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NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

Radiation Errors in Air Ducts Under Nonisothermal
Conditions Using Thermocouples, Thermistors, and

A Resistance Thermometer

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no. 26


1. Introduction.

2. Description of apparatus.

3. Calibration.--

4. Method of testing--

5. Results..

6. Errors in measurement-

7. Summary and discussion.

8. References..









Radiation Errors in Air Ducts Under Nonisothermal Conditions Using Thermocouples, Thermistors, and a Resistance Thermometer

Joseph C. Davis*

Studies were made to determine the radiation error in temperature measurements made with thermocouples, thermistors, and a resistance thermometer in moving air at velocities ranging from 300 to 1300 fpm when the temperature of the duct wall surrounding the air stream was from 0 to 50 deg F higher than that of the air in the center of the duct. To eliminate all but the variable under study, conduction errors were minimized to a point where they were almost nonexistent by using Chromel P-constantan thermocouple wire and by employing other techniques. Radiation effects were studied when the probe housing the three types of temperature sensors was unshielded and again when it was shielded. The studies showed that when the sensors were unshielded and the temperature difference between the duct wall and the air was 50 deg F (28 K, approximately), the error in the sensors was about 3.8 deg F (2.1 K) for an air velocity of 300 fpm (1.5 m/s) and 1.0 deg F (0.6 K) for an air velocity of 1300 fpm (6.6 m/s). When the sensors were shielded, the error was about 0.2 deg F (0.1 K) for 300 and 500 fpm velocities and the same duct wall air-temperature difference. Tests were not performed at 1300 fpm with the sensors shielded because theory indicated that radiation error would be negligible at this velocity. Under the test conditions that prevail in the testing of air conditioners and heat pumps in laboratories, it should be possible to reduce the error in temperature measurement of the moving air to about 0.2 deg F (0.1 K) by a suitable combination of air mixers, duct insulation, radiation shields, and calibration techniques.

Key words: Conduction error; radiation error; resistance thermometer; temperature measurement; thermistor; thermocouple.

•Present address : 4534–47th St., N.W., Washington, D.C. 20016.

1. Introduction

Accuracy of measurement of the temperature of moving air depends, among other things, on the effectiveness of precautions taken to minimize conduction and radiation errors. It is known that in the determination of the thermodynamic properties of moving air, these errors can be significant at air velocities below 1000 fpm and when the temperature of the surroundings, such as a duct wall bordering a stream of moving air, is 20 deg F different from that of the air at the position of the sensor. However, the literature does not show much information on the magnitude of error at these velocities and temperature differences.

The error in determining the capacity of an air conditioner or a heat pump in a laboratory can be as high as 5 percent if the error in the temperature measurement from these sources is neglected, even though the temperature difference between the air and the duct wall may not exceed 6 deg F. Similarly, the measurement of the moisture generation capacity of a humidifier can be as much as 10

percent in error if corrections are not made to the observed temperature.

In a previous paper by Davis, Faison, and Achenbach [1]' showing the results of the study of the errors of thermocouples, thermistors, and mercury-in-glass thermometers used in moving air, and where the temperature of the duct wall was essentially the same as that of the sensors, it was shown that the principal errors under those conditions were due to change in performance of the sensors between calibrations, and to false readings due to thermal lag of the sensors. Other smaller sources of error found in the study were self-heating of the thermistors, parallax difficulties in reading the mercury-in-glass thermometers, orientation of the thermometers, and impact error due to the energy of motion of the air stream.

Shielded and unshielded temperature sensors are widely recommended in various standard test pro


1 Figures in brackets indicate the literature references on page 12.

study now being reported, thermocouples and thermistors were used, but because of placement problems, and because a better calibration reference was needed, a platinum-resistance thermometer was used instead of a mercury-in-glass thermometer.

cedures for air conditioning, heating, and refrigerating equipment for indicating the temperature of moving air in ducts under conditions where the temperature of the duct wall may be significantly different from the air temperature in the duct. This study was designed to evaluate the magnitudes of the radiation errors for three common types of sensors, used with or without shielding, for a range of air velocities and a range of temperature differences between the duct wall and the moving air, and to indicate application techniques that would minimize conduction errors. In the previous studies, thermocouples, thermistors, and mercury-in-glass thermometers were used. In the

2 Throughout this paper, the more substantive results are given not only in the British units now customary in this country, but also in the International System of Units (abbreviated as SI). This is done in recognition of the position of the USA as a signatory to the General Conference on Weights and Measures, which gave official status to the SI system of units in 1960. To assist readers interested in making use of the coherent system of SI units, the exact conversion factors used in this paper are : Length

1 inch = 0.0254 meter. Velocity

100 ft/min = 9.0508 meter/ second Temperature difference i deg F=5/9 deg C = 5/9 K (kelvin)

2. Description of Apparatus The tests employed a well-insulated, round metal duct with an air-mixing device near the inlet. Air was drawn through the duct at velocities sufficiently high to produce turbulent flow. All temperature measurements were performed at a station seven duct diameters downstream of the mixing device. The duct walls were heated for a distance of 3.7 duct diameters upstream and 3.7 downstream of this station. A temperature boundary layer along the duct wall started at the lead

с ing edge of the heated section, and grew in thickness in the flow direction. At the test station, this boundary layer was still quite thin. The remainder of the volume of air was essentially isothermal so that the conduction of heat through the air to the temperature sensors was not significant. All temperature measurements at this station

B were made near the axis at the center of the isothermal volume of fluid. The magnitude of the radiation error was directly assessed by obtaining measurements with and without radiation shields and comparing them with measurements made with specially constructed reference sensors.

