The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 46
Текст из файла (страница 46)
The commercial rangeis from about 2000 to 30,000 W. Representative values of the sensitivity coefficient (% change inresistance per degree C) is given in Table 4.6.3 and resistance values themselves, in Table 4.6.4.TABLE 4.6.3 Thermistor Temperature CoefficientVariations with TemperatureTemp. °C–183–80–40025100327© 1999 by CRC Press LLCConditionLiquid oxygenDry iceFrozen mercuryIce pointRoom temperatureBoiling waterMelting leadDR/R, %–61.8–13.4–9.2–6.7–5.2–3.6–1.44-189Heat and Mass TransferTABLE 4.6.4Thermistor Resistance Variation with TemperatureTemp., °CRes., WTemp., °CRes., W–80–40–30–20–101.6675.7939.8621.8712.4602510012015073552252152.887.741.9MKKKKProprietary probes are available which “linearize” thermistors by placing them in combination withother resistors to form a circuit whose overall resistance varies linearly with temperature over somerange.
These compound probes can be summed, differenced, and averaged as can any linear sensor.Modern manufacturing practices allow matched sets to be made, interchangeable within +/–0.1°C.Thermal Characteristics. Thermistor probes are generally interrogated using a low current, either ACor DC. A level of about 10 mA would be typical. With a probe resistance of 10 K W, 0.01 W must bedissipated into its surrounding material. This current results in the probe running slightly above thetemperature of the medium into which it is installed: the “self-heating” effect.
Since thermistors areoften used where very small changes in temperature are important, even small amounts of self-heatingmay be important.The self-heating response is discussed in terms of the “dissipation constant” of the probe, in milliwattsper degree C. The dissipation constant depends on the thermal resistance between the thermistor and itssurroundings. For fluid-sensing probes, the self-heating varies with velocity and thermal conductivity,while for solid immersion probes, it varies with the method of attachment and type of substrate.Dissipation constants for representative probes are given in Table 4.6.5. The self-heating effect mustbe considered in calibration as well as in use.The transient response of a thermistor is more complex than that of a thermocouple and, size for size,they are not as well suited to transient measurements.TABLE 4.6.5 Representative Thermal DissipationConstants for Two Thermistor Probe DesignsEnvironment1.0-cm Disk5.0-cm CylinderStill airStill oilStill waterOil at 1 m/sec8 mW/C55—2501 mW/C—3.5—Thermistor probes are sold with calibration tables of resistance vs.
temperature at some specifiedaccuracy, on the order of +/–0.1 or 0.2 K, depending on the grade of probe purchased. These tables aretypically in increments of 1 K. For computer interpretation, they should be fit to the Steinhart-Hart form2and the coefficients determined for least error.1= A0 + A1 ln( R) + A3 ln R 3T( )(4.6.5)Resistance Temperature DetectorsThe terms resistance temperature detector (RTD) and resistance thermometer are used interchangeablyto describe temperature sensors containing either a fine wire or a thin film metallic element whoseresistance increases with temperature. In use, a small current (AC or DC) is passed through the element,and its resistance measured.
The temperature of the element is then deduced from the measured resistanceusing a calibration equation or table lookup.© 1999 by CRC Press LLC4-190Section 4RTDs are used both for standards and calibration laboratories and for field service.
Field-service probesare generally encased in stainless steel protective tubes with either wire or film elements bonded to sturdysupport structures. They are made to take considerable physical abuse. Laboratory standard-grade probesare often enclosed in quartz tubes, with the resistance wire mounted in a strain-free manner on a delicatemandrel.High-quality resistance thermometers have been used as defining instruments over part of the rangeof the IPTS. Because of this association with high-precision thermometry, resistance thermometers ingeneral have acquired a reputation for high precision and stability. Commercial probes, however, are fardifferent in design from the standards-grade probes, and their stability and precision depend on theirdesign and manufacture.RTDs are often recommended for single-point measurements in steady-state service at temperaturesbelow 1000°C where longtime stability and traceable accuracy are required and where reasonably goodheat transfer conditions exist between the probe and its environment.They are not recommended for use in still air, or in low-conductivity environments.
RTDs self-heat,which causes an error when the probes are used in a situation with poor heat transfer. They are notrecommended for transient service or dynamic temperature measurements unless specifically designedfor such service. The probes tend to have complex transient characteristics and are not amenable tosimple time-constant compensation.Physical Characteristics. The physical characteristics of any given resistance thermometer represent acompromise between two opposing sets of requirements. For accuracy, repeatability, and speed ofresponse, a delicate, low-mass sensing element is desired, supported in a strain-free manner in goodthermal contact with its surroundings.
