College of Engineering and Science
Department of Mechanical and Civil Engineering
ME 41700
Heat Transfer
Lab 03
Temperature Profile in Solids
Prepared by: Waleed Alqarni
Date Submitted: 02/23/2021
Table of Contents
Introduction ................................................................................................................ 3
Objective .................................................................................................................... 3
Equipment Used......................................................................................................... 3
Procedure................................................................................................................... 3
Results ....................................................................................................................... 4
Temperature Distribution Curves ............................................................................ 4
Rod 1 (Aluminum 1” Dia)..................................................................................... 4
Rod 2 (Aluminum 0.5” Dia) .................................................................................. 4
Rod 3 (Steel 1” Dia) ............................................................................................ 5
Heat Dissipation Rate and Efficiency ...................................................................... 5
Discussion .................................................................................................................. 5
Measured Temperature Distribution ....................................................................... 5
Experimental vs Theoretical Temperature Distributions ......................................... 5
Comparison for Rod 1 ......................................................................................... 6
Comparison for Rod 2 ......................................................................................... 6
Comparison for Rod 3 ......................................................................................... 6
Accuracy of Determination...................................................................................... 7
Conclusion ................................................................................................................. 7
Appendices ................................................................................................................ 8
Data Collected............................................................................................................ 8
List of Figures
Figure 1 Heat transfer lab apparatus setup 3
Figure 2 Temperature distribution curve for time parameters in rod 1 4
Figure 3 Temperature distribution curve for time parameters in rod 2 4
Figure 4 Temperature distribution curve for time parameters in rod 3 5
Figure 5 Experimental vs Theoretical temperature distributions along the rod 1 6
Figure 6 Experimental vs Theoretical temperature distributions along the rod 2 6
Figure 7 Experimental vs Theoretical temperature distributions along the rod 3 7
List of Tables
Table 1 Calculated heat dissipation and system efficiency for each rod 5
Table 2 Raw data from lab performance for rod 1 8
Table 3 Raw data from lab performance for rod 2 8
Table 4 Raw data from lab performance for rod 3 9
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Introduction
In the proceeding lab, rods of different size and materials are used analogous to fins
to observe the convection heat losses throughout the process. The experiment will
depict the steady state flow development in the system over time.
Objective
To experimentally determine the temperature distribution over the fin (rod) and
compare it with the theoretical profile to notice the conformance and probable errors
associated. Also, the lab is used to calculate the heat dissipate in various rods and the
efficiency of heat transfer through them.
Equipment Used
Three rods (two aluminum of size 1 inch and 0.5 inch respectively and one steel of 1
inch diameter). The rods are connected to a steam inlet valve which flows the steam
through each rod. Ten thermocouples are attached on each rod at a known distance
to measure the temperature during steam flow in the form of voltage which is then
converted to temperature reading.
Figure 1 Heat transfer lab apparatus setup
Procedure

Set up the apparatus and start the system by discharging the steam flow
through first rod.
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

Open TPIS software from the computer and note the readings of all
thermocouples with equal intervals until steady state is achieved.
Repeat the procedure for remaining two rods and jot down the lab data for
further calculations.
