ME3122-1 Temperature Measurement by LIN SHAODUN A0066078X Group 1A Date 28-Aug-2012
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ME3122-1
Temperature Measurement
by
LIN SHAODUN A0066078X
Group 1A
Date 28-Aug-2012
TABLE OF CONTENTS
RAW DATA 1
CALCULATION AND DISCUSSION 3
DISCUSS EXPERIMENTAL ERRORS 6
CONCLUSION 7
1
RAW DATA
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 15 min 30 min
mV oC mV
oC mV
oC
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
2
Plot the data from Table 1 to obtain the calibration curves:
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 Thermocouple without
Ice Point
Thermocouple
with Ice Point
0.9988 mV/C 12.918 mV/C 0.0428 mV/C 0.0428 mV/C
y = 0.9988x - 0.5803
R² = 1
0
10
20
30
40
50
60
70
80
0 10 20 30 40 50 60 70 80
RT
D O
utp
ut
(mV
)
Temperature (C)
RTD calibration curve
y = 12.918x - 296.72
R² = 0.9993
0
100
200
300
400
500
600
700
800
0 10 20 30 40 50 60 70 80
Th
erm
isto
r O
utp
ut
(mV
) Temperature (C)
Thermistor calibration curve
y = 0.0428x - 0.9794
R² = 0.9998
y = 0.0428x - 0.1044
R² = 0.9999
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 10 20 30 40 50 60 70 80
Th
erm
oco
up
le O
utp
ut
(mV
)
Temperature (C)
Thermocouple calibration curve
W/O Ice Pt
W Ice Pt
3
CALCULATION 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 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:
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.
20
30
40
50
60
70
80
0 5 10 15 20 25 30 35 40 45 50
Tem
per
atu
re (C
)
Distance in Perspex Rod (mm)
Tempareture Profile
0 min
15 min
30 min
4 0
0.5
1
1.5
2
0
0.2
0.4
0.6
0.8
1
0
10
20
30
40
50
60
70
80
tx
Te
mp
era
ture
Temperature profilebecome linear at steady state
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.
5
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 15 min 30 min oC
Err %
oC
Err %
oC
Err %
Channel 6 at 50 mm apart from the hot end
(Embedded thermocouple wire) 23.7 26.3 28.1
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%
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.
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.
-2%
-1%
0%
1%
2%
3%
4%
5%
6%
7%
8%
0 min 15 min 30 min
Rel
ativ
e p
erce
nta
ge
erro
r %
Channel 7 for surface
thermocouple wire
Channel 8 for surface
RTD
Channel 9 for surface
thermistor
6
DISCUSS EXPERIMENTAL ERRORS
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 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 been 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 0.5C, 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.
7
CONCLUSION
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 Good Better Best
Cost Best Good Better
The advantages and disadvantages of 3 sensors are list as below:
Sensors Advantages Disadvantages
Thermocouples
Simple. Rugged
High temperature operation
Low cost
No resistance lead wire problem
Point temperature sensing
Fastest response to temperature
changes.
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
RTD
Most stable over time
Most accurate
Most repeatable temperature
measurement
Very resistant to contamination /
corrosion of the RTD element
High cost
Slowest response time
Low sensitivity to small temperature
change
Sensitivity to vibration
Decalibraton if used beyond sensor’s
temperature rating
Somewhat fragile.
Thermistors
High sensitivity to small temperature
changes.
Temperature measurement become
more stable with use
Copper or nickel extension wire can
be used.
Limited temperature range
Fragile
Some initial accuracy drift
Decalibraton if used beyond sensor’s
temperature rating
Lack of standards for replacement
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