For durability, a rugged sensor is indicated, mounted firmly to asturdy structure inside a robust, sealed protection tube.Both the short-term calibration (resistance vs. specimen temperature) and the long-term stability (drift)are directly affected by the mechanical configuration of the probe. The electrical resistance of the sensingelement is a function of its temperature and state of mechanical strain (Figure 4.6.6).FIGURE 4.6.6 Slack-wire platinum resistance thermometer.The sensing elements used in field-service RTD probes range from thin metallic films deposited onrectangular ceramic wafers (0.5 ´ 1.0 ´ 2.0 mm) with pigtail leads (0.25 mm diameter and 2.5 cm long)to glass-encapsulated, wire-wound mandrels (4 mm in diameter and 2.0 cm long), again with pigtailleads. Bonding the sensor to its support provides good mechanical protection to the element, but subjectsthe element to strain due to thermal expansion.
As long as this process is repeatable, the calibration isstable.Electrical Characteristics. RTDs are available commercially with resistances from 20 to 20,000 W with100 W being common. Bifilar windings are frequently used in wire-wound elements, to reduce the© 1999 by CRC Press LLC4-191Heat and Mass Transferelectrical noise pickup.
This is more important in the quartz-jacketed probes than in those with stainlesssteel protection tubes. Twisted pair lead wires are recommended.Thermal Characteristics. Figure 4.6.7 shows a simplified cross section of a typical resistance thermometer and a thermal circuit which can be used to discuss its behavior. In forming such a thermal circuitmodel, each element of the probe is described by its resistive and capacitive attributes followingconventional heat transfer practice. The principal components are•••••TheTheTheTheTheexternal thermal resistance per unit length;thermal capacitance of the protective tube per unit length, CT;radial internal thermal resistance between the sensor and the protective tube, Rint;capacitance of the sensor element and its support, Csensor;axial internal thermal resistance of the stem, per unit length, RT.SensorPowerSupplyoWRintoRexoCTRextRextoRexCTRextoRexSensorCSensoroCTRextTubeCTubeooo1Rex = Dy ; Rext = hA ; C=MckaSpecimenFIGURE 4.6.7 Thermal circuit representation of a typical resistance thermometer.This circuit can be used to predict the temperature distribution within the probe both at steady state andduring transients and can be refined, if needed, by subdividing the resistance and capacitance entities.Steady-State Self-Heating.
Interrogating an RTD by passing a current through it dissipates power in theelement, shown in Figure 4.6.7 as W, which goes off as heat transfer through the internal and externalresistances. This self-heating causes the sensing element to stabilize at a temperature higher than itssurroundings and constitutes an “error” if the intent is to measure the surrounding temperature. Theamount of the self-heating error depends on three factors:• The amount of power dissipated in the element,• The internal thermal resistance of the probe, as a consequence of its design, and• The external thermal resistance between the surface of the probe and the surrounding material.The self-heating temperature rise is given by Equation (4.6.6):Tsens - Tsurr = W ( Rint + Rext )(4.6.6)The internal thermal resistance of a probe, Rint, measured in degree C per watt, describes the temperature rise of the sensing element above the surface temperature of the probe, per unit of power dissipated.The internal thermal resistance can be deduced from measurements of the sensor temperature at severaldifferent current levels when the probe is maintained in a well-stirred ice bath, where the external thermalresistance is very low.
The slope of the apparent temperature vs. power dissipated line, °C/W, is theinternal thermal resistance. When an RTD is used in a gas or liquid, the external resistance between the© 1999 by CRC Press LLC4-192Section 4probe and its surroundings must be estimated from standard heat transfer data. The external resistanceis 1/(hA), °C/W.A typical cylindrical probe exposed to still air will display self-heating errors on the order of 0.1 to1.0°C per mW (commercial probes of 1.5 to 5 mm in diameter). At 1 m/sec air velocity, the self-heatingerror is reduced to between 0.03 and 0.3°C. In water at 1 m/sec velocity, the self-heating effect wouldbe reduced by a factor of four or five compared to the values in moving air, depending on the relativeimportance of the internal and the external thermal resistances.Calibration and Drift.
The relationship between resistance and temperature must be determined for eachprobe or acquired from the manufacturer. Generally speaking, the reported values will require interpolation.The resistance–temperature characteristic of a probe may drift (i.e., change with time) while the probeis in service. Manufacturers of laboratory-grade probes will specify the expected drift rate, usually interms of the expected error in temperature over an interval of time.
Two sample specifications are “0.01C per 100 hours” for a low-resistance, high-temperature probe (0.22 W at 0°C, 1100°C maximum servicetemperature) and “0.01 C per year” for a moderate-resistance, moderate-temperature probe (25.5 W at0°C, 250°C maximum service temperature). Drift of the resistance-temperature relationship takes placemore rapidly at high temperatures.Radiation DevicesSurface temperatures and gas temperatures can be deduced from radiation measurements. Surfacetemperature measurements are based on the emitted infrared energy, while gas-temperature measurementsuse specific emission lines from the gas itself or from a tracer inserted into the gas.Commercial surface-temperature measurement systems (single-point) are available, at low cost, whichcan measure temperature to +/–1% of reading, above 38°C, if the emissivity of the surface is known.The device referenced requires a spot size of 1.25 cm diameter, viewed from 75 cm.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
