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Computerized, Transient Hot-Wire Computerized, Transient Hot-Wire Thermal Conductivity (HWTC) Thermal Conductivity (HWTC)
Apparatus Apparatus For NanofluidsFor Nanofluids
The 6th WSEAS International Conference on HEAT and MASS TRANSFER The 6th WSEAS International Conference on HEAT and MASS TRANSFER ((WSEAS - HMT'09WSEAS - HMT'09))
Ningbo, China, January 10-12, 2009Ningbo, China, January 10-12, 2009
M. Kostic & Kalyan C. SimhamM. Kostic & Kalyan C. SimhamDepartment of Mechanical EngineeringDepartment of Mechanical EngineeringNORTHERN ILLINOIS UNIVERSITYNORTHERN ILLINOIS UNIVERSITY
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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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INTRODUCTIONNanofluids 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
* (reprinted with permission; reference listed within this table are with respect to (Manna et al 2005))
*
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Nanofluid Preparation Methods
• One Step (Direct Evaporation and Condensation) Method
Fig1: Improved new-design for the one-step, direct evaporation-condensation nanofluid production
apparatus, (Kostic 2006)
• Two Step Method or Kool-aid Method
• Chemical Method
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Thermal Conductivity• Material Property• Determines ability to conduct heat• Important for thermal Management
Classification of Thermal Conductivity Measurement
Techniques for FluidsSteady State
Methods
Non-Steady State Methods
Horizontal Flat Plate MethodVertical Coaxial Cylinder MethodSteady State Hot-Wire Method
Line Source (Hot-Wire) MethodCylindrical Source MethodSpherical Source MethodPlane Source Method
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Transient Hot-Wire Method for Fluids• Fast and Accurate
Advantages:
• Minimize (or even avoid) Convection
• Minimum Conduction and Radiation losses
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
Electrical CircuitFlexible ConnectionsInstrumenta
tion
Data Acquisition
Optimize to Reduce Noise
Develop ProgramCalibratio
nStandard 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
Boundary Conditions
Ideal case:Line source has an infinite thermal conductivity and zero heat capacity
rTr
rrtT
f
11
0t 0rand
0t rand f
r kq
rTr
2lim
0
0,lim
trTr
Where T is the final temperature, T0 is the initial temperature,r is the radial distance andt is the timeq is heat flux is thermal diffusivitykf is Thermal Conductivity
0TTT
f
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• The temperature change at a radial distance r, from the heat source is conforms to a simple formula by applying boundary conditions
• At any fixed radial distance, in two instances in time the equation, the temperature change can be represented as
trEi
kq
TtrTtrTff 44
,,2
0
.........
!22
4
!11
44ln
4),(
222
20
tr
tr
rt
kqTtrTT fff
f
1
212 ln
4 tt
kqTT
f
series expansion of the exponential integration
=0.5772 is the Euler’s constant Where,
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Thermal Conductivity
• A plot of temperature against the natural logarithm of time results in a straight line, the slope being propositional to kf
Tdtdq
k f
)ln(4
Practical application of hot-wire method• The ideal case of continuous line is approximated
with a finite wire embedded in a finite medium
Figure 2.1 Typical plot of temperature change against time for hot-wire experiment (Johns et al 1988)
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Nanofluids Thermal Conductivity Methods By
Other AuthorsAuthor, Year Nanofluid Thermal Conductivity
Measurement MethodWang 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 cellHot-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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ooo
f
CtBt
AtkqT ln1ln
4Where,
...2
ln24
ln 2
w
f
w
o
i
f
o
fo k
krr
kk
rA
i
i
f
fo
w
w
i
iw
fo
kkr
kkr
kB 22
21
w
o
w
w
i
i
i
w
if
o
wiiww
ifwo r
rkkkrr
kkkr
C ln112
24118
222
222 4
ln2
1
o
f
i
i
f
fo
w
w
i
iw
f rkk
rkk
rk
oo CtBt ln1 is due to the presence of the insulation layer on the wire
oA T shifts (i.e. offsets) the plot of
against ln (t), without changing the slope
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Insulation Coating Influence on Thermal Conductivity
Measurement
• 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
Yu and Choi (2006)
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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 ThreadingLocking Nut
(calibrated weight for required spring tension) To the Data Acquisition System
Connectors and Calibration Guage Holder
D-Type Connector
T-Type Thermocouples
Hot-Wire Voltage Output Wires
Power Supply Connector
Cell Cap with Rectangular Cuts(for wire outlet)
Special Shape Sliding Fit Hole(avoids turning of spring)
Striped Stranded Copper Wire (to provide flexiblity and avoid backlash)
Tension Spring (spring constant 0.02 N/mm)
Constant Voltage Input Wires
Wire Holder
Hot-Wire Guiding Block(off-centered)
Sliding Tube (aligns the hot-wire)
Wire Protection Clip # 1
Mea
sure
men
t Sec
tion
149.
