The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 48
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The outermost isotherm is 30°C, and the eventsare spaced apart at 5°C intervals. Determination of the temperatures from a multiple-event image requiresthat the temperature be known at one point in the image.Liquid Crystals in Water. Liquid crystals can be used to mark the temperature distribution in water andsome other liquids by adding a small quantity of encapsulated liquid crystal material to the liquid andphotographing the color distribution using planar lighting.
Velocity and temperature distributions can be© 1999 by CRC Press LLCHeat and Mass Transfer4-195FIGURE 4.6.9 Multi-event liquid crystal used to visualize the isotherm pattern above a heated spot in mixedconvection.FIGURE 4.6.10 Liquid crystal visualization of the velocity and temperature distribution in a water-filled tank.determined by photographing the liquid crystal particles using a known exposure time. The temperatureis deduced from the particle color, and the velocity by the length of the streak its image forms. Figure4.6.10 shows the velocity and temperature distributions in a shear-driven, water-filled cavity 30 sec afterthe impulsive start of belt motion.
In this view, the belt is at the top of the image, and moved from leftto right. The water was stably stratified initially, with the top being 4°C hotter than the bottom. Thistechnique was demonstrated by Rhee et al. (1984) and has been used by several workers.Image Processing. Several schemes have been proposed to remove the subjectivity from interpretationof liquid crystal images. Akino et al.
(1989), and others, have processed RGB video images of narrowband images using multiple filters to extract images of specified isochromes, related to temperaturesthrough a calibration. Hollingsworth et al. (1989) processed RGB images of wide-band images using© 1999 by CRC Press LLC4-196Section 4chromaticity coordinates (hue, saturation, and intensity) and extracted temperature at each pixel, ratherthan along isochromes.Heat FluxHeat flux to or from a surface can be measured directly, using heat flux meters, or inferred from anoverall energy balance, or inferred from temperature–time measurements at the surface or within thebody.
There are no primary standards for heat flux measurement.Three general classes of heat flux meters are in common use: slug calorimeters, planar heat fluxgauges (sometimes called Schmidt–Boelter gauges), and circular foil gauges (sometimes called Gardongauges). Sensitivities range from microvolts per kW/m2 to millivolts per W/m2. Planar gauges can beused for radiant or convective heat loads.
Circular foil gauges should be used only for radiant loads.Slug CalorimeterThe slug calorimeter is an energy balance transducer consisting of a known mass of material instrumentedso that its temperature can be measured. A simple version is shown in Figure 4.6.11. If losses arenegligibly small and the mass and the specific heat are constant, the instantaneous heat flux is deducedfromq˙ in¢¢ A = Mcwhere TMcAt=====¶T¶t(4.6.8)Average temperature of the slug, CMass of the slug, kgSpecific heat, J/kg·CFace area, m2TimeFIGURE 4.6.11 A simple slug calorimeter.The variation of slug temperature with time is used to infer net heat transfer rate to the gauge. Slugcalorimeters are used mainly when the heat flux, or the heat transfer coefficient, is expected to berelatively constant. They are of less value when the input flux changes arbitrarily because of theinaccuracies inherent in differentiating the signals.Planar Heat Flux GaugePlanar heat flux gauges use Fourier’s law to deduce the heat flux from a steady-state measurement ofthe temperature difference across a thin sheet of thermally insulating material.
The planar gauge geometryis shown in Figure 4.6.12. The working equation for a planar gauge is© 1999 by CRC Press LLC4-197Heat and Mass TransferFIGURE 4.6.12 A typical planar heat flux gauge.EMF = Ne DT =where Netkq²=====Netq˙ ¢¢k(4.6.9)number of junction pairs,thermoelectric power of the thermoelement, mV/Cthickness of the insulator, mconductivity of the insulator, W/m·Cheat flux through the gauge, W/m2The figure shows one thermocouple junction on the top and one on the bottom surface of the insulator.Most gauges use multiple junctions.
The thermoelements may be wire (down to 0.025 mm diameter) orthin films deposited on the insulator (10 to 20 Å). The assembly is usually sandwiched between twosheets of protective material to form an integral unit. Up to 150°C application temperature, these unitsare often made of Kapton, and provided with a contact adhesive. They may be as thin as 0.15 mm overall.Gauges should not be removed and reinstalled without recalibration, as the act of removing themfrom the surface may delaminate the gauge, changing its thermal resistance, and therefore its calibration.Circular Foil GaugesA circular foil gauge consists of a thin circular disk of metal supported by its edge from a structure ofconstant and uniform temperature. The circular foil gauge is often called a Gardon gauge.
