ME3122-1
Temperature Measurement
LIN SHAODUN A0066078X
by Group Date
1A 28-Aug-2012
R AW D AT A
C ALCULATION
1
AND
D ISCUSSION
3
D ISCUSS E XPERIMENTAL E RRORS
6
C ONCLUSION
7
R AW D AT A Table 1 Calibration Data
Temp
Vout(RTD)
Vout(Thermistor)
Thermocouple w/o ice-pt
Thermocouple with ice-pt
( C)
Ch. 8 (mV)
Ch. 9 (mV)
Ch. 10 (mV)
Ch. 11 (mV)
22.5
21.76
0
0
0.87
40.5
39.93
215.0
0.74
1.62
50.0
49.56
347.3
1.16
2.03
60.0
59.30
482.8
1.58
2.45
70.0
69.34
614.7
2.02
2.89
80.0
79.23
732.4
2.46
3.33
Table 2 Transient Readings for Temperature Along Perspex Rod:
Clock Time
0 min o mV C
15 min o mV C
30 min o mV C
Channel 1 at 0 mm apart from the hot end
3.04
73.5
3.16
76.3
3.20
77.2
Channel 2 at 10 mm apart from the hot end
1.51
37.7
1.85
45.7
2.09
51.3
Channel 3 at 20 mm apart from the hot end
1.32
33.3
1.75
43.3
1.96
48.2
Channel 4 at 30 mm apart from the hot end
1.05
27.0
1.35
34.0
1.57
39.1
Channel 5 at 40 mm apart from the hot end
0.94
24.4
1.12
28.6
1.28
32.3
Channel 6 at 50 mm apart from the hot end (Embedded thermocouple wire)
0.91
23.7
1.02
26.3
1.10
28.1
Channel 7 for surface thermocouple wire
0.92
23.9
1.03
26.5
1.13
28.8
Channel 8 for surface RTD
24.83
25.4
27.17
27.8
29.23
28.8
Channel 9 for surface thermistor
15.55
24.2
39.30
26.0
58.93
29.8
1
Plot the data from Table 1 to obtain the calibration curves: Thermistor calibration curve
RTD calibration curve 80
800
70
) 700 V m ( 600 t u p 500 t u O r 400 o t s 300 i m r e 200 h T
y = 0.9988x - 0.5803 R² = 1
) V60 m ( t 50 u p t u 40 O D30 T R20
10
y = 12.918x - 296.72 R² = 0.9993
100
0
0 0
10
20
30
40
50
60
70
80
Temperature ( C)
0
10
20
30
40
50
60
70
80
Temperature ( C)
Thermocouple calibration curve 3.5 ) V3.0 m ( t 2.5 u p t u2.0 O e l p1.5 u o c o 1.0 m r e h0.5 T
y = 0.0428x - 0.1044 R² = 0.9999 W/O Ice Pt W Ice Pt
y = 0.0428x - 0.9794 R² = 0.9998
0.0 0
10
20
30
40
50
60
70
80
Temperature ( C)
From above graph, the sensitivity of different temperature measuring system can be determined as follow: Table 3 Sensitivity of different temperature measuring system
RTD
Thermistor
0.9988 mV/ C
12.918 mV/ C
Thermocouple without
Thermocouple
Ice Point
with Ice Point
0.0428 mV/ C
0.0428 mV/ C
2
C ALCULATION
AND
D ISCUSSION
1. Comparison of temperature coefficient magnitudes
The temperature coefficient of RTD is
The temperature coefficient of thermistor is
) ( ) Compare above data, one can see that the temperature coefficient of thermistor is 11 times higher than RTD in magnitude. Thermistors have a negative temperature coefficient (NTC) as its resistance decreases with increasing temperature. 2. Temperature distribution distribution in Perspex Rod
Base on the calibration curve obtained for thermocouple, the temperature distribution in Perspex Rod is calculated based on voltage output in Table 2. The temperature profile is plotted as follow: Tempareture Profile 80 70
0 min
) C ( 60 e r u t a r 50 e p m 40 e T
15 min 30 min
30 20 0
5
10
15
20
25
30
35
40
45
50
Distance in Perspex Rod (mm)
3. Comment on temperature profile graph
From above graph, one can see that the temperature in Perspex rod decreases along the direction away from the heat source, and with longer duration, temperature increases for all test points.
3
Would you expect a linear temperature profile?
I didn’t expect a linear temperature profile. Under steady-state, one-dimensional conditions with no energy generation the temperature profile will be linear in homogeneous media base on heat transfer equation:
In this experiment, above criteria were not met:
a) The heat transfer in Perspex rod had not yet reached steady-state. b) The heat transfer in Perspex rod is not an ideal one-dimensional case. c) The Perspex rod might not be homogeneous , e.g.
Did you obtain a linear temperature profiles? If not, can you explain why?
