Computerized, Transient Hot-Wire Thermal
Conductivity (HWTC) Apparatus
For Nanofluids
The 6th WSEAS International Conference on HEAT and MASS TRANSFER
(WSEAS - HMT'09)
Ningbo, China, January 10-12, 2009
M. Kostic & Kalyan C. Simham
Department of Mechanical Engineering
NORTHERN ILLINOIS UNIVERSITY
www.kostic.niu.edu
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Overview
INTRODUCTION
OBJECTIVE
THEORY OF HOT-WIRE METHOD
PRACTICAL APPLICATION OF HOT-WIRE
METHOD
DESIGN OF HOT-WIRE CELL
INSTRUMENTATION
DATA ACQUISTION
CALIBRATION
UNCERTAINTY ANALYSIS
RESULTS
CONCULSIONS
RECOMMENDATIONS
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INTRODUCTION
Nanofluids are colloidal suspensions of
nanoparticles, nanofibers, nanocomposites in
common fluids
They are found to have enhanced thermal properties,
especially thermal conductivity
Thermal conductivity values of nanofluids may be
substantially higher than related prediction by
classical theories
No-well established data or prediction formula
suitable to all nanofluids
Experimental thermal conductivity measurement of
nanofluids is critical
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Table 1: Summary of landmark development in nanofluids
*
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* (reprinted with permission; reference listed within this table are with respect to (Manna et al 2005))
Nanofluid Preparation Methods
• One Step (Direct
Evaporation and
Condensation) Method
• Two Step Method or Koolaid Method
• Chemical Method
Fig1: Improved new-design for the one-step, direct
evaporation-condensation nanofluid production
apparatus, (Kostic 2006)
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Thermal Conductivity
• Material Property
• Determines ability to conduct heat
• Important for thermal Management
Classification of Thermal Conductivity Measurement
Techniques for Fluids
Horizontal Flat Plate Method
Steady State Methods
Vertical Coaxial Cylinder Method
Steady State Hot-Wire Method
Line Source (Hot-Wire) Method
Non-Steady State Methods
Cylindrical Source Method
Spherical Source Method
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Plane Source Method
Transient Hot-Wire Method for Fluids
Advantages:
• Fast and Accurate
• Minimum Conduction and Radiation losses
• Minimize (or even avoid) Convection
Classification of Hot-Wire Methods
• Standard Cross Wire Method
• Single Wire, Resistance Method
• Potential Lead Wire Method
• Parallel Wire Method
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OBJECTIVE
Design
 Device to Suspend Hot-Wire
 Reduce Nanofluid Sample Size
 Minimize End Errors
 Uniform Tension on Hot-Wire
 Separate Wires for Power and Voltage
 Monitor Temperature
 Mechanism to Calibrate Hotwire
Tension
 Flexibility for Cleaning and Handling
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OBJECTIVE
Instrumentation
Electrical Circuit
Flexible Connections
Data Acquisition
Optimize to Reduce Noise
Develop Program
Calibration
Standard Fluids
Uncertainty
Analysis
Thermal Conductivity
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Principle of Hot-Wire Method
• An infinitely long and thin, ideal continuous line source
dissipating heat into an infinite medium, with constant heat
generation
General Fourier’s Equation
1 T 1   T 

r

 f t
r r  r 
Boundary Conditions
Where T  T  T0
  T 
q
T is the final temperature,
t  0 and r  0
lim r 
  
r 0
T0 is the initial temperature,
2k f
  r 
r is the radial distance and
lim T r , t   0
t  0 and r  
t is the time
r 
q is heat flux
 f is thermal diffusivity
kf is Thermal Conductivity
Ideal case:
Line source has an infinite thermal conductivity and
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zero heat capacity
• The temperature change at a radial distance r, from the heat source is
conforms to a simple formula by applying boundary conditions
 r2 
q

T r , t   T r , t   T0 
Ei

4k f  4 f t 
series expansion of the exponential integration

 r 2   r 2 2


 



 
 4 f t    4 f t   4 f t 
q 


T  T (r , t )  T0 

 ..  ....... 
   ln  2   
4k f 
1

1
!
2

2
!
r

 





