Heat Conduction Through Various Material in a Series of Bars
MECH595 – Introduction to Heat Transfer
Professor M. Zenouzi
Prepared by:
Andrew Demedeiros, Ryan Ferguson, Bradford Powers
October 22, 2009
1
Abstract
This laboratory explores the phenomenon of linear heat conduction in various materials. The thermal
contact resistance and thermal conductivity of unknown materials are calculated using a measured
temperature profile. Graphical representations are presented along with calculated figures.
2
Contents
Introduction .................................................................................................................................................. 4
Theory ........................................................................................................................................................... 4
Procedure...................................................................................................................................................... 6
Results ........................................................................................................................................................... 6
Brass 1” to Brass 1” ................................................................................................................................... 7
Brass 1” to Brass 1” to Brass 1” ................................................................................................................ 8
Brass 1” to Stainless Steel 1” to Brass 1” .................................................................................................. 9
Brass 1” to Brass 0.5” to Brass 1” ........................................................................................................... 10
Brass 1” to Paper to Brass 1” .................................................................................................................. 11
Brass 1” to thermal grease to Brass 1” ................................................................................................... 12
Discussion of Results ................................................................................................................................... 13
Conclusion ................................................................................................................................................... 13
Appendix ..................................................................................................................................................... 15
Raw Thermocouple and Power Readings ............................................................................................... 15
3
Introduction
This laboratory studies the phenomenon of linear thermal conduction including the effect of
thermal contact resistance and thermal conductivity of materials. The Hampden Model H-6862-CDL
multi-section bar module is used to study these properties. This setup is shown in Figure 1.
Figure 1 ~ Hampden H-6862-CDL
This device provides heat via an electric heater. The power and heat generation is monitored by
a digital wattmeter and a series of thermocouples. For the study of linear heat conduction two or three
sections are placed in the machine. Each piece consists of a metal sample encased in thermoplastic
insulation. It should be noted that in an ideal setup, no heat would be lost through the insulation. While
heat is lost to the environment on this device, this loss will be treated as negligible.
Materials tested include 1” brass, ½” brass, 1” stainless steel, and paper. Additionally the
effectiveness of a silicon thermal compound was evaluated.
Theory
In this laboratory experiment heat flux in the axial direction in a brass bar was to be calculated.
To calculate the heat flux across the brass bar equation 1 was used.
Eq. 1
4
Thermal resistance for the bar can be calculated by Equation 2.
Eq. 2
Thermal resistances help to create a “thermal circuit”, it allows the circuit to be expressed
symbolically, which becomes simpler and easier to solve.
To calculate the total axial heat flux per unit area, equation 3 is used. Area is omitted.
Eq. 3
Applying an energy balance to the axial heat conduction system, it is shown that all energy
entering the system exits the system, resulting in zero net stored energy. Being that the bar is very well
insulated radially, it is clear that all heat transferred is in the axial direction.
Eq. 4
Where Ein signifies the energy applied to the system, and Eout is the energy transferred via
conduction.
Input heat flux into the system can be calculated by dividing the total input power by the cross
sectional area of the bar, shown in equation 5.
Eq. 5
Thermal conductivity, k can be calculated using the following equation and then solving for k. In
order to do this though, the value of q must be known. As seen below in Equation 6.
5
Eq. 6
Procedure
The procedure of this experiment is provided below.
1. Connect the thermocouples into the heater jacks on the linear panel.
2. Plug in the heater power cord into the heater socket on the linear panel.
3. Clamp the desired linear panel between the heat transfer assemblies.
4. Power the device with 120 VAC. Switch on the main AC circuit breaker. Open and run the
LabView software.
5. Set desired temperature. Allow time for steady state to be reached. At this point the wattmeter
and temperature reading will stabilize.
6. Repeat for each desired material, replacing the panels and allowing for steady state to be
reached.
Results
The results for the tested samples are provided below. The data for each sample is provided in
its own section. Detailed temperature records are provided in the appendix at the end of this report.
The heat transfer rate per area was calculated using Fourier’s law:
q' ' x = K
∆T
L
Where k is the thermal conductivity
The contact resistances are calculated using the following formula:
Rt'',c =
T A − TB
q' ' x
6
Brass 1” to Brass 1”
ΔT
L
Kbook
A
q''
q
Rc
ktotal
100
90
80
70
Temp ˚C
60
50
40
30
20
10
0
0
0.02
0.04
0.06
0.08
0.1
0.12
Thermocouple location
7
0.14
67.78
0.127
109
0.000506
58171.4
29.47
0.000935
244.69
˚C
m
W/m·K
m2
W/m2
W
K·m2/W
W/m·K
Brass 1” to Brass 1” to Brass 1”
ΔT
L
Kbook
A
q''
q
Rc
ktotal
100
90
80
70
Temp ˚C
60
50
40
30
20
10
0
0
0.02
0.04
0.06
0.08
0.1
0.12
Thermocouple location (m)
8
0.14
127
0.1778
109
0.000506
77857.1
39.45
0.000813
328
˚C
m
W/m·K
m2
W/m2
W
K·m2/W
W/m·K
Brass 1” to Stainless Steel 1” to Brass 1”
ΔT
L
Kbook
A
q''
q
Rc
k
ktotal
100
90
80
70
Temp ˚C
60
50
40
30
20
10
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
Thermocouple location (m)
9
0.18
0.2
123
0.178
109
0.000506
75320.2
38.16
0.000796
17.55
332
˚C
m
W/m·K
M2
W/m2
W
K·m2/W
W/m·K
W/m·k
Brass 1” to Brass 0.5” to Brass 1”
ΔT
L
Kbook
A
q''
q
Rc
k
ktotal
100
90
80
70
Temp ˚C
60
50
40
30
20
10
0
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Thermocouple location (m)
10
0.16
0.18
0.2
189
0.178
109
0.000506707
115735.9551
58.64427403
0.00048482
137.93
476
˚C
m
W/m·k
m2
W/m2
W
K·m2/W
W/m·k
W/m·k
Brass 1” to Paper to Brass 1”
ΔT
L
Kbook
A
q''
q
Rc
ktotal
90
80
70
Temp ˚C
60
50
40
30
20
10
0
0
0.02
0.04
0.06
0.08
0.1
Thermocouple location (m)
11
0.12
0.14
100
0.127
109
0.000506
85826.7
43.489
0.000472
378
˚C
m
W/m·K
m2
W/m2
W
K·m2/W
W/m·K
Brass 1” to thermal grease to Brass 1”
ΔT
L
Kbook
A
q''
q
Rc
ktotal
90
80
70
Temp ˚C
60
50
40
30
20
10
0
0
0.02
0.04
0.06
0.08
0.1
Thermocouple location (m)
12
0.12
0.14
87
0.127
109
0.000506
74669.2
37.835
0.000252
611
˚C
m
W/m·K
M2
W/m2
W
K·m2/w
W/m·K
Discussion of Results
The data displayed on the pages above show the linear temperature distribution for each
combination of material. The tables to the right of the graphs display the calculated results for each
material.
