7-41
7-46 Wind is blowing parallel to the wall of a house. The rate of heat loss from that wall is to be determined for two cases.
Assumptions 1 Steady operating conditions exist. 2 The critical Reynolds number is Recr = 5105. 3 Radiation effects are
negligible. 4 Air is an ideal gas with constant properties.
Properties The properties of air at 1 atm and the film temperature
of (Ts + T)/2 = (12+5)/2 = 8.5C are (Table A-15)
7340.0Pr
/sm 10413.1
C W/m02428.0
25–
=
=
=
k
Analysis Air flows parallel to the 10 m side:
The Reynolds number in this case is
6
m) m/s](10)3600/100042[(
VL
Air
V = 42 km/h
T = 5C
L
Ts = 12C
7-43
T
[C]
Qconv
[W]
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
18649
17861
17074
16288
15503
14719
13936
13154
12373
11592
10813
10035
9257
8481
7705
6930
6157
5384
4612
3841
3071
0 2 4 6 8 10
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
T [C]
Qconv [W]
7-44
7-48E Warm air blowing over the inner surface of an automobile windshield is used for defrosting ice accumulated on the
outer surface. The convection heat transfer coefficient for the warm air blowing over the inner surface of the windshield,
necessary to cause the accumulated ice to begin melting, is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Heat transfer through the windshield is one-dimensional. 3 Thermal
properties are constant. 4 Heat transfer by radiation is negligible. 5 The outside air pressure is 1 atm. 6 The critical Reynolds
number is Recr = 5105.
Properties The properties of air at the film temperature of Tf = (8°F + 32°F)/2 = 20°F are k = 0.01336 Btu/h∙ft∙R,
= 1.379
10−4 ft2/s, Pr = 0.7378 (from Table A-15E).
Analysis On the outer surface of the windshield, the Reynolds number at L = 20 in. is
5
)ft 12/20)(ft/s 46667.150(
VL
iw
o
hkt
h
/1//1
+
For the ice to begin melting, the outer surface temperature of the windshield (
os
T,
) should be at least 32°F. The convection
heat transfer coefficient for the warm air blowing over the inner surface of the windshield is
RftBtu/h 5.36 2=
−
−
−
−
−
=
−
−
1
2
1
,,
,,
RftBtu/h 8.0
ft 12/2.0
RftBtu/h 042.9
1
F)328(
F)7732(
1
woso
ios
o
ik
t
TT
TT
h
h
Discussion To keep the ice from accumulating for the given conditions, the convection heat transfer coefficient for the warm
air blowing over the inner surface of the windshield needs to be at least 5.36 Btu/h∙ft2∙R or higher.
7-46
7-50 Prob. 7-49 is reconsidered. The effects of the train velocity and the rate of absorption of solar radiation on the
equilibrium temperature of the top surface of the car are to be investigated.
Analysis The problem is solved using EES, and the solution is given below.
“GIVEN”
Vel=95 [km/h]
w=2.8 [m]
L=8 [m]
q_dot_rad=380 [W/m^2]
T_infinity=30 [C]
“PROPERTIES”
Fluid$=’air’
k=Conductivity(Fluid$, T=T_film)
Pr=Prandtl(Fluid$, T=T_film)
rho=Density(Fluid$, T=T_film, P=101.3)
mu=Viscosity(Fluid$, T=T_film)
nu=mu/rho
T_film=1/2*(T_s+T_infinity)
“ANALYSIS”
Re=(Vel*Convert(km/h, m/s)*L)/nu
“Reynolds number is greater than the critical Reynolds number. We use combined laminar and turbulent flow
relation for Nusselt number”
Nusselt=(0.037*Re^0.8-871)*Pr^(1/3)
h=k/L*Nusselt
q_dot_conv=h*(T_s-T_infinity)
q_dot_conv=q_dot_rad
Vel
[km/h]
Ts
[C]
10
15
20
25
30
35
40
45
50
55
60
65
70
99
72.06
61.02
54.87
50.91
48.12
46.04
44.43
43.14
42.08
41.2
40.45
39.8
40
50
60
70
80
90
100
Ts [C]
7-47
Qrad
[W/m2]
Ts
[C]
100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
500
31.98
32.47
32.97
33.46
33.96
34.46
34.95
35.45
35.95
36.45
36.95
37.45
37.95
38.45
38.95
39.45
39.96
100 150 200 250 300 350 400 450 500
32
34
36
38
40
qrad [W/m2]
Ts [C]
7-48
7-51 Solar radiation is incident on the glass cover of a solar collector. The total rate of heat loss from the collector, the
collector efficiency, and the temperature rise of water as it flows through the collector are to be determined.
Assumptions 1 Steady operating conditions exist. 2 The critical Reynolds number is Recr = 5105. 3 Heat exchange on the
back surface of the absorber plate is negligible. 4 Air is an ideal gas with constant properties. 5 The local atmospheric
pressure is 1 atm.