 

Where,  =0.5772 is the Euler’s constant
• At any fixed radial distance, in two instances in time the equation, the
temperature change can be represented as
T2  T1 
t 
q
ln  2 
4k f  t1 
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• A plot of temperature against the natural logarithm of time results in
a straight line, the slope being propositional to kf
Thermal Conductivity
q d ln( t )
kf 
4 dT
Practical application of hot-wire method
• The ideal case of continuous line is approximated with a
finite wire embedded in a finite medium
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Figure 2.1 Typical plot of temperature change against time for hot-wire experiment (Johns et al 1988)
Nanofluids Thermal Conductivity
Methods By Other Authors
Author, Year
Nanofluid Thermal Conductivity
Measurement Method
Wang et al (1999)
Horizontal flat plate method
Lee et al (1999), Yu et al
(2003) and Vadasz (2006)
Vertical, single wire, hot-wire method
Assael et al (2004)
Two wires, hot-wire method
Manna et al (2005)
Thermal comparator
Ma (2006)
Horizontal, single wire, hot-wire method
Simham (2008)
Vertical, single wire, hot-wire method
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Hot-wire Method for Nanofluid
• Nanofluids are electrically conducting fluids
• Availability of nanofluids
• Thermal expansion of wire
• Cleaning of the cell
Hot-Wire Method for Electrically Conducting Fluids
Problems identified by Nagasaka and Nagashima (1981)
• Possible current flow through the liquid, resulting in
ambiguous measurement of heat generated in the wire,
• Polarization of the wire surface,
• Distortion of small voltage signal due to combination of
electrical system with metallic cell through the liquid.
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q
T 
4k f
1


ln t  Ao  t Bo ln t  C o 


Where,
 4 f
Ao  ln  2
 ro 
1
Bo 
2k f
rw2
Co 
8
kf
 2k f
ro

ln

 ...
 k
rw 2k w
i


k i 
 2  k i k w  2  k f

  ro

rw  








w 
i 
 f
  i


 k f  k i


 k w
2
 1
1  4
2 
1  rw2
 ro  1

  



 

