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20-81
20-89 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.
20-82
20-90E The components of an electronic device located in a horizontal duct of rectangular 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
1-
23
R 001786.0R)460100/(1/1
726.0Pr
/sft 101809.0
FBtu/h.ft. 01529.0
f
T
k
92.5F and 1 atm for the forced air, the mass flow rate of air and
Btu/h 6.346F)85100)(FBtu/lbm. 2404.0)(lbm/h 60602.1()( inoutpforced TTcmQ
Noting that radiation heat transfer is negligible, the rest of the 180 W heat generated must be dissipated by natural
180 W
L = 4 ft
Air duct
6 in 6 in
Air
100F
80F
20-83
2
2
ft 4)ft 5.0)(ft 4(2
F.Btu/h.ft843.0)57.27(
ft 5.0
FBtu/h.ft. 01529.0
side
side
A
Nu
L
k
h
which is sufficiently close to the assumed value of 120F used in the evaluation of properties and h. Therefore, there is no
20-84
20-91E 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
1-
R 001724.0R) 460120/(1/1
723.0Pr
f
T
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,
W180 totalnatural QQ
(b) We start the calculations by “guessing” the surface temperature to be 160F for the evaluation of the properties and h. We
will check the accuracy of this guess later and repeat the calculations if necessary.
Horizontal top surface: The characteristic length is
ft 2222.0
ft) 6/12+ft 2(4
ft) ft)(6/12 4( p
A
Ls
c
. Then,
5
223
3-12
2
3
10534.9)723.0(
)/sft 101923.0(
)ft 2222.0(R) 80160)(R 001724.0)(ft/s 2.32(
Pr
)(
cs LTTg
Ra
87.16)10534.9(54.054.0 4/154/1 RaNu
bottomtop
c
top
AA
Nu
L
k
h
2
2
ft 2)ft 12/6)(ft 4(
F.Btu/h.ft197.1)87.16(
ft 2222.0
FBtu/h.ft. 01576.0
437.8)10534.9(27.027.0 4/154/1 RaNu
FBtu/h.ft. 01576.0 2
k
180 W
L = 4 ft
6 in 6 in
20-85
F)80](FBtu/h. )4009.125983.02197.1[(
W1
Btu/h 3.41214
W180
s
T
20-87
20-93 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
)7202.0(
)/sm 10896.1(
)m 10(K)306)(K 003003.0)(m/s 81.9(
225
31-2
s
T
Assuming the Rayleigh number is within 1010 < RaL < 1013, the
Nusselt number for vertical plate is
3/1
Ra1.0Nu L
or
3/1
Ra1.0
m 10
K W/m02808.0
L
h
(2)
The outer surface area of the exhaust stack is
2
The rate of heat loss from the exhaust gases in the exhaust stack
can be determined from
W6000C )30(C)J/kg 1600)(kg/s 125.0()( outinloss TTcmQ p
The heat loss on the outer surface of the exhaust stack by radiation and convection can be expressed as
solar
4
surr
4
loss ][ ][ qTTTTh
A
Q
sss
s
(3)
Equations (1), (2), and (3) can be solved simultaneously to get the surface temperature. Copy the following lines and paste on
a blank EES screen to solve the above equation:
A_s=31.42
D=1
g=9.81
k=0.02808
L=10
Pr=0.7202
q_incindent=500
nu=1.896e-5
sigma=5.670e-8
Ra_L=g*beta*(T_s-T_inf)*L^3/nu^2*Pr
C87.5
s
T
Now, we need to check if the assumption that the exhaust stack can be treated as a vertical plate is valid:
L
L
)m 10(35
3535
20-89
K
K
Nu
L
k
h
c
2
W/m683.2)31.10(
m 1.0
W/m02603.0
W1.8C)2044)(m 1257.0)( W/m683.2()( 22
bottom KTThAQss
The total heat loss by natural convection is
W157.9 1.82.166.133
bottomtopsideconv QQQQ
The radiation heat loss from the tank is
W101.1
444282
44
rad
)K 27320()K 27344()K W/m1067.5)(m 1257.01257.0382.1)(4.0(
)( surrss TTAQ
20-92
20-97E A small cylindrical resistor mounted on the lower part of a vertical circuit board. The approximate surface
temperature of the resistor is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 The local atmospheric
1-
23
R 001587.0
R)460170(
11
7161.0Pr
/sft 10222.0
FBtu/h.ft. 01692.0
f
T
k
and repeat the calculations if necessary. The characteristic length in this case is the diameter of resistor,
in. 2.0 DLc
Then,
)ft 12/2.0)(R 120220)(R 001587.0)(ft/s 2.32(
)(
3-12
3
DTTg
Q
0.1 W
D = 0.2 in
20-93
20-98E 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
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
Furnace
= 0.1
D = 8 ft
20-94
20-99 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
20-95
20-100 A spherical vessel is completely submerged in a large water-filled tank. The rates of heat transfer from the vessel by
natural convection, conduction, and forced convection are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The surface temperature is constant.
20-96
20-101 A double-pane window consisting of two layers of glass separated by an air space is considered. The rate of heat
transfer through the window and the temperature of its inner surface are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 Radiation effects are
negligible. 4 The pressure of air inside the enclosure is 1 atm.
Properties We expect the average temperature of the air gap to be roughly the
4
225
3-12
2
3
21 10065.5)7336.0(
)/sm 10426.1(
)m 03.0)(K 15)(K 003534.0)(m/s 81.9(
Pr
)(
LTTg
Ra
20-98
20-103 A solar collector consists of a horizontal tube enclosed in a concentric thin glass tube is considered. The pump
circulating the water fails. The temperature of the aluminum tube when equilibrium is established is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Air is an
ideal gas with constant properties. 3 The local atmospheric
1-
25
K 003284.0
K)2735.31(
11
7278.0Pr
/sm 10622.1
C W/m.02599.0
f
T
k
Analysis This problem involves heat transfer from the aluminum tube to the glass cover, and from the outer surface of the
glass cover to the surrounding ambient air. When steady operation is reached, these two heat transfers will be equal to the rate
Do =7 cm
Di = 5 cm,
= 1
Air space
20-99
1-
25
K 003203.0
K)27317.39(
11
7257.0Pr
/sm 10694.1
C W/m.02656.0
f
T
k
