19–26
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
15644
14984
14324
13665
13007
12349
11692
11036
10381
9727
9073
8420
7768
7116
6466
5816
5166
4518
3870
3223
2577
0 2 4 6 8 10
2000
4000
6000
8000
10000
12000
14000
16000
T¥ [C]
Qconv [W]
19–27
19–30E 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
24 10863.8
/sft 10379.1
L
Since 5 105 < ReL < 107, the flow is a combined laminar and turbulent flow. Using the proper relation for Nusselt number,
the average heat transfer coefficient on the outer surface of the windshield is
o
Lh
19–29
19–32 Prob. 19–31 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.
w=2.8 [m]
L=8 [m]
q_dot_rad=200 [W/m^2]
T_infinity=30 [C]
“PROPERTIES”
55
60
65
70
75
80
85
90
95
100
105
120
36.32
35.86
35.47
35.13
34.84
34.58
34.35
34.14
33.96
33.79
33.64
33.25
30
40
Vel [km/h]
19–30
Qrad
[W/m2]
Ts
[C]
100
125
150
175
200
225
250
275
300
325
350
375
400
425
450
475
500
32.56
33.2
33.84
34.49
35.13
35.78
36.42
37.07
37.72
38.37
39.02
39.67
40.32
40.97
41.63
42.28
42.94
100 150 200 250 300 350 400 450 500
32
34
36
38
40
42
44
qrad [W/m2]
Ts [C]
19–31
19–33 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
7282.0Pr
Analysis (a) Assuming wind flows across 2 m surface, the
Reynolds number is determined from
6
25 10036.1
/sm 10608.1
m) m/s)(2 3600/100030(
Re
VL
L
which is greater than the critical Reynolds number. Using the
Nusselt number relation for combined laminar and turbulent flow,
the average heat transfer coefficient is determined to be
1378)7282.0](871)10036.1(037.0[Pr)871Re037.0(
3/18.063/18.0
k
hL
Nu
The rate of heat loss from the collector by radiation is
)(
44282
44
surrssrad TTAQ
700 W/m2
V = 30 km/h
T = 25C
L = 2 m
Solar radiation
Ts = 35C
19–33
19–35 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.
19–34
19–36 Air flow in parallel over the upper surface of a flat plate while the lower surface is subjected to uniform heat flux. The
surface temperature at x = 1.5 m is to be determined.
Assumptions 1 Steady operating conditions exist. 2 Local atmospheric pressure is 1 atm. 3 The critical Reynolds number is
Recr = 5 105.
19–36
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]
19–37
19–38 Air flows in parallel over a flat plate where the first-half length has a constant surface temperature and the second-half
length is subjected to uniform heat flux. The local convection heat transfer coefficients at x = 1 and 3 m are to be determined.
Assumptions 1 Steady operating conditions exist. 2 Local atmospheric pressure is 1 atm. 3 The critical Reynolds number is
Recr = 5 105.
34.105)7282.0()124378(332.0PrRe332.0Nu 3/15.03/15.0
x x
x
k
xh
95.248)7282.0()373134(453.0PrRe453.0Nu 3/15.03/15.0
x x
x
k
xh
Thus,
K W/m02588.0
k
19–39
x [m] Rex Ts [°C] Tf [°C] hx [W/m2∙K]
0.2 24875 50 30 6.092
0.3 37313 50 30 4.974
0.4 49751 50 30 4.308
0.5 62188 50 30 3.853
0.6 74626 50 30 3.517
0.8 99501 50 30 3.046
1.0 124377 50 30 2.725
1.2 149252 50 30 2.487
1.4 174128 50 30 2.303
1.6 199003 50 30 2.154
1.8 223878 50 30 2.031
2.0 248754 50 30 1.927
2.0 254093 42.70 26.35 2.630
2.2 278198 44.30 27.15 2.507
2.6 325924 47.29 28.65 2.306
3.0 373058 50.07 30.03 2.146
3.4 419648 52.66 31.33 2.016
3.8 465736 55.11 32.56 1.906
4.0 488603 56.29 33.14 1.858
0 0.5 1 1.5 2 2.5 3 3.5 4
1
2
3
4
5
6
7
x [m]
hx [W/m2·K]
0 0.5 1 1.5 2 2.5 3 3.5 4
35
40
45
50
55
60
T [°C]
Ts
Tf