  w  i   i  w 
 2   f  i  ki
1

2k f
 k i k w   ro

 ln 

  i  w   rw




k i 
 2  k i k w  2  k f
 4 f
  ro

rw  
 ln 2







w 
i 
 f
  i
 ro 
1 t Bo ln t  Co  is due to the presence of the insulation layer on the wire
Ao shifts (i.e. offsets) the plot of T against ln (t), without changing the slope
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Insulation Coating Influence on Thermal
Conductivity Measurement
Yu and Choi (2006)
•
•
The results of numerical simulation and experimental test show
that, for most of the engineering applications, the relative
measurement error of the thermal conductivity caused by the
insulation coating are very small if the slopes of the temperature
rise – logarithmic time diagram are calculated for large time values
No correction to insulation coating is necessary even for the
conditions that the insulation coating thickness is comparable to the
wire radius, and that the thermal conductivity of the insulation
coating is lower than that of the measured medium
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Reasons For Adapting Single Wire Method
•
•
•
•
•
Simplicity of Operation
Low Cost
Easy Insulation Coating
Easy Construction
Design Optimized
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•
•
•
•
Design Parameters
Size of the wire (i.e., Wire radius)
Type of insulation coating
Length of the wire
Sample size (length and radius of the cell)
Selected Design Parameters
•
•
•
•
•
Wire Diameter 50.8 µm
Teflon Insulation coating thickness 25.4 µm
Measured length of wire (after fabrication) is 0.1484 m
Diameter of bounding wall is 0.0144 m
Length of sample is 0.165 m
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Calibration Gauge
(to guard spring rod and
calibrate the spring tension)
Spring Rod with Threading
Locking Nut
(calibrated weight for required
spring tension)
Power Supply Connector
To the Data Acquisition System
Connectors and
Calibration Guage Holder
Special Shape Sliding Fit Hole
(avoids turning of spring)
D-Type Connector
Cell Cap with Rectangular Cuts
(for wire outlet)
Hot-Wire Voltage Output Wires
T-Type Thermocouples
Tension Spring
(spring constant 0.02 N/mm)
Constant Voltage Input Wires
Sliding Tube
(aligns the hot-wire)
Wire Holder
Striped Stranded Copper Wire
(to provide flexiblity and avoid backlash)
Hot-Wire Guiding Block
(off-centered)
Inner Wire Guide
Soldered Joint # 1
Wire Protection Clip # 1
Outer Shell
(test-fluid reservoir)
Measurement Section
149.2 mm
Teflon Coated Platinum Hot-Wire
Ø 0.0508 mm
Coating Thickness 0.0245 mm
Inner Semi-Circular
Hot-Wire Holder
Wire Protection Clip # 2
Threaded Nut
Soldered Joint # 2
Off-Centered Alignment Ring
Teflon Sealing
Cell Base Plate
Thermocouple at the Bottom
L45°
Wire Protection Clip # 3
Insulated Copper Wire
Ø 0.254 mm
Threaded Hole in Base Plate
(Assembly and Cleaning)
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Fig 2: Cross-sectional front view of improved transient hot-wire thermal Conductivity Cell
Calibration Gauge
(to guard spring rod and
calibrate the spring tension)
Spring Rod with Threading
Locking Nut
(calibrated weight for required
spring tension)
Power Supply Connector
To the Data Acquisition System
Connectors and
Calibration Guage Holder
Special Shape Sliding Fit Hole
(avoids turning of spring)
D-Type Connector
Cell Cap with Rectangular Cuts
(for wire outlet)
Hot-Wire Voltage Output Wires
T-Type Thermocouples
Tension Spring
(spring constant 0.02 N/mm)
Wire Holder
Constant Voltage Input Wires
Striped Stranded Copper Wire
(to provide flexiblity and avoid backlash)
Sliding Tube
(aligns the hot-wire)
Hot-Wire Guiding Block
(off-centered)
Inner Wire Guide
Fig 2: Top half cross-sectional front view of transient hot-wire thermal conductivity cell
Soldered Joint # 1
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Wire Protection Clip # 1