2 m
m
Soldered Joint # 1
Teflon Coated Platinum Hot-WireØ 0.0508 mm
Coating Thickness 0.0245 mm
Soldered Joint # 2
Wire Protection Clip # 2
Wire Protection Clip # 3
Cell Base Plate
Off-Centered Alignment Ring
Insulated Copper Wire Ø 0.254 mm
Teflon Sealing
Threaded Hole in Base Plate(Assembly and Cleaning)
Outer Shell(test-fluid reservoir)
Inner Semi-Circular Hot-Wire Holder
Thermocouple at the Bottom L45°
Threaded Nut
Inner Wire Guide
Fig 2: Cross-sectional front view of improved transient hot-wire thermal Conductivity Cell
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Calibration Gauge(to guard spring rod and calibrate the spring tension)
Spring Rod with ThreadingLocking Nut
(calibrated weight for required spring tension) To the Data Acquisition System
Connectors and Calibration Guage Holder
D-Type Connector
T-Type Thermocouples
Hot-Wire Voltage Output Wires
Power Supply Connector
Cell Cap with Rectangular Cuts(for wire outlet)
Special Shape Sliding Fit Hole(avoids turning of spring)
Striped Stranded Copper Wire (to provide flexiblity and avoid backlash)
Tension Spring (spring constant 0.02 N/mm)
Constant Voltage Input Wires
Wire Holder
Hot-Wire Guiding Block(off-centered)
Sliding Tube (aligns the hot-wire)
Wire Protection Clip # 1
Mea
sure
men
t Sec
tion
149.
2 m
m
Soldered Joint # 1
Teflon Coated Platinum Hot-WireØ 0.0508 mm
Coating Thickness 0.0245 mm
Soldered Joint # 2
Wire Protection Clip # 2
Wire Protection Clip # 3
Cell Base Plate
Off-Centered Alignment Ring
Insulated Copper Wire Ø 0.254 mm
Teflon Sealing
Threaded Hole in Base Plate(Assembly and Cleaning)
Outer Shell(test-fluid reservoir)
Inner Semi-Circular Hot-Wire Holder
Thermocouple at the Bottom L45°
Threaded Nut
Inner Wire GuideFig 2: Top half cross-sectional front view of transient hot-wire thermal conductivity cell
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Calibration Gauge(to guard spring rod and calibrate the spring tension)
Spring Rod with ThreadingLocking Nut
(calibrated weight for required spring tension) To the Data Acquisition System
Connectors and Calibration Guage Holder
D-Type Connector
T-Type Thermocouples
Hot-Wire Voltage Output Wires
Power Supply Connector
Cell Cap with Rectangular Cuts(for wire outlet)
Special Shape Sliding Fit Hole(avoids turning of spring)
Striped Stranded Copper Wire (to provide flexiblity and avoid backlash)
Tension Spring (spring constant 0.02 N/mm)
Constant Voltage Input Wires
Wire Holder
Hot-Wire Guiding Block(off-centered)
Sliding Tube (aligns the hot-wire)
Wire Protection Clip # 1
Mea
sure
men
t Sec
tion
149.
