me3122-2 lab forced convection heat transfer
DESCRIPTION
ME3122-2 Lab Forced Convection Heat TransferTRANSCRIPT
ME3122E Lab 2 Forced
Convection Heat Transfer
by
LIN SHAODUN A0066078X
Group 1A
Date 13-Sept-2012
TABLE OF CONTENTS
RAW DATA 1
SAMPLE CALCULATION 6
DISCUSSION 10
CONCLUSION 12
1
RAW DATA
Table 1 Aluminum Sphere
Time (s) Pressure head
(mm water)
Sphere
Temperature
(C)
Atmosphere
Temperature
(C)
(
)
0 16.631 128.824 23.161 0.000 0.000
30 15.836 113.350 23.362 -0.159 4.041
60 15.942 97.608 23.370 -0.351 8.081
90 15.749 86.231 23.212 -0.517 12.122
120 15.430 77.293 23.130 -0.670 16.163
150 14.779 69.664 23.166 -0.822 20.203
180 15.517 63.183 23.218 -0.973 24.244
210 15.015 57.524 23.390 -1.126 28.284
240 14.978 52.714 23.339 -1.278 32.325
270 15.342 48.606 23.224 -1.428 36.366
300 15.248 45.018 23.250 -1.581 40.406
330 16.394 41.911 23.209 -1.735 44.447
360 15.831 39.361 23.482 -1.883 48.488
390 14.814 37.135 23.413 -2.032 52.528
420 15.197 35.222 23.250 -2.181 56.569
450 14.735 33.576 23.329 -2.330 60.610
480 15.480 32.183 23.411 -2.475 64.650
510 15.935 31.068 23.476 -2.610 68.691
540 15.772 29.998 23.404 -2.758 72.732
Average 15.507 58.972 23.305 - -
2
Graph 1a Aluminum Sphere
Graph 1b Aluminum Sphere
y = -0.0377x - 0.0454
R² = 0.9995
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0 10 20 30 40 50 60 70 80
ln[(
T -
T∞)
/ (T
i - T
∞)]
αt / ro²
ln[(T - T∞) / (Ti - T∞)] vs. αt/ro² (Aluminium)
y = -0.1621x + 102.75
R² = 0.8655
0
20
40
60
80
100
120
140
0 50 100 150 200 250 300 350 400 450 500 550
Tem
per
atu
re (C
)
Time (Sec)
Temperature vs. Time (Aluminium)
3
Table 2 Brass Sphere
Time (s) Pressure head
(mm water)
Sphere
Temperature
(C)
Atmosphere
Temperature
(C)
(
)
0 16.089 136.267 23.577 0.000 0.000
30 15.192 123.162 23.428 -0.124 1.638
60 15.164 111.505 23.457 -0.248 3.276
90 15.405 101.353 23.413 -0.371 4.913
120 15.636 92.267 23.368 -0.495 6.551
150 15.555 84.140 23.499 -0.621 8.189
180 15.829 77.060 23.770 -0.746 9.827
210 15.841 70.734 23.700 -0.872 11.464
240 14.685 65.270 23.592 -0.995 13.102
270 15.386 60.441 23.569 -1.118 14.740
300 15.148 56.133 23.494 -1.242 16.378
330 15.058 52.326 23.508 -1.367 18.015
360 14.633 49.011 23.588 -1.490 19.653
390 15.325 46.116 23.464 -1.611 21.291
420 14.510 43.540 23.595 -1.732 22.929
450 14.899 41.276 23.574 -1.853 24.566
480 14.525 39.361 23.685 -1.968 26.204
510 14.330 37.592 23.797 -2.087 27.842
540 13.880 36.085 23.726 -2.201 29.480
570 14.504 34.761 23.535 -2.313 31.117
600 14.536 33.472 23.624 -2.436 32.755
630 14.400 32.461 23.792 -2.544 34.393
660 14.285 31.521 23.852 -2.656 36.031
690 14.507 30.705 23.948 -2.765 37.668
720 13.922 29.932 23.777 -2.881 39.306
Average 14.930 60.660 23.613 - -
4
Graph 2a Brass Sphere
Graph 2b Brass Sphere
y = -0.0736x - 0.0224
R² = 0.9996
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0 5 10 15 20 25 30 35 40 45
ln[(
T -
T∞)
/ (T
i - T
∞)]
αt / ro²
ln[(T - T∞) / (Ti - T∞)] vs. αt/ro² (Brass)
y = -0.1316x + 108.04
R² = 0.8662
0
20
40
60
80
100
120
140
0 100 200 300 400 500 600 700
Tem
per
atu
re (C
)
Time (Sec)
Temperature vs. Time (Brass)
5
Table 3 Teflon Sphere
Time (s) Pressure head
(mm water)
Sphere
Temperature
(C)
Atmosphere
Temperature
(C)
(
)
0 15.365 106.013 23.853 0.000 0.000
30 14.621 102.988 23.971 -0.038 0.007
60 13.898 98.450 23.822 -0.097 0.015
90 14.088 95.465 23.714 -0.138 0.022
120 13.321 93.396 23.779 -0.167 0.029
150 13.080 91.889 23.999 -0.189 0.036
180 13.683 90.574 23.757 -0.208 0.044
210 14.502 89.215 23.788 -0.229 0.051
240 14.201 87.986 23.741 -0.248 0.058
270 14.088 86.651 23.954 -0.269 0.066
300 14.171 85.267 24.054 -0.291 0.073
330 13.807 83.876 23.807 -0.314 0.080