(aligns the hot-wire)
Hot-Wire Guiding Block
(off-centered)
Inner Wire Guide
Wire Protection Clip # 1
Soldered Joint # 1
Outer Shell
(test-fluid reservoir)
Teflon Coated Platinum Hot-Wire
Ø 0.0508 mm
Coating Thickness 0.0245 mm
Measurement Section
149.2 mm
Inner Semi-Circular
Hot-Wire Holder
Wire Protection Clip # 2
Threaded Nut
Thermocouple at the Bottom
Soldered Joint # 2
L45°
Off-Centered Alignment Ring
Wire Protection Clip # 3
Insulated Copper Wire
Ø 0.254 mm
Teflon Sealing
Threaded Hole in Base Plate
(Assembly and Cleaning)
Cell Base Plate
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Fig 3: Bottom half cross-sectional front view of transient hot-wire thermal conductivity cell
Thermocouple
at the middle
Off-Centered
Alignment Ring
Semi-Circular
Hot-Wire Holder
(Off Centered)
Base Plate
Threaded Nut
Outer Shell
(test-fluid reservoir)
Ø14.371mm
Ø17.424mm
Protection Clip
Fig 4: Cross sectional top view of the hot-wire cell at the middle
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Sliding Hole
Calibration Guage
D-Type Connector
(thermocouples and wire voltage
measurement using
data acquisition system)
Locking Nut
(calibrated weight fpr required
spring tension)
Connectors and
Calibration Guage Holder
Power Supply Connector
Fixing Nut
Tension Spring
Constant Voltage Input
Wire Holder
T-Type Thermocouple
Hot-Wire Voltage Output Wires
Wire Holder
Fixing Nut
Outer Shell
(test-fluid reservoir)
Threaded Nut
(soldered to outer shell )
Cell Base Plate
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Fig 5: Isometric view of transient hot-wire thermal conductivity cell
Tension Spring
Locking Screw
(avoids the axial movement
of calibration guage)
Sliding tube
Thermocouple at the Top
L15°
Rectangular hole
on the Inner Cell
(for guiding the wires out)
Thermocouple at the Middle
L75°
Wire Guiding Hole
(to guide the aligned wires out)
Thermocouple at the Bottom
L45°
Off-Centered Alignment Ring
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Fig 6: Left-side view of transient hot-wire thermal conductivity cell without the outer cell, base plate and protection
pins
Off-Centered
Alignment Ring
(Provides Rigidity
to the other end
of the wire)
Uniform Tension
on the Platinum Wire
Sliding Tube
(causes free movement
without friction)
Tension Spring
(spring constant
0.02 N/mm)
Calibration Guage
(guards the spring rod
and protects the platinum wires
for sudden shocks)
Calibrated Weight
(for required spring tension
within elastic modulus
of the platinum hot-wire)
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Fig 7: Calibration position of the hot-wire cell
(1) Spring Rod
ΔZcal
Zcal
ΔZ0
Spring Assembly
(2) Locking Nut
Cell Cap
Fwa  W1  W2  W3  W4
(3) Tension Spring
Spring Constant ζs
Initial Spring Force Fsi
(4) Sliding Tube
Where,
Weight of
Weight of
Weight of
Weight of
Fwa = 0.1997 N
Z cal 
Fwa
spring rod,W1 = 0.00708 N
locking nut, W2 = 0.1762 N
tension spring,W3 = 0.0115 N
sliding tube,W4 = 0.00490 N
W1  W2  W3   Fsi
s
Z cal = 0.0056 m
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Fig 8: Fabricated transient hot-wire thermal conductivity apparatus cell
Instrumentation
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Figure 5.1 Schematics of electrical circuit with data acquisition system
Measurement Procedure
• The wire is heated with electrical constant power supply at step
time
• The wire simultaneously serves as the heating element and as
the temperature sensor
• The change in resistance of the wire due to heating is measured
in time using a Wheatstone bridge circuit
• The temperature increase of the wire is determined from its
change in resistance
• Thermal conductivity is determined from the heating power and
the slope of temperature change in logarithmic time
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Signal Analysis
Bridge Balance
R1 Rw0