2 m
m
Soldered Joint # 1
Teflon Coated Platinum Hot-WireØ 0.0508 mm
Coating Thickness 0.0245 mm
Soldered Joint # 2
Wire Protection Clip # 2
Wire Protection Clip # 3
Cell Base Plate
Off-Centered Alignment Ring
Insulated Copper Wire Ø 0.254 mm
Teflon Sealing
Threaded Hole in Base Plate(Assembly and Cleaning)
Outer Shell(test-fluid reservoir)
Inner Semi-Circular Hot-Wire Holder
Thermocouple at the Bottom L45°
Threaded Nut
Inner Wire Guide
Fig 3: Bottom half cross-sectional front view of transient hot-wire thermal conductivity cell
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Off-Centered Alignment Ring
Base Plate
Threaded Nut
Outer Shell(test-fluid reservoir)
Protection Clip
Semi-Circular Hot-Wire Holder
(Off Centered)
Thermocouple at the middle
Ø14.371mm
Ø17.424mm
Fig 4: Cross sectional top view of the hot-wire cell at the middle
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Calibration GuageD-Type Connector (thermocouples and wire voltagemeasurement using data acquisition system)
Locking Nut(calibrated weight fpr required
spring tension)
Power Supply Connector Connectors and Calibration Guage Holder
Fixing Nut
Outer Shell(test-fluid reservoir)
Sliding Hole
Tension Spring
Cell Base Plate
Wire Holder Fixing NutWire Holder
T-Type Thermocouple
Hot-Wire Voltage Output WiresConstant Voltage Input
Threaded Nut (soldered to outer shell )
Fig 5: Isometric view of transient hot-wire thermal conductivity cell
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Thermocouple at the TopL15°
Thermocouple at the MiddleL75°
Thermocouple at the BottomL45°
Rectangular hole on the Inner Cell(for guiding the wires out)
Sliding tube
Locking Screw(avoids the axial movementof calibration guage)
Wire Guiding Hole(to guide the aligned wires out)
Off-Centered Alignment Ring
Tension Spring
Fig 6: Left-side view of transient hot-wire thermal conductivity cell without the outer cell, base plate and protection pins
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Calibrated Weight(for required spring tensionwithin elastic modulus of the platinum hot-wire)
Calibration Guage (guards the spring rod
and protects the platinum wires for sudden shocks)
Tension Spring (spring constant 0.02 N/mm)
Sliding Tube(causes free movement without friction)
Off-Centered Alignment Ring (Provides Rigidity to the other end of the wire)
Uniform Tensionon the Platinum Wire
Fig 7: Calibration position of the hot-wire cell
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Spring Assembly
Where,Weight of spring rod,W1 = 0.00708 NWeight of locking nut, W2 = 0.1762 NWeight of tension spring,W3 = 0.0115
NWeight of sliding tube,W4 = 0.00490 N
ΔZcalZcal
ΔZ0
(1) Spring Rod
(2) Locking Nut
Cell Cap
(3) Tension Spring
(4) Sliding Tube
Fwa
Spring Constant ζs
Initial Spring Force Fsi
waF = 0.1997 N
4321 WWWWFwa
s
sical
FWWWZ
321
calZ = 0.0056 m
www.kostic.niu.eduFig 8: Fabricated transient hot-wire thermal conductivity apparatus cell
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Instrumentation
Figure 5.1 Schematics of electrical circuit with data acquisition system
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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 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
• The change in resistance of the wire due to heating is measured in time using a Wheatstone bridge circuit
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Signal AnalysisBridge Balance
3
0
2
1
RR
RR w
32
10 R
RR
Rw
Resistance of the hot wire
21
1
30
0
RRR
RRRRR
VVww
wwinout
The bridge voltage output
in
out
in
out
wt
VV
RRR
VV
RRRR
R
212
2113
The Resistance change of Hot-Wire
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00
121