The 1” brass to 1” brass setup resulted in a thermal conductivity value of 244.69 W/m·K. The 1”
brass section had a calculated thermal conductivity of 328 W/m·K and the ½” insert had a value of 476
328 W/m·K. This is an average value of 350 W/m·K. This compares to a book value of 110 W/m·K for
cartridge brass (70% Cu, 30% Zn).
For the sample in which the brass sections where connected through paper the calculated k
value for the system was 378 W/m·K. Since the paper was thin, it was difficult to obtain a thermal
conductivity value for just the paper with the laboratory equipment. Although paper would generally be
considered an insulator, the extremely thin nature of the paper compared to the brass bars would make
this property subtle.
For the brass enhanced with the thermal grease the overall system thermal conductivity was
calculated to be 611 W/m·K. This is significantly greater than the value calculated for the brass bars
alone. This shows that the thermal paste is enhancing the ability of the brass to transfer heat.
Finally the 1” stainless steel segment resulted in a combined system thermal conductivity of 332
W/m·K. The book value conductivity for stainless steel is 480 W/m·K.
Conclusion
The data and results calculated from this experiment where somewhat mixed. Many of the
calculated thermal conductivity values for the materials were either too high or low considering the
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generally accepted book values. There are several situations that could have brought about this lack of
accuracy.
First it is possible that not sufficient time was taken between changing materials and taking
measurements. Given that the results were supposed to be taken at near steady-state conditions a
delay of at least five time constants should have been taken between changing materials and taking
temperature measurements. This most likely explains the large difference between temperatures in the
two bars (especially in the 1” brass to 1” brass example).
It is also possible that the instruments and thermocouples where configured incorrectly. This
would have also disrupted the results.
Although the detailed calculation are questionable the generally trend of the heat flow is
obvious. In all examples it is clear that the temperature distribution is transitioning from high to low in
the direction of heat flow.
14
Appendix
Raw Thermocouple and Power Readings
1” Brass- 1” Brass
Left Bar
Right bar
Water in
Water out
Heater Temp
Thermocouple Temp ˚F Temp ˚c
0
201
93.8889
0.0254
190
87.7778
0.0508
185
85
0.051
87
30.5556
0.1016
82
27.7778
0.127
79
26.1111
76
24.4444
76
24.4444
296
146.667
1” Brass – 1” Stainless – 1” Brass
Left Bar
Right bar
Water in
Water out
Heater Temp
1” Brass- 1” Brass - 1” Brass
Thermocouple
Left Bar
0
0.0254
0.0508
0.0762
0.1016
0.127
Center Bar
Water in
Water out
Heater Temp
-
Temp ˚F Temp ˚c
203
95
196
91.1111
190
87.7778
89
31.6667
86
30
85
29.4444
74
23.3333
74
23.3333
296
146.667
1” Brass – 0.5” Brass – 1” Brass
Thermocouple Temp ˚F Temp ˚c
0
193
89.44
0.0254
184
84.44
0.0508
178
81.11
0.127
70
21.11
0.1524
70
21.11
0.1778
70
21.11
74
23.33
74
23.33
268
131.1
Thermocouple
Left Bar
Right bar
15
0
0.0254
0.0508
0.127
0.1524
0.1778
Temp ˚F Temp ˚c
189
87.2222
180
82.2222
179
81.6667
78
25.5556
77
25
75
23.8889
1” Brass – Paper – 1” Brass
Thermocouple
Left Bar
Right bar
0
0.0254
0.0508
0.127
0.1524
0.1778
1” Brass – Thermal Grease – 1” Brass
Temp ˚F Temp ˚c
189
87.2222
180
82.2222
179
81.6667
78
25.5556
77
25
75
23.8889
Left Bar
Right bar
Water in
Water out
Heater Temp
16
Thermocouple Temp ˚F
Temp ˚c
0
183 83.88889
0.0254
169 76.11111
0.0508
154 67.77778
0.051
120 48.88889
0.1016
107 41.66667
0.127
96 35.55556
74 23.33333
74 23.33333
269 131.6667