(1/1
726.0Pr
=+==
=
f
T
Air duct
D = 4 in
Air
85F
22 cfm
100F
Air
80F
150 W
L = 5 ft
9-128
9-147 A 10-m tall exhaust stack discharging exhaust gases at a rate of 0.125 kg/s is subjected to solar radiation and natural
convection at the outer surface. The outer surface temperature of the exhaust stack is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Properties are constant. 3 The surface temperature is constant. 4 Air is an
ideal gas.
Properties The properties of air at 60°C are k = 0.02808 W/m∙K,
= 1.896 10−5 m2/s, Pr = 0.7202 (from Table A-15). Also,
β = 1/Tf = 0.003003 K-1.
Analysis Assume that the exhaust stack can be treated as a
vertical plate, the Rayleigh number is
Pr
)(
Ra
2
3
−
=
s
L
LTTg
9-130
K
k
W/m02603.0
W101.1=
9-131
9-149 A cold cylinder is placed horizontally in hot air. The rates of heat transfer from the stack with and without wind cases
are 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.
Properties The properties of air at 1 atm and the film temperature of (Ts+T)/2 = (40+10)/2 = 25C are (Table A-15)
1–
25
K 003356.0
K)27325(
11
7296.0Pr
/sm 10562.1
C W/m.02551.0
=
+
==
=
=
=
−
f
T
k
Analysis (a) When the stack is exposed to 10 m/s winds, the heat transfer will be by forced convection. We have flow of air
over a cylinder and the heat transfer rate is determined as follows:
825,76
/sm 10562.1
m) m/s)(0.12 10(
Re 25 =
== −
VD
2.208)7296.0()825,76(027.0PrRe027.0Nu 3/1805.03/1805.0 ===
(from Table 7-1)
C. W/m27.44)2.208(
m 12.0
C W/m.02551.0
Nu 2=
== D
k
h
W7510=−=−= C)1040)(m 1512.0)(C. W/m27.44()( 22
conv forced
s
TThAQ
(b) Without wind the heat transfer will be by natural convection. The characteristic length in this case is the outer diameter of
the cylinder,
m. 12.0== DLc
Then,
6
3-12
3
)m 12.0)(K 1040)(K 003356.0)(m/s 81.9(
)( =
−
−
DTTg
Air
T = 40C
Ts = 10C
L = 15 m
D = 12 cm
9-134
9-152E An industrial furnace that resembles a horizontal cylindrical enclosure whose end surfaces are well insulated. The
highest allowable surface temperature of the furnace and the annual cost of this loss to the plant are 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.
Properties The properties of air at 1 atm and the anticipated film
temperature of (Ts+T)/2 = (140+75)/2=107.5F are (Table A-15E)
1–
23
R 001762.0
R)4605.107(
11
7249.0Pr
/sft 101852.0
FBtu/h.ft. 01546.0
=
+
==
=
=
=
−
f
T
k
Analysis The solution of this problem requires a trial-and-error approach since the determination of the Rayleigh number and
thus the Nusselt number depends on the surface temperature which is unknown. We start the solution process by “guessing”
the surface temperature to be 140F for the evaluation of the properties and h. We will check the accuracy of this guess later
and repeat the calculations if necessary. The characteristic length in this case is the outer diameter of the furnace,
ft. 8== DLc
Then,
10
3-12
3
)ft 8)(R 75140)(R 001762.0)(ft/s 2.32(
)( =
−
−
DTTg
L = 13 ft
Furnace
= 0.1
Air
T = 75F
D = 8 ft
9-135
9-153 A spherical tank made of stainless steel is used to store iced water. The rate of heat transfer to the iced water and the
amount of ice that melts during a 24-h period are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 Thermal resistance of the
tank is negligible. 4 The local atmospheric pressure is 1 atm.
Properties The properties of air at 1 atm and the film temperature of
(Ts+T)/2 = (0+20)/2 = 10C are (Table A–15)
1–
25
K 003534.0
K)27310(
11
7336.0Pr
/sm 10426.1
C W/m.02439.0
=
+
==
=
=
=
−
f
T
k
Analysis (a) The characteristic length in this case is Lc = Do = 6.03 m. Then,
1.5 cm
Iced water
Di = 6 m
0C
Q
Ts = 0C
T = 20C