Properties The properties of air at the film temperature of
C 302/)2535(=+
are (Table A-15)
7282.0Pr
/sm 10608.1
C W/m.02588.0
25–
=
=
=
k
Analysis (a) Assuming wind flows across 2 m surface, the
Reynolds number is determined from
6
m) m/s)(2 3600/100030(
VL
W2.741
=
and
W1169=+=+= 2.7419.427
radconvtotal QQQ
(b) The net rate of heat transferred to the water is
0.209===
−=
−=−=
W1478
W309
W1169) W/m)(700m 2.12)(88.0( 22
in
net
collector
outoutinnet
Q
Q
QAIQQQ
(c) The temperature rise of water as it flows through the collector is
W4.309
net
Q
700 W/m2
V = 30 km/h
T = 25C
Solar radiation
Ts= 35C
Tsky = –40C
7-52
b=h/(rho_plate*c_p_plate*L_c)
ln((T_s_f-T_infinity)/(T_s_i-T_infinity))=-b*t
7-54
7-56 Liquid mercury is flowing in parallel over a flat plate, (a) the local convection heat transfer coefficient at 5 cm from the
leading edge and (b) the average convection heat transfer coefficient over the entire plate are to be determined.
Assumptions1 Steady operating conditions exist. 2 Surface temperature is uniform throughout the plate. 3 Thermal properties
are constant. 4 The critical Reynolds number is Recr = 5105.
Properties The properties of liquid mercury at Tf = (250°C + 50°C)/2 = 150°C are k = 10.07780 W/m∙K,
= 8.514 10−8
m2/s, Pr = 0.0152 (from Table A-14).
Analysis (a) The Reynolds number at x = 0.05 m is
5
)m 05.0)(m/s 3.0(
Vx
7-56
7-58 A silicon chip is mounted flush in a substrate that provides an unheated starting length. The surface temperature at the
trailing edge of the chip is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Thermal properties are constant. 3 The critical Reynolds number is Recr =
5105. 4 Only the upper surface of the chip is conditioned for heat transfer. 5 Heat transfer by radiation is negligible.
Properties The properties of air at 50°C are k = 0.02735 W/m∙K,
= 1.798 10−5 m2/s, Pr = 0.7228 (from Table A-15).
Analysis The Reynolds number at the trailing edge (x = 0.030 m) is
4
25 10171.4
/sm 10798.1
)m 030.0)(m/s 25(
Vx
x
Since Rex< 5 105 at the trailing edge, the flow over the entire heated section is laminar. Using the proper relation for
Nusselt number, the local heat transfer coefficient at the trailing edge (x = 0.030 m) can be determined:
3/14/3
)0for (
])/(1[
Nu
Nu x
x
x
−
==
→
3/14/3
3/15.0
])/(1[
PrRe453.0
x
x
k
hx
x
−
=
K W/m3.102
])30/15(1[
)7228.0()10171.4(453.0
)m 030.0(
)K W/m02735.0( 2
3/14/3
3/15.04
=
−
=
x
h
Then the surface temperature at the trailing edge of the chip is
)(/
−= TThAQ s
→
C80.8=+
=+= C20
K W/m3.102
)m 015.0/( W)4.1(/
2
2
T
h
AQ
Ts
Discussion The assumed temperature of 50°C for evaluating the air properties turned out to be a good estimation, since Tf =
(80.8°C + 20°C)/2 = 50.4°C.
7-57
7-59 An ASTM A437 B4B stainless steel bolt is embedded at mid-length of a 1-m long plate. The minimum suitable
temperature for the bolt is −30°C. Cold gas flows in parallel over the plate’s upper surface. The plate is subjected to a
uniform heat flux of 250 W/m2. The surface temperature of the plate at the location where the bolt is embedded is to be
determined.
Assumptions 1 The flow is steady and incompressible. 2 Uniform heat flux subjected to plate. 3 Edge effects of plate are
negligible. 4 The critical Reynolds number is Recr = 5 × 105.
Properties The properties of the gas are given as Pr = 0.7440, k = 0.01979 W/m∙K, and ν = 9.319 × 10−6 m2/s
Analysis The Reynolds number at the end of the plate is
7-59
7-61 Air flows in parallel over the upper surface of a flat plate while the lower surface is subjected to uniform heat
flux.The local convection heat transfer coefficient, local surface temperature, and local film temperature along the plate are to
be evaluated.
Assumptions 1 Steady operating conditions exist. 2 Local atmospheric pressure is 1 atm. 3 The critical Reynolds number is
Recr = 5105. 4 Flow is laminar (this assumption will be verified).
Analysis For laminar flow, the relation for local Nusselt number along a flat plate subjected to uniform heat flux is
3/15.0
x
xh ==
x [m] Rex Ts [°C] Tf [°C] hx [W/m2∙K]
0.2 26550 102.5 58.74 9.260
0.3 37847 122.3 68.63 7.552
0.4 48397 139.0 76.99 6.534
0.5 58358 153.7 84.36 5.839
0.6 67831 167.1 91.04 5.326
0.7 76889 179.4 97.18 4.928
0.8 85585 190.8 102.9 4.607
0.9 93962 201.6 108.3 4.341
1.1 109884 221.5 118.2 3.923
1.3 124860 239.7 127.3 3.605
1.5 139035 256.5 135.8 3.354
1.7 152521 272.3 143.6 3.148
1.9 165401 287.2 151.1 2.976
7-60
0 0.5 1 1.5 2 2.5 3
50
100
150
200
250
300
350
400
x [m]
T [°C]
Ts
Tf
0 0.5 1 1.5 2 2.5 3
2
3
4
5
6
7
8
9
10
x [m]
hx [W/m2·K]