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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
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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
* * (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 Two Step Method or Kool-aid 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 Vertical Coaxial Cylinder Method Steady State Hot-Wire Method Steady State Methods Line Source (Hot-Wire) Method Cylindrical Source Method Spherical Source Method Plane Source Method Non-Steady State Methods
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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 Design
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OBJECTIVE Instrumentation Data Acquisition Calibration
Electrical Circuit Flexible Connections Instrumentation Optimize to Reduce Noise Develop Program Data Acquisition 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 Boundary Conditions Where T is the final temperature, T0 is the initial temperature, r is the radial distance and t is the time q is heat flux is thermal diffusivity kf is Thermal Conductivity and Ideal case: Line source has an infinite thermal conductivity and zero heat capacity
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series expansion of the exponential integration
The temperature change at a radial distance r, from the heat source is conforms to a simple formula by applying boundary conditions series expansion of the exponential integration = is the Euler’s constant Where, At any fixed radial distance, in two instances in time the equation, the temperature change can be represented as
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Practical application of hot-wire method
A plot of temperature against the natural logarithm of time results in a straight line, the slope being propositional to kf Thermal Conductivity 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 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)
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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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is due to the presence of the insulation layer on the wire
Where, is due to the presence of the insulation layer on the wire 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
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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Selected 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 m Diameter of bounding wall is m Length of sample is m
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Fig 2: Cross-sectional front view of improved transient hot-wire thermal Conductivity Cell
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Fig 2: Top half cross-sectional front view of transient hot-wire thermal conductivity cell
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Fig 3: Bottom half cross-sectional front view of transient hot-wire thermal conductivity cell
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Fig 4: Cross sectional top view of the hot-wire cell at the middle
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Fig 5: Isometric view of transient hot-wire thermal conductivity cell
Fig 5: Isometric view of transient hot-wire thermal conductivity cell
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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
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Fig 7: Calibration position of the hot-wire cell
Fig 7: Calibration position of the hot-wire cell
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Spring Assembly = 0.0056 m = 0.1997 N Where,
ΔZcal Zcal ΔZ0 (1) Spring Rod (2) Locking Nut Cell Cap (3) Tension Spring (4) Sliding Tube Fwa Spring Constant ζs Initial Spring Force Fsi Spring Assembly Where, Weight of spring rod,W1 = N Weight of locking nut, W2 = N Weight of tension spring,W3 = N Weight of sliding tube,W4 = N = N = m
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Fig 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 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 Resistance of the hot wire
The bridge voltage output The Resistance change of Hot-Wire
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The Temperature change of Hot-Wire
The Voltage Drop Across the Hot-Wire Heat Flux per Unit Length at any Instant of Time 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 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
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Calibration Reference Temperature
Two Standard Fluids Ethylene Glycol and Water Reference Temperature Resistances of the Wheatstone bridge circuit are measured as , = Ω = m = Ω = Ω Where, = Ω = Ω/°C is the the slope of dRw vs T = 8.22 Ω
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for ethylene glycol and distilled water
Figure 6.1: Wire temperature change against time (in logarithmic scale) for ethylene glycol and distilled water
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Figure 6.2: Heat input per unit length against time (for ethylene glycol and water)
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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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Ethylene glycol, shows the bias and precision error in measurement
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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for distilled water, shows the bias and precision error in measurement
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 Table 6.1: Uncertainty in repeatability of measured thermal conductivity Fluid Reference [W/m°C] Measured Bias Error Precision Error (95 %) Uncertainty Ethylene Glycol (32.5 °C) 0.254 0.253 % 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
Rearranging in terms of the measured resistance change in the wire Uncertainty
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Uncertainty in Heat Input per Unit Length
is the precision error in the average heat input per unit length Uncertainty in Wire Voltage
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Uncertainty in Total Resistance Change
Uncertainty in Measured Bridge Voltage Input Uncertainty in Measured Bridge Voltage Output
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Uncertainty in Resistances
Uncertainty in Multimeter Uncertainty in Resistance R1 Uncertainty in Resistance R2 Uncertainty in Resistance R3 Uncertainty in Resistance R3
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Uncertainty in Temperature Coefficient of Resistance
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
Uncertainty in Slope of Total Resistance Change against Logarithmic Time
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Table 7.2: Percentage uncertainties Uncertainty (%) 1.629 2.274 1.627
0.231 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
Figure 7.1: Nanofluid thermal conductivity measurement of 1 vol % of copper in ethylene glycol
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Copper In Water Nanofluid
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 ). 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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