wTCR
w
w
wtwt
TCR RR
RRR
T
The Temperature change of Hot-Wire
3RRRV
Vwt
wtinRw
The Voltage Drop Across the Hot-Wire
wtw
Rw
RLV
q2
Heat Flux per Unit Length at any Instant of Time
Tdtdqk f
)ln(
4
Thermal Conductivity
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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 SCXI-1102/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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Start
BridgeBalance
MeasureResistance
Calculate Initial Resistance R w0
Average Temperature of the Cell
Voltage Output V out
Measure Temperature at Top, Middle and Bottom
of Hot-Wire Cell
YESIf Vout >= 0.001 V
Measure Bridge Output Voltage V out
and time tPlot Vout Vs Ln(t)
Measure Bridge Input Voltage V in
Measure Temperature at Top, Middle and Bottom
of Hot-Wire Cell
Average Temperature of the Cell
CalculateWire Voltage V Rw
Plot Temperature Vs Ln(time)
Calculate Change in Temperature
Calculate Slope of Temperature and Ln(Time) for Specified Time Range
Calculate Heat Input
per unit length 'q'
Calculate Thermal Conductivity
Store All
Data
Time Ranges
NO
Initialize VariablesR1, R2, R3, TCR, Lw
Measurement Time
Sampling Rate
Calculate TotalChange in Resistance
End
Figure 5.3: LabVIEW Program Algorithm for Thermal Conductivity Measurement
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CalibrationTwo Standard Fluids Ethylene Glycol and Water
210 21 tTtTTTr
Reference Temperature
Resistances of the Wheatstone bridge circuit are measured as
1R = 2270.6 Ω
2R = 2161.1 Ω
3R = 7.715 Ω
0wR = 8.106 Ω
wL= 0.1484 m
wTCR RZ
,
wR = 8.22 Ω
Z = 0.02652 Ω/°C is the the slope of dRw vs TZ
Where,
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0
2
4
6
8
10
12
14
16
0.01 0.1 1 10 100
time, t [s]
Wire
Tem
pera
ture
Cha
nge,
ΔT
[°C
]
Ethylene GlycolDistilled WaterLog. (EG (2.0s - 6.0s))Log. (Water (2.0s-6.0s))
Figure 6.1: Wire temperature change against time (in logarithmic scale) for ethylene glycol and distilled water
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Heat Input per Unit Length in Time
5.54
5.545
5.55
5.555
5.56
5.565
5.57
0 5 10 15 20 25 30 35 40 45 50
Time, t [s]
Hea
t Inp
ut p
er U
nit L
engt
h, q
[W/m
]
WaterEthylene glycol
Figure 6.2: Heat input per unit length against time (for ethylene glycol and water)
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Calibration Data from (1 s-10 s)
5
6
7
8
9
10
11
12
13
14
1 10time, t [s]
Wire
Tem
pera
ture
Cha
nge,
ΔT
[°C
]
Ethylene GlycolDistilled Water
Valid time range for data reduction
Figure 6.3: Calibration data from time (1 s – 10 s), shows the selected time range for data reduction as 2s – 6 s, for ethylene glycol and water
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Repeatablity of Ethylene Glycol Thermal Conductivity Measurement
0.240
0.245
0.250
0.255
0.260
0.265
0 1 2 3 4 5 6 7 8 9 10
Measurement Set
Ethy
lene
Gly
col T
herm
al C
ondu
ctiv
ity, k f
eg [W
/m°C
]
Repeatability of EGLinear (Reference Value)Linear (Mean)
Figure 6.4: Results of repeatability measurement of thermal conductivity for
Ethylene glycol, shows the bias and precision error in measurement
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Repeatability of Water Thermal Conductivity Measurement
0.580
0.590
0.600
0.610
0.620
0.630
0.640
0.650
0 1 2 3 4 5 6 7 8 9 10
Measurement Set
Wat
er T
herm
al C
ondu
ctiv
ity, k
fw [W
/m°C
]
Repeatablity of WaterLinear (Reference)Linear (Mean)
Figure 6.5: Results of repeatability measurement of thermal conductivity for distilled water, shows the bias and precision error in measurement
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Calibration Results
FluidReferen
ce [W/m°C]
Measured
[W/m°C]
Bias Error