A constantanfoil is often used, with a copper support structure. Two copper wires complete the circuit: one attachedto the center of the foil disk and one to the support structure. The copper–constantan thermocouple thusformed produces an EMF determined by the temperature difference from the center of the foil disk toits rim. That temperature difference is directly proportional to the average heat flux on the disk. A crosssectional view of a circular foil gauge is shown in Figure 4.6.13.FIGURE 4.6.13 A water-cooled circular foil gauge (Gardon gauge).The working equation for a circular foil gauge isEMF = ewhere e = thermoelectric power, mV/C© 1999 by CRC Press LLCR2q˙ ¢¢4kt(4.6.10)4-198Section 4Rktq²====radius of the disk, mthermal conductivity of the disk, W/m·Cthickness of the disk, mheat flux absorbed by the disk, W/m2 (must be uniform)The output signal is thus directly proportional to the heat flux on the disk.
Cooling passages are frequentlybuilt into the support structure to maintain the edge of the disk (the heat sink for the foil disk) at constanttemperature.CalibrationCalibration of the Gardon-type heat flux meters is most easily done by comparison, using a radiationcalibrator.Planar gauges can be calibrated either by conduction or radiation, but the results will depend on thecalibration method for some guages.Sensor Environmental ErrorsTemperature sensors generate signals in response to their own temperatures, but are usually installed tomeasure the temperature of some fluid or solid. There is heat transfer between the sensor and all of itssurroundings, with the result that the sensor usually equilibrates at some temperature different from thefluid or solid it is installed in.
This difference is considered an error in the measurement.Similarly, heat flux gauges are generally installed so one can infer the heat flux which would havebeen there had the gauge not altered the system behavior. But heat flux gauges do disturb the system,and the heat flux at the gauge location, when the gauge is there, may be significantly different from thatwhich would have been there without the gauge. This system disturbance effect must also be consideredan error.Steady-State Errors in Gas-Temperature MeasurementAll immersion-type temperature sensors (thermocouples, resistance detectors, and thermistors) are subject to the same environmental errors, which are frequently larger than the calibration errors of thesensors.
Large probes are usually affected more than small ones; hence, RTDs and thermistors (selectedby investigators who wish to claim high accuracy for their data) are more vulnerable to environmentalerrors (due to their larger size and their self-heating errors). This aspect of accuracy is sometimesoverlooked.Sensor installations for gas-temperature measurements should be checked for all three of the usualsteady-state environmental errors: velocity error, radiation error, and conduction error. The same equations apply to all sensors, with appropriate dimensions and constants.velocity error:Ev = (1 - a )radiation error:Er =conduction error:Ec =where Ev = velocity error, °a = recovery factor, —© 1999 by CRC Press LLCV22 gc Jc pse 44T - Tsurrh sens(Tgas - Tmounté hAc ùcosh ê Lúêë kAk úû( 4.6.11))( 4.6.12)( 4.6.13)Heat and Mass TransferandVgcJcp====velocity, ft/secuniversal gravitational constantJoules constant, ff/bf/Btuspecific heat, Btu/lbm, °FErseh==============radiation error, °RStefan-Boltzmann constantemissivityheat transfer coefficient, Btu/secft2, °Findicated temperature, °Rsurrounding temperature, °Rconduction error, °Rgas temperature, °Rmount temperature, °Rlength of exposed junction, ftheat transfer coefficient, Btu/secft2, °Fheat transfer area, ft2thermal conductivity, Btu/secftconduction area, ft2TsensTsurrEcTgasTmountLhAckAk4-199Velocity error depends upon the recovery factor, which varies with the Prandtl number of the fluid.
ThePrandtl numbers of most liquids are greater than 1; hence, the recovery factor a is greater than 1 andprobes tend to read higher than the stagnation temperature in high-speed liquid flows. With thermistorsand RTDs in liquids, the self-heating effect and the velocity error both tend to cause high readings. Ingases, where the Prandtl number is less than 1, the two effects are of opposite sign and may partly canceleach other.Radiation and conduction errors vary inversely with the heat transfer coefficient. Both tend to belarger for larger-diameter probes since, all other factors remaining the same, the heat transfer coefficientwill be lower for a large-diameter probe.
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