I didn’t obtain a linear temperature profile. The equation for conduction of heat in one dimension for a homogeneous body has the form
Solve the PDE with initial condition and boundary condition, we have: ∑ ∫
Obviously, this is not a linear function. Plot the PDE solution in Matlab one can see that the linear temperature profile only can be obtained when approaches steady state.
80
Temperature profile become linear at steady state
70
60
e 50 r u t a r e 40 p m e 30 T 20 10 0 1 0.8
2 0.6
1.5 0.4
x
1 0.2
0.5 0
0
t
4
4. Determine the relative percentage error of 3 surface -mounted sensors
Here is the table to compare the relative percentage error of 3 surface-mounted sensors vs. embedded thermocouple: Clock Time
0 min o
C
Err %
15 min o
C
Err %
30 min o
C
Err %
Channel 6 at 50 mm apart from the hot end (Embedded thermocouple wire)
23.7
Channel 7 for surface thermocouple wire
23.9
0.84%
26.5
0.76%
28.8
2.49%
Channel 8 for surface RTD
25.4
7.17%
27.8
5.70%
28.8
2.49%
Channel 9 for surface thermistor
24.2
2.11%
26.0
-1.14%
29.8
6.05%
26.3
28.1
8% % 7% r 6% o r r e e 5% g a t n 4% e c r 3% e p e 2% v i t a 1% l e R 0%
-1%
Channel 7 for surface thermocouple wire Channel 8 for surface RTD Channel 9 for surface thermistor 0 min
1 5 mi n
30 min
-2%
The findings from above result: a) The relative percentage error is quite small for all cases, which means it is feasible to use surface-mounted sensor to measure the body temperature without embedding the sensor into the body if doesn’t require high accuracy. accuracy. b) Among 3 sensors, the thermocouple wire has smallest relative percentage error, probably because it the same type of sensor as Channel 6, so the calibration error is minimized, while for RTD and thermistor, since they are calibrated using own calibration curve, which might introduce some error due to linearity and sensitivity difference.
5
D ISCUSS E XPERIMENTAL E RRORS 1. Possible source of errors
Possible source of errors are list as follow: A. Human error
a. When take the reading from master thermometer, the eye level may not align with the mercury level, which causing parallax error and and it will affect the accuracy of readout. b. The mercury level falls between two small divisions was read based on estimation. c. To determine whether the thermal-steady state has b een reached, just use “gut feeling” to judge, it may not be accurate. B. Equipment error
a. Some of the sensor channel is instable; the reading is oscillating all the time, the read out has been obtained based on estimation. b. When taking the reading from Ch. 1 to Ch. 9 for transient state measurement, need to switch to different channel and record reading, it will not represent the actual temperature at that particular time. c. The resolution of master thermometer is 0.5 C, which will affect the accuracy of
readout. d. The temperature controller does not response fast enough due to its PID control algorithm. The temperature of the system fluctuated slightly when On/Off the heater. C. System error
a. When calculate the gradient of calibration curve, different fitting method to form a straight line will affect the result. b. We assume the calibration curve is linear, so the nonlinearity of the sensor has been ignored. 2. Ways to improve the experiment
Base on above observations, here are some suggestions to improve the experiment: a. Use digital thermometer as master thermometer to eliminate read out error. b. Use LabView and Data Acquisition hardware to capture the voltage output from sensors, the sensor output from all channels can be captured concurrently, without any time delay caused by switching of different channels. c. Use a better temperature controller to minimize the fluctuation of system temperature.
6
C ONCLUSION
After this experiment, I had learnt characteristics of different types of temperature sensors and how to measure the temperature distribution along a Perspex rod. I also learnt how to calibrate each type of sensor and measure the surface temperature using different sensors. After this experiment, I had better understanding about the temperature distribution along a body. The comparison of 3 sensors: Criteria
Thermocouple
RTD
Thermistor
Temp Range
-267°C to 2316°C
-240°C to 649°C
-100°C to 500°C
Accuracy
Good
Best
Good
Linearity
Better
Best
Good
Sensitivity Sensitivit y
Good
Better
Best
Cost
Best
Good
Better
The advantages and disadvantages of 3 sensors are list as below: Sensors
Advantages
Thermocouples
Simple. Rugged High temperature operation Low cost No resistance lead wire problem Point temperature sensing Fastest response to temperature changes.
Disadvantages
RTD
Most stable over time Most accurate Most repeatable temperature measurement Very resistant to contamination / corrosion of the RTD element
Thermistors
High sensitivity to small temperature changes. Temperature measurement become more stable with use Copper or nickel extension wire can be used.
Least stable, least repeatable Low sensitivity to small temperature changes Extension wire must be of the same thermocouple type Wire may pick up radiated electrical noise if not shielded Lowest accuracy High cost Slowest response time Low sensitivity to small temperature change Sensitivity to vibration Decalibraton if used beyond sensor’s temperature rating Somewhat fragile. Limited temperature range Fragile Some initial accuracy drift Decalibraton if used beyond sensor’s temperature rating Lack of standards for replacement
7