Precision
Error(95 %)
Uncertainty
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 %
Table 6.1: Uncertainty in repeatability of measured thermal conductivity
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Uncertainty in Thermal Conductivity
Tdtdqk f
)ln(
4
RwTCR
wwTCRf Z
qRRdtdqRk 1
4)ln(
4 00
Rearranging in terms of the measured resistance change in the wire
22
0
22
0
RwTCRf Z
R
fR
w
f
TCR
fq
fk u
Zk
uRk
uk
uqk
u
Uncertainty
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Uncertainty in Heat Input per Unit Length
2222
qLw
Rwt
VRw
q PuLqu
Rqu
Vqu
wwtRw
qPis the precision error in the average heat input per unit length
%. 1.63quq
2
3
22
3
RRw
Rwt
RwV
in
RwV u
RV
uRV
uVV
uwtinRw
Uncertainty in Wire Voltage
%. 0.706 RwV VuRw
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Uncertainty in Total Resistance Change
222
3
2
2
2
1321
outinwt V
in
wtV
out
wtR
wtR
wtR
wtR u
VR
uVR
uRR
uRR
uRR
u
%. 0.813 wtR Ruwt
Uncertainty in Measured Bridge Voltage Input
% 0.535 inV Vuin
Uncertainty in Measured Bridge Voltage Output
%0.1outV Vuout
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220 mmcmmmmd uuu
Uncertainty in ResistancesUncertainty in Multimeter
2211 RmmdR Buu
Uncertainty in Resistance R1
Uncertainty in Resistance R2
Uncertainty in Resistance R3
%. 0.1 11RuR
2222 RmmdR Buu
2233 RmmdR Buu
%. 0.2522RuR
%. 0.516 33RuR
03210
2
3
2
2
2
1ww RR
wR
wR
wR Bu
RR
uRR
uRR
u
Uncertainty in Resistance R3
%. 1.6300wR Ru
w
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Uncertainty in Temperature Coefficient of Resistance 22
wTCR R
w
TCRZ
TCR uR
uZ
u %. 2.275 TCRTCRu
Hot-Wire Resistance Vs Temperature
Rw = 0.026521 T + 7.698728r2 = 0.999036
8.45
8.5
8.55
8.6
8.65
8.7
8.75
8.8
8.85
8.9
8.95
29 31 33 35 37 39 41 43 45
Temperature, T [°C]
Hot
-Wire
Res
ista
nce
Rw [Ω
]
Figure 6.7 Calibration of Temperature Coefficient of Resistance of Teflon Coated Platinum Hot-Wire
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Uncertainty in Length of Hot-Wire
222FSeVCdL LLuu
w %. 0.0661 wL Lu
w
Uncertainty in Slope of Total Resistance Change against Logarithmic Time
2
00
21
lnln
RRRR N
ii
N
iiR
RZyxZa
ttN
NSS
RR ZaZ Stu 1%95,200
0.2314% RZ ZuR
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quq
TCRTCRu
00 wR Ruw
RZ ZuR
fk kuf
Table 7.2: Percentage uncertainties
Uncertainty (%)
1.629
2.274
1.627
0.231
3.245
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Nanofluid thermal conductivity Measurement
• Copper, particle size 35 nm
• Ethylene glycol and Water
Base Fluid:
Nanoparticles:
Concentration:• 1 volumetric %
Physical Stabilization:• Ultrasonication
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Copper in Ethylene Glycol NanofluidMeasured Thermal Conductivity Ratio of
1 vol% of Copper in Ethylene Glycol Nanofluid
Mean= 1.1282
1
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
0 1 2 3 4 5 6
Measurement Set
Ther
mal
Con
duct
ivity
ratio
kn feg/k
feg
1% vol Cu in EG
Linear (Mean)
Figure 7.1: Nanofluid thermal conductivity measurement of 1 vol % of copper in ethylene glycol
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Copper In Water Nanofluid
Measured Thermal Conductivity Ratio of 1 vol% of Copper in Water Nanofluid
Mean = 1.1595
1.0000
1.0500
1.1000
1.1500
1.2000
1.2500
1.3000
1.3500
0 1 2 3 4 5 6
Measurement Set
Ther
mal
con
duct
ivity
Rat
io kn fw
/kfw
1% vol Cu in Water
Linear (Mean)
Figure 7.2: Nanofluid thermal conductivity measurement of 1 vol % of copper in water
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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 Hot-wire 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 non-linear 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