Results
Relevant formulae as specified in appendix (from lab manual) are used to determine
the theoretical temperature distribution, heat transferred and efficiency of the system
for each rod. The results for each rod are given below,
Temperature Distribution Curves
Rod 1 (Aluminum 1” Dia)
Temperature Distribution for Rod 1
390,000
Temperature (K)
370,000
350,000
330,000
310,000
290,000
270,000
0
0,2
0,4
0,6
0,8
1
Length down the fin (m)
Figure 2 Temperature distribution curve for time parameters in rod 1
Rod 2 (Aluminum 0.5” Dia)
Temperature Distribution for Rod 2
390,000
Temperature (K)
370,000
350,000
330,000
310,000
290,000
270,000
0
0,2
0,4
0,6
0,8
1
Length down the fin (m)
Figure 3 Temperature distribution curve for time parameters in rod 2
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Rod 3 (Steel 1” Dia)
Temperature Distribution for Rod 3
390,000
Temperature (K)
370,000
350,000
330,000
310,000
290,000
270,000
0
0,2
0,4
0,6
0,8
1
Length down the fin (m)
Figure 4 Temperature distribution curve for time parameters in rod 3
Heat Dissipation Rate and Efficiency
The heat dissipation rate for all rods is tabulated below,
Table 1 Calculated heat dissipation and system efficiency for each rod
Rod Specification
Aluminum 1” Dia
Aluminum 0.5” Dia
Steel 1” Dia
Heat Dissipation Rate
(W)
Finite
Infinite
Length
Length
27.123
27.252
9.631
9.635
27.123
27.252
Efficiency (%)
Finite
Length
33.19%
23.57%
33.19%
Infinite
Length
33.35%
23.58%
33.35%
Discussion
Measured Temperature Distribution
The calculated distribution curves show that there is an unsteadiness in the data if it
were promptly collected and the system is not given the time to stabilize the
parameters. Furthermore, the plots show that the conformance towards a steady set
of values increases with the increase in time, but it stops after a certain period. After
that period, it is safe to say that the steady conditions in the system have been
achieved. Also, the curves show the decrease in temperature with the increase in
distance (length of fins) from the heating source; this conduction phenomenon clearly
conforms to the theoretical concept of heat distribution through a conductive body.
Experimental vs Theoretical Temperature Distributions
To thoroughly understand the comparison, a plot has been prepared for each rod
individually which compares the steady states of both theoretical as well as
experimental readings.
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Comparison for Rod 1
The resulting plot below shows very close approximation between the two curves
which indicates conformance and a verification to the theoretical formulae implied.
Theor. vs Exp. Comparison for Rod 1
390,000
Temperature (K)
370,000
350,000
330,000
310,000
290,000
270,000
0
0,2
0,4
0,6
0,8
1
Length down the fin (m)
Figure 5 Experimental vs Theoretical temperature distributions along the rod 1
Comparison for Rod 2
The resulting plot below shows even closer approximation between the two curves
than for rod 1, which again indicates conformance and a verification to the theoretical
formulae implied.
Theor. vs Exp. Comparison for Rod 2
390,000
Temperature (K)
370,000
350,000
330,000
310,000
290,000
270,000
0
0,2
0,4
0,6
0,8
1
Length down the fin (m)
Figure 6 Experimental vs Theoretical temperature distributions along the rod 2
Comparison for Rod 3
The resulting plot below shows high-end deviation between the two curves which
indicates that the system or the rod material (steel) is not suitable for heat transfer or
the equation used is not applicable for the said material type.
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Theor. vs Exp. Comparison for Rod 3
390,000
Temperature (K)
370,000
350,000
330,000
310,000
290,000
270,000
0
0,2
0,4
0,6
0,8
1
Length down the fin (m)
Figure 7 Experimental vs Theoretical temperature distributions along the rod 3
Accuracy of Determination
The resulting heat dissipation for both finite and infinite lengths of rods along with their
respective efficiencies show conformance to each other. The resulting heat dissipation
values also indicate that as the size of fin rods increases, the heat transfer increases
as well.
Conclusion
The above lab is a detailed demonstration of heat dissipation through solid fins. The
notion is depicted with the analogy of rods as fins by determining the temperature
distributions and the associated heat transfer properties of each material and size of
rod. The results show conformance to the theoretical relations and concepts which
marks the experiment as successful. There are however, some errors in the readings
which maybe due to calibration of thermocouples or the minor heat losses
unaccounted for during the experiment performance.