Two nearly identical thermocouples, two nearly identical thermistors, and the resistance thermometer comprised a probe which was part of a rigid assembly designed to prevent flexure of the

D leads and to minimize conduction losses. The probe was placed longitudinally in the center of the duct and parallel to the direction of the flow of moving air. Figure 1 shows the assembly consist- FIGURE 1. The probe housing two thermocouples, two ing of the probe (A); a cage-like structure housing

thermistors, and a resistance thermometer. bare lead wires for minimizing conduction errors

The Ice-bath for the thermocouples is housed in the cabinet in

the lower portion of the figure. Conduction errors were mini(B); a hollow, phenolic cylindrical structure (C), mized with the use of the cage-like structure housing the bare

lead wires. which served to thermally insulate the plastic tube carrying the leads through the duct wall and which was useful in determining if there were in the instrument room which was remotely loany conduction errors involved during testing cated. Wire leads to the measuring equipment in (experiments performed to make this determina- the instrument room for the thermocouples and the tion are described later); and a wooden cabinet resistance thermometers were permanently con(D), which housed an ice bath and a junction nected to the assembly. box. The junction box, which had gold-plated Details of the probe are shown in figure 2. The connectors to minimize corrosion, was used to con- two thermocouples, the two thermistors, and the nect the thermistor leads to the thermistor bridge resistance thermometer were fixed in a rigid man

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FIGURE 2. Diagram of the probe-end showing the two

thermocouples, one of the two thermistors, and the capsule-type platinum resistance thermometer.

Each of the two bead-type thermistors had a nominal resistance of 2000 N at 77 °F. Dimensional details of one of the thermistors are shown in figure 3. The two lead wires within the glass stem were made of untinned wire having a low thermal conductivity, and having a coefficient of expansion approximately equal to that for glass. According to the manufacturer, the “dissipation constant” in still air is 25 sec; beta 3 (a material constant) at 25 °C (77 °F) is 3465+175 K; and

R. (0 °C) the resistance ratio,

R. (32 °F)

is R. (50 °C) R. (122 °F) 7.1. The parameter R is the resistance of the thermistor measured when a low level of electric power, small enough so as not to heat it appreciably, is applied. The manufacturer advised that the thermistors supplied had been aged at elevated temperatures, a precaution which is regarded as necessary to impart stability. [3] A modified ratio bridge was used with the thermistors. The bridge was constructed so that the dial reading was nearly linearly related to the temperature of the air. [4] Shielded microphone cables were used to connect the wires from the junction box in the probe assembly to the thermistor switch, in the instrument room. Goldplated connectors were used at the thermocouple selector switch.

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ner at the end of the probe, and the leads, insulated in vinyl plastic sheathing, were fixed rigidly through the center of thin-walled methyl methacrylate tubing bent at a right angle (fig. 1). Holes about 0.1 in diameter were placed in the tubing to allow the flow of air across the insulated lead wires thereby further reducing conduction and errors due to reradiation of heat from the plastic tubing to the wires (figs. 1 and 2).

The leads running from the probe to the ice-bath and the junction box in the assembly were rigidly fixed into the U-shaped methyl methacrylate tubing between (C) and (D) by filling the tubing completely with epoxy resin. This rigidization reduced cold-working of the wires which could cause a change in results from calibration to calibration. The tubing was insulated with spongerubber and with a reflective covering.

The thermocouples in the probe were of No. 30 B and S gage (0.010 in) Chromel P and constantan wires. Each junction was about 18 in long. All-copper switches were used in the electrical cir cuit of the thermocouple system. The ice bath consisted of two wells filled with oil inserted in an insulated Dewar flask containing slushy ice. The wells were immersed to a depth of more than 6 in in the ice, and the junctions were placed near the bottoms of the wells. This procedure was recommended by Caldwell [2]. The floating ice in the bath was maintained at a sufficient depth to extend below the bottoms of the wells at all times. The ice bath was stirred about every 3 hr. The use of Chromel P-constantan thermocouple wires further helped minimize conduction error because of their low thermal conductivity, which was about 6 Btu hr -1 ft - deg F- for chromel and about 13 Btu hr •' ft - deg F-1 for constantan as compared copper which is about 200 Btu hr -- ft -- deg F-1

The wires connecting the assembly to the switch and to the potentiometer in the instrument room were copper. A precision-type laboratory potentiometer was used for measurment of voltage. It was capable of direct reading to within luV and of interpolation to within 0.14 V, corresponding to 0.03 deg F and 0.003 deg F, respectively, when Chromel P-constantan thermocouples are used.

A capsule-type platinum resistance thermometer 1.63 in long with a diameter of 0.25 in was used. The capsule was made of polished platinum. Four lead wires from the capsule were connected to long copper wires leading to the Mueller bridge in the instrument room. These four lead wires are needed in Mueller bridge measurements to compensate for effects in lead wire resistances. The bridge was capable of reading to the nearest 0.0001 1, corresponding to a temperature resolution of 0.002 deg F.

A schematic drawing of the apparatus is shown in figure 4. The test duct, 12 ft long, was made of brass, had a wall of 1/8 in thickness, and had a diameter of 10 in O.D. It was heated around the measuring section with electrical heating cables for a distance of 3 ft upstream and 3 ft downstream from the probe. The duct was insulated along its entire length. There was an access door at the top of the duct with an access mechanism for placing the probe in the duct. This door had





(7 7.)

3 Beta is approximately constant. It appears in the equation R=Roe where T is any Kelvin temperature, and T, is the temperature at which R. was determined.

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