360 13.787 82.418 24.038 -0.339 0.088
390 14.335 80.815 23.893 -0.367 0.095
420 13.694 79.153 23.962 -0.397 0.102
450 13.880 77.509 24.007 -0.427 0.109
480 13.855 75.826 23.928 -0.459 0.117
510 14.412 74.089 24.061 -0.493 0.124
540 13.952 72.375 23.929 -0.528 0.131
570 14.175 70.644 24.028 -0.564 0.139
600 14.301 69.022 23.984 -0.599 0.146
630 14.724 67.319 23.914 -0.638 0.153
660 14.083 65.655 23.906 -0.677 0.161
690 13.998 64.027 23.916 -0.717 0.168
720 14.220 62.453 23.862 -0.757 0.175
750 13.556 60.944 24.051 -0.797 0.182
780 14.283 59.434 23.995 -0.839 0.190
810 14.351 58.015 24.024 -0.879 0.197
840 14.482 56.612 23.900 -0.921 0.204
870 13.399 55.304 23.862 -0.962 0.212
900 14.429 53.974 24.013 -1.006 0.219
930 14.202 52.765 24.199 -1.047 0.226
960 14.469 51.562 23.921 -1.089 0.233
990 14.383 50.377 24.095 -1.133 0.241
1020 13.799 49.254 24.012 -1.177 0.248
1050 13.283 48.213 24.038 -1.219 0.255
1080 14.243 47.183 23.924 -1.262 0.263
1110 14.602 46.206 24.064 -1.305 0.270
1140 14.012 45.233 23.953 -1.350 0.277
1170 13.979 44.363 23.978 -1.392 0.285
1200 13.903 43.502 24.133 -1.435 0.292
1230 14.012 42.541 23.803 -1.485 0.299
1260 14.718 41.882 23.748 -1.521 0.306
1290 14.682 41.121 23.859 -1.565 0.314
1320 14.979 40.351 23.866 -1.611 0.321
1350 14.646 39.681 23.956 -1.652 0.328
Average 14.217 51.519 23.960 - -
6
Graph 3a Teflon Sphere
Graph 3b Teflon Sphere
y = -4.993x + 0.0632
R² = 0.989
-1.8
-1.6
-1.4
-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0 0.04 0.08 0.12 0.16 0.2 0.24 0.28 0.32
ln[(
T -
T∞)
/ (T
i - T
∞)]
αt / ro²
ln[(T - T∞) / (Ti - T∞)] vs. αt/ro² (Teflon)
y = -0.048x + 99.372
R² = 0.987
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400
Tem
per
atu
re (C
)
Time (Sec)
Temperature vs. Time (Teflon)
7
SAMPLE CALCULATION
1. Method 1: Lumped-heat-capacity method
Table 4 Calculation of convective heat transfer coefficient
Sphere Material Aluminum Brass Teflon
Gradient of curve
-0.0377 -0.0736 -4.993
Biot Number
( ⁄ )
0.0042 0.0082 0.555
Validity of the lumped-
heat-capacity method
Convective heat transfer
coefficient
2. Method 2
Table 5 Calculation of convective heat transfer coefficient
Sphere
Material Aluminum Brass Teflon
Gradient of curve
-0.1621 -0.1316 -0.048
(
)
( )
( )
( )
24.150 26.599 6.047
( )
( )
( )
( )
8
3. Method 3: Empirical relation (Whitaker)
Table 6 Calculation of convective heat transfer coefficient
Sphere Material Aluminum Brass Teflon
Initial sphere temp, K 401.97 409.42 379.16
Average sphere temp, K 332.12 333.81 324.67
Average ambient temp, K 296.46 296.76 297.11
0.709 0.709 0.709
1.190 1.189 1.188
0.0155 0.0149 0.0142
√
15.99 15.70 15.32
51997 50958 49658
( )
( )
169.71 168.18 160.78
0.02597 0.02599 0.02602
88.15 87.43 83.68
9
4. Method 4: Heisler Chart
Table 7 Calculation of convective heat transfer coefficient
Sphere Material Aluminum Brass Teflon
Initial sphere temp, 401.97 409.42 379.16
Average sphere temp, 332.12 333.81 324.67
Average ambient temp, 296.46 296.76 297.11
Y axis
0.338 0.329 0.336
X axis
28.284 14.740 0.233
⁄
⁄ 78 44 0.05
Convective heat transfer
coefficient 105.6 116.4 280.0
10
Table 8 Experimentally determined convective heat transfer coefficients
Spheres Reynolds
Number
Convective Heat Transfer Coefficient, W/m2 K
Method 1 Method 2 Method 3 Method 4
Aluminum 51997 103.55 86.21 88.15 105.6
Brass 50958 125.61 91.42 87.43 116.4
Teflon 49658 23.30 27.94 83.68 280.0
DISCUSSION
1. Compare the convective heat transfer coefficients of the methods 1, 2 and 4 with that
obtained from the method 3. Give a brief account on possible causes of the discrepancy
in the values of the heat transfer coefficient obtained from method #3.