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Appendices
Data Collected
The data obtained through lab performance is given below,
Table 2 Raw data from lab performance for rod 1
Experimental
Data
t=0
minutes
Thermocoupl Distance(in
es
ch)
1
0
T(℃)
2
1.5
3
4
4
6.25
5
9.25
6
12.25
7
18.25
8
24.25
9
30
10
36
t=5
minute
s
T(℃)
t=10
minute
s
T(℃)
t=15
minute
s
T(℃)
t=20
minute
s
T(℃)
21.5519 91.146 92.724 92.903
4
6
1
21.5771 81.087 85.032 85.946
1
3
21.632 60.024 67.607 69.591
2
4
5
21.6529 48.268 59.352 61.882
6
2
8
20.1497 37.758 53.363 56.364
1
1
9
20.2238 29.618 46.210 49.271
5
3
20.2396 21.862 32.815 35.263
2
8
1
20.2188 20.761 26.788 27.885
5
2
20.3697 20.595 23.126 24.427
6
5
7
20.3456 20.514 21.975 23.048
1
5
9
93.701
5
86.575
8
70.125
7
62.968
t=25
minute
s
T(℃)
93.259
3
86.566
6
70.376
1
63.475
3
57.909 58.241
9
9
51.184 52.241
4
9
37.174 38.328
3
2
29.93 30.65
25.673
9
24.135
1
26.667
2
25.083
7
Table 3 Raw data from lab performance for rod 2
Experiment
al Data
t=0
minutes
Thermocou Distance(i
ples
nch)
1
0
T(℃)
2
1.5
20.9112
3
4
20.8991
4
6.25
20.8612
20.7779
t=5
minut
es
T(℃)
t=10
minute
s
T(℃)
t=15
minute
s
T(℃)
t=20
minute
s
T(℃)
t=25
minute
s
T(℃)
107.1
2
89.46
31
67.30
02
49.87
9
108.59
108.48
5
93.034
4
74.644
2
59.240
7
109.16
3
93.341
5
75.173
9
60.558
108.71
5
93.133
2
75.081
8
59.897
9
92.410
4
73.291
4
57.658
2
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5
9.25
20.837
6
12.25
20.7824
7
18.25
20.6365
8
24.25
20.2013
9
30
20.5578
10
36
20.6041
36.80
9
28.80
59
22.16
62
20.74
1
20.72
53
20.78
46
45.965
1
37.875
7
28.599
9
24.060
4
22.170
7
21.630
4
47.549
1
39.303
8
29.607
24.722
2
22.568
3
21.916
3
48.554
2
40.388
2
30.495
8
25.397
4
22.960
2
22.225
2
48.545
2
40.502
9
30.763
7
25.614
23.178
2
22.431
3
Table 4 Raw data from lab performance for rod 3
Experiment
al Data
t=0
minutes
Thermocou Distance(i
ples
nch)
1
0
T(℃)
2
1.5
20.3433
3
4
20.4831
4
6.25
20.3442
5
9.25
19.9116
6
12.25
19.8402
7
18.25
19.945
8
24.25
19.9088
9
30
20.3197
10
36
20.3447
20.3961
t=5
minut
es
T(℃)
t=10
minute
s
T(℃)
t=15
minute
s
T(℃)
t=20
minute
s
T(℃)
t=25
minute
s
T(℃)
95.08
88
55.10
29
23.50
76
20.49
14
20.07
36
20.01
43
20.10
33
20.05
51
20.37
43
20.37
06
101.79
2
71.269
8
38.118
7
24.414
9
20.868
9
20.231
8
20.193
8
20.092
9
20.503
9
20.577
9
103.06
1
74.493
3
41.238
9
27.277
7
21.511
2
20.381
8
20.241
103.94
8
76.427
8
43.930
1
29.186
8
22.310
4
20.624
4
20.342
9
20.236
3
20.705
7
20.809
4
103.92
4
77.400
5
45.537
4
30.505
4
22.988
20.143
7
20.588
1
20.677
9
20.840
1
20.368
8
20.238
2
20.701
9
20.801
9
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