R2
R3
Resistance of the hot wire
Rw 0
The bridge voltage output
R1

R3
R2
 Rw0  Rw
R1 
Vout  Vin 


R


R

R
R

R
w
3
1
2
 w0
The Resistance change of Hot-Wire
Rwt

 Vout 

R3  R1  R1  R2 

 Vin 


 Vout 

 R2  R1  R2 

 Vin 
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The Temperature change of Hot-Wire
T 
Rw
1 Rwt 2  Rwt1

TCR
Rw0
TCR Rw0
The Voltage Drop Across the Hot-Wire
VRw 
Vin Rwt
Rwt  R3
Heat Flux per Unit Length at any Instant of Time
q
VRw 2
Lw Rwt
Thermal Conductivity
kf 
q d ln( t )
4  d T
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Computerized Data Acquisition
• Data acquisition hardware and software are optimized to minimize
signal noise and enhance gathering and processing of useful data
Types of Data Measured
• Bridge voltage output
• Bridge voltage input
• Hot-wire Voltage
• Temperature of fluid
Programming in LabVIEW
• A program has been written in LabVIEW application software to
automatically calculate thermal conductivity
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Data Acquisition Hardware
• PCI – 6024E, Multifunctional DAQ Board
(E–series family, PCI, PCMCIA bus, 16 single-ended/ 8 differential channel
analog inputs, 12 bit input resolution, 200 kS/s maximum sampling rate, ± 0.05
V to ± 10 V input range, 2 analog inputs, 12 bit output resolution, 10
kSamples/s output range, 8 digital I/O, two 24 bit counter timer, digital trigger)
• SCXI – 1000, 4 Slot Signal Conditioning Chassis
(shielded enclosure for SCXI module, low – noise environment for signal
conditioning, forced air cooling, timing circuit)
•
SCXI – 1102, 32 Differential Channel Thermocouple Input Module
(programmatic input range of ± 100 mV to ± 10 V per channel, overall gain of
1 – 100, hardware scanning of cold junction sensor, 2 Hz low pass filtering per
channel, relay multiplexer, over voltage protection of ± 42 V, 333 kS/s
maximum sampling rate, 0-50 ºC operation environment temperature)
• SCXI – 1303, 32 Channel Isothermal Terminal Block for
Thermocouple modules
(SCXI front end mountable terminal block for SCXI-1100 and SCXI1102/B/C, cold junction compensation sensor, open-thermocouple detection
circuitry, isothermal construction for minimizing errors due to thermal gradient,
cold junction accuracy for 15-35 ºC is 0.5 ºC and for 0-15 ºC & 25-50 ºC is
0.85 ºC, repeatability is 0.35 ºC)
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Data Acquisition Hardware
• SCXI – 1122, 16 Differential Channel Isolated Universal Input
Module
(DC input coupling, nominal range ± 250 V to ± 5 mV with overall gain of 0.01
to 2000, over voltage protection at 250 Vrms, maximum working voltage in each
input should remain with 480 Vrms of ground and 250 Vrms of any other
channel, cold junction compensation, bridge compensation, isolated voltage and
current excitation, low pass filter setting at 4 kHz or 4 Hz, shunt calibration, 16
relay multiplexer, 100 Samples/s (at 4 kHz filter) and 1 Sample/s (at 4 Hz filter),
two 3.333 V excitation level sources)
• SCXI – 1322, Shielded Temperature Sensor Terminal Block
(SCXI front end mountable terminal block for SCXI -1122, on board cold
junction sensor)
• SCXI – 1349, Shielded Cable Assembly
(adapter to connect SCXI systems to plug-in data acquisition devices, mounting
bracket for secure connection to the SCXI chassis)
• SH68-68-EP, Noise Rejecting, Shielded Cable
(Connects 68-pin E Series devices (not DAQ cards) to 68-pin accessories,
individually shielded analog twisted pairs for reduced crosstalk with high-speed
boards)
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Figure 5.3: LabVIEW Program Algorithm for Thermal Conductivity Measurement
Calibration
Two Standard Fluids Ethylene Glycol and Water
Reference Temperature
Tr  T0 
,
1
T t1   T t 2 
2
Resistances of the Wheatstone bridge circuit are measured as
R1 = 2270.6 Ω
Lw = 0.1484 m
R2 = 2161.1 Ω
 TCR  Z  Rw
R3 = 7.715 Ω
Rw 0 = 8.106 Ω
Where,
Z  = 0.02652 Ω/°C
Z  is the the slope of dRw vs T
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Rw = 8.22 Ω
16
Wire Temperature Change, ΔT [°C]
Ethylene Glycol
Distilled Water
Log. (EG (2.0s - 6.0s))
Log. (Water (2.0s-6.0s))
14
12
10
8
6
4
2
0
0.01
0.1
1
10
time, t [s]
Figure 6.1: Wire temperature www.kostic.niu.edu
change against time (in logarithmic scale)
for ethylene glycol and distilled water
100
Heat Input per Unit Length in Time
5.57
Water
Ethylene glycol
Heat Input per Unit Length, q [W/m]
5.565
5.56
5.555
5.55
5.545
5.54
0
5
10
15
20
25
30
35
40
45
50
Time, t [s]
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Figure 6.2: Heat input per unit length
against time (for ethylene glycol and water)
Calibration Data from (1 s-10 s)
14
Ethylene Glycol
Distilled Water
13
Wire Temperature Change, ΔT [°C]
12
11
10
9
Valid time range for data reduction
8
7
6
5
1
10
time, t [s]
Figure 6.3: Calibration data
from time (1 s – 10 s), shows the
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selected time range for data reduction as 2s – 6 s, for ethylene glycol and water
Repeatablity of Ethylene Glycol Thermal Conductivity Measurement
Repeatability of EG
Linear (Reference Value)
Linear (Mean)
Ethylene Glycol Thermal Conductivity, kfeg [W/m°C]
0.265
0.260
0.255
0.250
0.245
0.240
0
1
2
3
4
5
6
7
8
9
Measurement Set
Figure 6.4: Results of repeatability measurement of thermal conductivity for
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Ethylene glycol, shows the bias and precision error in measurement
10
Repeatability of Water Thermal Conductivity Measurement
Repeatablity of Water
Linear (Reference)
Linear (Mean)
0.650
Water Thermal Conductivity, kfw [W/m°C]
0.640
0.630
0.620
0.610
0.600
0.590
0.580
0
1
2
3
4
5
6
7
8
9
Measurement Set
Figure 6.5: Results of repeatability measurement of thermal conductivity
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for distilled water, shows the bias and precision error in measurement
10
Calibration Results
Table 6.1: Uncertainty in repeatability of measured thermal conductivity
Measured
Bias Error
[W/m°C]
Precision
Error
(95 %)
Uncertainty
Fluid
Reference
[W/m°C]
Ethylene
Glycol
(32.5 °C)
0.254
0.253
- 0.395 %
2.03 %
2.06 %
Distilled
water
(~ 26 °C)
0.612
0.619
1.2 %
2.23 %
2.52 %
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Uncertainty in Thermal Conductivity
kf 
q d ln( t )
4  d T
Rearranging in terms of the measured resistance change in the wire
k f  TCR Rw0
q d ln( t )
q 1
 TCR Rw0
4 d Rw
4 Z R
Uncertainty
 k f
  k f
  k f
  k f

