19–41
Flow across Cylinders and Spheres
19–41C For the laminar flow, the heat transfer coefficient will be the highest at the stagnation point which corresponds to
0
. In turbulent flow, on the other hand, it will be highest when
is between
120 and 90
.
19–42 A steam pipe is exposed to windy air. The rate of heat loss from the steam is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Radiation effects are negligible. 3 Air is an ideal gas with constant
7232.0Pr
Analysis The Reynolds number is
4
25 10228.6
/sm 10784.1
m) (0.08]s/h) 0m/km)/(360 1000(km/h) (50[
Re
VD
The Nusselt number corresponding to this Reynolds number is
1.159
000,282
10228.6
1
7232.0/4.01
)7232.0()10228.6(62.0
3.0
000,282
Re
1
Pr/4.01
PrRe62.0
3.0
5/4
8/5
4
4/1
3/2
3/15.04
5/4
8/5
4/1
3/2
3/15.0
k
hD
Nu
Air
V = 50 km/h
T = 7C
Pipe
D = 8 cm
Ts = 90C
19–43
19–44E A person extends his uncovered arms into the windy air outside. The rate of heat loss from the arm is to be
determined.
Assumptions 1 Steady operating conditions exist. 2 Radiation effects are negligible. 3 Air is an ideal gas with constant
19–45
Vel
[mph]
Qconv
[Btu/h]
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
250.4
278.7
305.4
331
355.7
379.5
402.7
425.2
447.3
468.9
490.1
511
531.5
551.7
571.7
591.4
10 15 20 25 30 35 40
200
250
300
350
400
450
500
550
600
Vel [mph]
Qconv [Btu/h]
19–46
19–46 The wind is blowing across a geothermal water pipe. The average wind velocity is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Radiation effects are negligible. 3 Air is an ideal gas with constant
properties. 4 The local atmospheric pressure is 1 atm.
7241.0Pr
Analysis The rate of heat transfer from the pipe is the
energy change of the water from inlet to exit of the pipe,
and it can be determined from
T = 15C
Water
19–50
19–50E A fan is blowing air over the entire body of a person. The average temperature of the outer surface of the person is to
be determined for two cases.
Assumptions 1 Steady operating conditions exist. 2 Radiation effects are negligible. 3 Air is an ideal gas with constant
7260.0Pr
Analysis The Reynolds number is
4
24 10317.3
/sft 10809.1
ft) ft/s)(1 (6
Re
VD
The proper relation for Nusselt number corresponding to this Reynolds number is
4
/sft 10809.1
VD
000,282
Re
1
Pr)/4.0(1
PrRe62.0
3.0
5/4
8/5
4/1
3/2
3/15.0
k
hD
Nu
V = 6 ft/s
T = 85F
Person, Ts
300 Btu/h
D = 1 ft
19–51
19–51E An electrical resistance wire is cooled by a fan. The surface temperature of the wire is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Radiation effects are negligible. 3 Air is an ideal gas with constant
properties. 4 The local atmospheric pressure is 1 atm.
7124.0Pr
Analysis The Reynolds number is
7.692
/sft 10406.2
ft) 12ft/s)(0.1/ (20
Re 24
VD
T = 85F
Resistance
wire
D = 0.1 in
19–53
19–53 A cylindrical hot water tank is exposed to windy air. The temperature of the tank after a 45-min cooling period is to be
estimated.
Assumptions 1 Steady operating conditions exist. 2 Radiation effects are negligible. 3 Air is an ideal gas with constant
properties. 4 The surface of the tank is at the same temperature as the water temperature. 5 The heat transfer coefficient on
the top and bottom surfaces is the same as that on the side surfaces.
Properties The properties of water at 80C are (Table A-15)
kg/m 8.971 3
7228.0Pr
Analysis The Reynolds number is
Air
5
m) (0.50m/s
3600
100040
VD
Water tank
D =50 cm
L = 95 cm
19–54
19–54 Prob. 19–53 is reconsidered. The temperature of the tank as a function of the cooling time is to be plotted.
Analysis The problem is solved using EES, and the solution is given below.
L=0.95 [m]
T_w1=80 [C]
T_infinity=18 [C]
Vel=40 [km/h]
time=45 [min]
19–56
19–56 A steam pipe is exposed to light winds in the atmosphere. The amount of heat loss from the steam during a certain
period and the money the facility will save a year as a result of insulating the steam pipes are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 The plant operates every
7255.0Pr
Analysis The Reynolds number is
4
25 10632.1
/sm 10702.1
m) (0.10m/s 1000/3600)(10
Re
VD
The Nusselt number corresponding to this Reynolds number is determined to be
000,282
Re
1
Pr)/4.0(1
PrRe62.0
3.0
5/4
8/5
4/1
3/2
3/15.0
k
hD
Nu
Wind
V = 10 km/h
T = 5C
Steam pipe
Ts = 75C
D = 10 cm
= 0.8
19–58
19–58 The average surface temperature of the head of a person when it is not covered and is subjected to winds is to be
determined.
Assumptions 1 Steady operating conditions exist. 2 Radiation effects are negligible. 3 Air is an ideal gas with constant
properties. 4 One-quarter of the heat the person generates is lost from the head. 5 The head can be approximated as a 30–cm–
7336.0Pr
kg/m.s 10802.1
5
C15@
,
s
Analysis The Reynolds number is
5
m) (0.3m/s 1000/3600)(25
VD
T = 10C
D =0.3 m
19–59
19–59 A light bulb is cooled by a fan. The equilibrium temperature of the glass bulb is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 The light bulb is in
spherical shape. 4 The local atmospheric pressure is 1 atm.
Properties We assume the surface temperature to be 100C for viscosity based on the problem statement. The properties of
7282.0Pr
kg/m.s 10181.2
5
C100@
,
s
Analysis The Reynolds number is
4
m) m/s)(0.1 (2
VD
= 0.9
T = 30C
19–60
19–60 Air flows over a spherical tank containing iced water. The rate of heat transfer to the tank and the rate at which ice
melts are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Radiation effects are negligible. 3 Air is an ideal gas with constant
properties. 4 The local atmospheric pressure is 1 atm.
7296.0Pr
kg/m.s 10729.1
5
C0@
,
s
Analysis The Reynolds number is
5
m) m/s)(1.8 (7
VD
T =25C
D =1.8
m
Iced
water