Casey Thompson, Erik Richardson, Ben Ward
Thermocouple Lab Thermocouples are devices used to measure temperatures. They can be especially helpful helpful when you want to compare temperature temperature differences between various materials or surfaces. For the lab two different metals, aluminum and and steel, were heated to a steady-state temperature. The aluminum plate was first heated to a steady-state temperature temperature of 200 °C. Next, the steel cylinder was placed placed onto the aluminum plate and allowed to heat to steady-state. The purpose of this lab was to model the system analytically and experimentally, comparing the results and determining potential error sources. The first step was to analytically model the system. It was necessary to calculate a Biot number number to determine if we could use lumped capacitance capacitance or not. Our Biot number ended up being 0.0005462, which was less than the 0.1 criteria required. The method we used involved Equation 1 below where
() ( ) T ss
(1)
is the steady-state temperature, T o represent initial specimen temperature, t is time, and τ
represents the time constant. Equation 1 allowed us to calculate calculate the temperature of the specimen over any time interval. The second part of the lab was to gather measured data using two thermocouples attached to the aluminum plate plate and the steel specimen, respectively. respectively. We heated the aluminum aluminum to steady-state, 184.1 °C, and then placed the steel cylinder on the aluminum. Measurements of the steel were taken every second until the steel reached a steady temperature, which ended up being 146.6 °C. The front panel and block diagram diagram of the Lab View program is is shown in Figure 1 in the appendix. This measured data was compared to the analytical model, as seen in Table 1 in the appendix. The next step was to try t ry and improve upon our analytical model through adding a standard contact resistance of air between the aluminum and steel specimen specimen of 0.00002 meters. This was done through modifying our conduction resistance, or Rk values, in our initial model. The improved model data is also included in Table Table 1 in the appendix. A comparison of these two models is illustrated in Figure 2 in the appendix. The last step of the lab was to modify the air gap between the aluminum and steel. The gap distance that we found to correlate to our experimental data was a distance of 0.004 mm. This made sense due to the quality of the machined surfaces of the aluminum and the steel. Figure 3 in the appendix shows the improvement of the mathematical model. There were several factors in the lab that introduced error into our system. One was a faulty hot plate that failed to maintain an initial steady temperature. A second hot plate was used to remedy this problem. Another problem was that the thermocouple tip had to be directly touching the surface of the metal in order to take accurate readings. Despite all these possible problems, our model was quite accurate and modeled the system well.
Casey Thompson, Erik Richardson, Ben Ward
APPENDIX Figure 1: Front panel and block diagram views
Table 1: Comparison of specimen data, analytical model, and improved analytical model Time
Specimen
Model
Model (air gap)
0
24.536
23.600
23.600
10
31.583
45.370
33.049
20
45.028
63.287
41.771
30
57.477
78.033
49.824
40
69.408
90.169
57.258
50
79.538
100.157
64.121
60
88.782
108.377
70.457
70
97.333
115.143
76.306
80
105.275
120.710
81.706
90
111.434
125.293
86.691
100
117.775
129.064
91.293
110
122.569
132.168
95.542
120
127.871
134.722
99.464
130
132.772
136.825
103.085
140
136.892
138.555
106.428
150
140.307
139.979
109.514
160
143.172
141.151
112.362
170
146.488
142.115
114.992
180
146.598
142.909
117.420
190
146.598
143.562
119.662
200
146.598
144.100
121.731
210
146.598
144.542
123.642
220
146.598
144.907
125.405
230
146.598
145.206
127.033
Casey Thompson, Erik Richardson, Ben Ward
Figure 2: Comparison plots of initial model and improved model
Figure 3: Improved model