 
u q   
u TCR   
u Rw 0   
u Z R 
 q
  TCR
  Rw0
  Z R

2
uk f
2
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2
2
Uncertainty in Heat Input per Unit Length
2
2
2
 q
  q
  q

u q  
uVRw   
u Rwt   
u Lw   Pq2
 VRw
  Rwt
  Lw

Pq is the precision error in the average heat input per unit length
u q q  1.63 %.
Uncertainty in Wire Voltage
2
2
 V
  V
  V

uVRw   Rw uVin    Rw u Rwt    Rw u R3 
 Vin
  Rwt
  R3

uVRw VRw  0.706 %.
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2
Uncertainty in Total Resistance Change
2
u Rwt
2
2
2
  Rwt
  Rwt

 Rwt
  Rwt
  Rwt
 
u R1   
u R2   
u R3   
uVin   
uVout 
 R1
  R2
  R3
  Vout
  Vin

u Rwt Rwt  0.813 %.
Uncertainty in Measured Bridge Voltage Input
uVin Vin  0.535 %
Uncertainty in Measured Bridge Voltage Output
uVo ut Vout  1.0 %
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2
Uncertainty in Resistances
u d mm  u0 2mm  uc 2mm
Uncertainty in Multimeter
Uncertainty in Resistance R1
Uncertainty in Resistance R2
Uncertainty in Resistance R3
u R1 
u d 2mm  BR2
u R2 
u d 2mm  BR2
u R3 
1
2
u d 2mm  BR2
3
Uncertainty in Resistance R3
2
u Rw 0
2
2

 R
  R
  R
  w u R1    w u R2    w u R3   BRw 0
 R1
  R2
  R3

u Rw 0 Rw0  1.63 %.
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u R1 R1  0.1 %.
u R2 R2  0.25 %.
u R3 R3  0.516 %.
Uncertainty in Temperature Coefficient of Resistance
2
uTCR
 
  

  TCR uZ     TCR u Rw 
 Z 
  Rw

2
u TCR  TCR  2.275 %.
Hot-Wire Resistance Vs Temperature
8.95
8.9
Hot-Wire Resistance Rw [Ω]
8.85
8.8
8.75
8.7
8.65
Rw = 0.026521 T + 7.698728
r2 = 0.999036
8.6
8.55
8.5
8.45
29
31
33
35
37
39
41
43
45
Temperature, T [°C]
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Figure 6.7 Calibration of Temperature Coefficient of Resistance of Teflon Coated Platinum Hot-Wire
Uncertainty in Length of Hot-Wire
u Lw 
2
2
2
u d VC
 Le   LFS 
u Lw Lw  0.0661 %.
Uncertainty in Slope of Total Resistance Change
against Logarithmic Time
S a1 Z
R
 S yx Z
NR
R
NR
N R  ln t 
i 0
2
i
 NR

