16–21
16–44 A 4-m diameter spherical tank filled with liquid oxygen at 1 atm and –183C 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
16–22
16–45 Prob. 16–44 is reconsidered. The rate of evaporation of liquid nitrogen as a function of the ambient air
temperature is to be plotted.
Analysis The problem is solved using EES, and the solution is given below.
“GIVEN”
Tair
[C]
mevap
[kg/s]
0
2.5
5
7.5
10
12.5
15
17.5
20
22.5
25
27.5
30
32.5
35
37.5
40
1.244
1.26
1.276
1.292
1.307
1.323
1.339
1.355
1.371
1.387
1.403
1.418
1.434
1.45
1.466
1.482
1.498
0 5 10 15 20 25 30 35 40
1.2
1.25
1.3
1.35
1.4
1.45
1.5
Tair [C]
mevap [kg/s]
16–23
16–46 Power required to maintain the surface temperature of a long, 25 mm diameter cylinder with an imbedded electrical
heater for different air velocities.
Assumptions 1 Temperature is uniform over the cylinder surface. 2 Negligible radiation exchange between the cylinder
surface and the surroundings. 3 Steady state conditions.
Analysis (a) From an overall energy balance on the cylinder, the power dissipated by the electrical heater is transferred by
LW /
not linear with respect to the air velocity.
V (m/s)
LW /
(W/m)
h (W/m2K)
1
450
22.0
2
658
32.2
4
983
48.1
8
1507
73.8
12
1963
96.1
Air velocity, V (m/s)
0 2 4 6 8 10 12 14
Convection coefficient, h (W/m2K)
20
40
60
80
100
Plot of convection coefficient (h) versus air velocity (V)
16–24
(b) To determine the constants C and n, plot h vs. V on log-log coordinates. Choosing C = 22.12 W/m2.K(s/m)n, assuring a
match at V = 1, we can readily find the exponent n from the slope of the h vs. V curve. From the trials with n = 0.8, 0.6 and
0.5, we recognize that n = 0.6 is a reasonable choice. Hence, the best values of the constants are: C = 22.12 and n = 0.6. The
details of these trials are given in the following table and plot.
V (m/s)
LW /
(W/m)
h (W/m2K)
n
Vh 12.22
(W/m2K)
n = 0.5
n = 0.6
n = 0.8
1
450
22.0
22.12
22.12
22.12
2
658
32.2
31.28
33.53
38.51
4
983
48.1
44.24
50.82
67.06
8
1507
73.8
62.56
77.03
116.75
12
1963
96.1
76.63
98.24
161.48
Air velocity, V (m/s)
2 4 6 8 20110
Convection coefficient, h (W/m2K)
20
40
60
80
100
h = 22.12V0.5
h = 22.12V0.6
h = 22.12V0.8
Data points from part (a)
16–26
16–48 Prob. 16–47 is reconsidered. The convection heat transfer coefficient as a function of the wire surface
D=0.002 [m]
T_infinity=20 [C]
T_s=180 [C]
16–29
16-54 A spherical probe in space absorbs solar radiation while losing heat to deep space by thermal radiation. The incident
radiation rate on the probe surface is to be determined.
Assumptions 1 Steady operating conditions exist and surface temperature remains constant. 2 Heat generation is uniform.
16–30
16–55 Spherical shaped instrumentation package with prescribed surface emissivity within a large laboratory room having
walls at 77 K.
Assumptions 1 Uniform surface temperature. 2 Laboratory room walls are large compared to the spherical package. 3 Steady
state conditions.
W
16–31
Surface temperature, °C
40 50 60 70 80 90
Power dissipation, W
2
4
6
8
10
= 0.20
= 0.25
= 0.30
(1) As expected, the internal power dissipation increases with increasing emissivity and surface temperature. Because the
(2) At a constant surface temperature, the power dissipation is linear with respect to the emissivity. The trends of the
W
16–32
Simultaneous Heat Transfer Mechanisms
simultaneously.
16–58C The human body loses heat by convection, radiation, and evaporation in both summer and winter. In summer, we can
winter to force the warm air at the top downward to increase the air temperature at the body level. This is usually done by
forcing the air up which hits the ceiling and moves downward in a gently manner to avoid drafts.
16–33
16–60 The right surface of a granite wall is subjected to convection heat transfer while the left surface is maintained as a
constant temperature. The right wall surface temperature and the heat flux through the wall are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer through the granite wall is one dimensional. 3 Thermal
conductivity of the granite wall is constant. 4 Radiation hest transfer is negligible.
C35.5
2
2
2
2
1
2
2
21
convcond
KW/m15)m20.0/(K)W/m8.2(
C)(22K)W/m15()m20.0/()CK)(50W/m8.2(
)/(
)/(
)(
T
T
hLk
hTLkT
T
TTh
L
TT
k
qq
Now that T2 is known, we can calculate the heat flux. Since the heat transfer through the wall by conduction is equal to heat
transfer to the outer wall surface by convection, we may use either the Fourier’s law of heat conduction or the Newton’s law
2W/m203)225.35()KW/m15()(
k = 2.8 W/m K
Granite
20 cm
16–35
16–62 Air is blown over a hot horizontal plate which is maintained at a constant temperature. The surface also loses heat by
radiation. The inside plate temperature is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer through the steel plate is one dimensional. 3 Thermal
conductivity of the steel plate is constant.
)m02.0()W2485(
LQ
Steel Plate
16–37
16–64 Two large plates at specified temperatures are held parallel to each other. The rate of heat transfer between the plates is
to be determined for the cases of still air, evacuation, regular insulation, and super insulation between the plates.
Assumptions 1 Steady operating conditions exist since the plate temperatures remain constant. 2 Heat transfer is one-
dimensional since the plates are large. 3 The surfaces are black and thus = 1. 4 There are no convection currents in the air
space between the plates.
22) for air, and k = 0.036 W/mC for fiberglass insulation (Table A-6 of Cengel and Ghajar).
Analysis (a) Disregarding any natural convection currents, the rates of conduction and
radiation heat transfer
 
W511
372139
W372)K 150()K 290()m1)(K W/m1067.5(1
)(
W139
m 0.02
K )150290(
)m C)(1 W/m01979.0(
radcondtotal
442428
4
2
4
1rad
22
21
cond
QQQ
TTAQ
L
TT
kAQ
s

Q
·
T1
T2
16–39
16–67E A spherical ball whose surface is maintained at a temperature of 170°F is suspended in the middle of a room at 70°F.
The total rate of heat transfer from the ball is to be determined.
Assumptions 1 Steady operating conditions exist since the ball surface and
the surrounding air and surfaces remain at constant temperatures. 2 The
thermal properties of the ball and the convection heat transfer coefficient are
Btu/h 140.34.99.130
radconvtotal QQQ
Air