Here is the comparison of Convective Heat Transfer Coefficient with different calculation
methods:
For Method 1(lumped-heat-capacity method), the result for Aluminum and Brass sphere is
higher (17% ~ 42%) than Method 3, while the result for Teflon sphere is significantly different
(72%) from Method 3.
The transient heat transfer processes such as cooling of a solid sphere are normally
multidimensional in nature because the temperature within the body is a function of time and at
least one space dimension. However, approximate analysis can be obtained if the Biot number
( ⁄ )
is small, under this condition, the variation of temperature with the spatial coordinates will
be negligibly small, such that the temperature can be taken as a function of time only. The
Lumped-heat-capacity type of analysis yields reasonable estimates when Biot number <0.1.
103.55 125.61
23.3
86.21 91.42
27.94
88.15 87.43 83.68 105.6
116.4
280
0
50
100
150
200
250
300
Aluminium Brass Teflon
Convec
tion C
oef
fici
ent Method 1
Method 2
Method 3
Method 4
11
From Table 4 one can see that the Biot number for Aluminum and Brass sphere is much smaller
than 0.1, while for Teflon sphere, the Biot number is larger than 0.1, hence, the Lumped-heat-
capacity method is not applicable for Teflon sphere and result in very large error.
Sphere Material Aluminum Brass Teflon
( ⁄ )
0.0042 0.0082 0.555
Validity of the lumped-
heat-capacity method
For Method 2, the result for Aluminum and Brass sphere is very close (2~5%) to Method 3,
while the result for Teflon sphere is significantly different (67%) from Method 3.
Method 2 has taken both convection and radiation into consideration, so the result is much closer
to Method 3 compare with Method 1.
For Method 4 (Heisler Chart), the result for Aluminum and Brass sphere is higher than
(20~33%) to Method 3, while the result for Teflon sphere is significantly higher (235%) than
Method 3. This is because the limitation of Heisler Chart as it doesn’t have enough resolution
when the is very small. In this experiment the thermal diffusivity of Teflon is much
smaller than Aluminum and Brass, which result in very small value in X-axis of Heisler Chart, so
that it is impossible to read an accurate Biot number from the chart, which directly affects the
calculation of convection coefficient.
For Method 3, the empirical relation (Whitaker) ignored some material properties like emissivity
and thermal diffusivity, and it also does not consider the radiation effect, which will introduce
some discrepancy in the result. For Method 3, it requires the following condition to be fulfilled so
that the empirical relation can be satisfied:
. From table 6, one can see that the P_r number is 0.709, which is in the marginal
condition; hence the method 3 calculation may not be very accurate in this case.
2. Comment on the values of heat transfer coefficients obtained from method 1, 2,
3 and 4.
Base on values of heat transfer coefficients obtained from method 1, 2, 3 and 4, here are the
comments:
1) Method1, only consider convection heat transfer and ignore radiation, so the convection
coefficient will be larger than actual value. And this method is not applicable when the
Biot number is larger than 0.1.
12
2) For Method 2, the Temperature vs. Time curve is non-linear, hence the
will not be a
constant value, but in the calculation, the nonlinearity of the curve is ignored, that will
introduce some discrepancy into calculation. Method 2 has taken both convection and
radiation into consideration, so the result is much closer to Method 3 compare with
Method 1.
3) For Method 3, the empirical relation (Whitaker) ignored some material properties like
emissivity and thermal diffusivity, and it also does not consider the radiation effect, which
will introduce some discrepancy in the result , that is the reason the convection coefficient
calculated by this method is very close for 3 very different materials.
4) For Method 4, the accuracy is depends on how user read the chart, for some material has
very low thermal diffusivity, the resolution of the chart is not enough, so it will create
huge error. It also does not consider the radiation effect, so the calculated convection
coefficient will be higher than actual value.
CONCLUSION
After this experiment, I have gone through the different kinds of configuration and practical
analysis on forced convective heat transfer process. I have understand well of their fundamental
principle, properties, characteristic.
By analyzing between graph and practical approach, I have learned about the practical
limitations. I have learnt about the relationship between flow across the sphere and heat transfer
from the sphere as well.
As a summary, by going through this experiment, I had gained the required topical knowledge of
forced convective heat transfer process from the sphere.