   ln t i 
 i 0

u Z R  t 200,95% S a1 Z R
u Z R Z R  0.2314%
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2
Table 7.2: Percentage uncertainties
Uncertainty
(%)
uq q
1.629
u TCR  TCR
2.274
u Rw 0 Rw0
1.627
uZR Z R
0.231
uk f k f
3.245
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Nanofluid thermal conductivity
Measurement
Nanoparticles:
• Copper, particle size 35 nm
Base Fluid:
• Ethylene glycol and Water
Concentration:
• 1 volumetric %
Physical Stabilization:
• Ultrasonication
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Copper in Ethylene Glycol Nanofluid
Measured Thermal Conductivity Ratio of
1 vol% of Copper in Ethylene Glycol Nanofluid
1.16
Thermal Conductivity ratio knfeg/kfeg
1.14
1.12
1.1
1% vol Cu in EG
1.08
Linear (Mean)
Mean= 1.1282
1.06
1.04
1.02
1
0
1
2
3
4
5
6
Measurement Set
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Figure 7.1: Nanofluid thermal conductivity measurement of 1 vol % of copper in ethylene glycol
Copper In Water Nanofluid
Measured Thermal Conductivity Ratio of
1 vol% of Copper in Water Nanofluid
1% vol Cu in Water
1.3500
Linear (Mean)
Mean = 1.1595
Thermal conductivity Ratio knfw/kfw
1.3000
1.2500
1.2000
1.1500
1.1000
1.0500
1.0000
0
1
2
3
4
5
6
Measurement Set
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Figure 7.2: Nanofluid thermal conductivity measurement of 1 vol % of copper in water
Improvements in Design
• Overall volume of the cell after fabrication is 35 ml
• Four wire arrangement to measure voltage drop
independently from power wiring
• Incorporated a spring to provide a uniform tension and
avoid any slackness due to expansion
• Effective off-centering mechanical design provides additional
room for wiring and thermocouples
• Three thermocouples to verify the uniformity of the fluid
temperature
• Electrical connection junctions are arranged on the cell for
flexibility in connections and handling
• Boundary induced errors are minimized
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Conclusion
• Designed and Fabricated a Hot-wire cell with
improvements
• Designed and Fabricated a Wheatstone bridge for Hotwire cell
• Optimized Data Acquisition Hardware
• Developed a LabVIEW Program for Measuring
Thermal Conductivity
• Calibrated the Apparatus with Standard Fluids
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Conclusion
•
•
•
•
Bias Error is within 1.5 %
Precision Error is within 2.5 %
Total Uncertainty within 3.5 % at 95 % Probability
Enhancement in Thermal Conductivity with
Copper in Ethylene glycol is 13 %
• Enhancement in Thermal Conductivity with
Copper in Water is 16 %
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RECOMMENDATIONS
•
•
•
•
•
The uncertainty analysis shows that the resistors are the major
contributors of error. This error can be reduced by using very
high precision resistors with extremely small temperature
coefficient of resistance.
In the present study, temperature coefficient of resistance was
determined through calibration over limited temperature
range. Precise calibration under well controlled conditions with
a larger temperature range would be beneficial.
At present, the resistances are manually measured. This
process can be automated in future.
The data acquisition and LabVIEW® can be programmed to
evaluate curvature of temperature versus logarithmic-time
dependence (at initial heat-capacity and later convection nonlinear regions), and automate evaluation if linear range relevant
for thermal conductivity measurement.
The hot-wire tension can be more accurately controlled using
a micrometer in place of the fixed calibration gauge.
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Acknowledgements
The authors acknowledge support by
National Science Foundation
(Grant No. CBET-0741078).
The authors are also grateful for help in mechanical design
and fabrication to Mr. Al Metzger, instrument maker and
technician supervisor at NIU.
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Thank You
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