Instrumentation Sensors Book

Example 10.8

How much heat is transferred from a 12m × 15m surface by convection, if the temperature difference between the front and back surfaces is 33°C and the surface has a heat transfer rate of 1.5 W/m2 K?

Q = 1.5 × 12 × 15 × 33 = 8.91 kW

Radiation is the emission of energy by electromagnetic waves, which travel at the speed of light through most materials that do not conduct electricity. For instance, radiant heat can be felt at a distance from a furnace where there is no conduction or convection. Heat radiation is dependent on factors, such as surface color, texture, shapes, and so forth. Information more than the basic relationship for the transfer of radiant heat energy given below should be factored in. The radiant heat transfer is given by:

where Q is the heat transferred, C is the radiation constant (dependent on surface color, texture, units selected, and so forth), A is the area of the radiating surface, T2 is the absolute temperature of the radiating surface, and T1 is the absolute temperature of the receiving surface.

Example 10.9

The radiation constant for a furnace is 0.11 × 10−8 W/m2 K4, the radiating surface area is 3.9 m2, the radiating surface temperature is 1,150K, and the room temperature is 22°C. How much heat is radiated?

Q = 0.11 × 10−8 × 3.9 × [(1,150)4 − (22 + 273)4]

Q = 0.429 × 10−8 × [174.9 × 1010 − 0.76 × 1010] = 7.47 × 103W

Example 10.10

What is the radiation constant for a wall 19 × 9 ft, if the radiated heat loss is 2.33 × 104 Btu/hr, the wall temperature is 553°R, and the ambient temperature is 12°C?

2.33 × 104 Btu/hr = C × 19 × 9 [(553)4 − (53.6 + 460)4]

C = 2.33 × 104/171(9.35 × 1010 − 6.92 × 1010)

C= 3.98 × 106/2.43 × 1010 = 1.64 × 104 Btu/hr ft2°F4

10.2.4Thermal Expansion

Linear thermal expansion is the change in dimensions of a material due to temperature changes. The change in dimensions of a material is due to its coefficient of thermal expansion, which is expressed as the change in linear dimension () per degree temperature change. The change in linear dimension due to temperature changes can be calculated from the following formula:

where L2 is the final length, L1 is the initial length, is the coefficient of linear thermal expansion, T2 is the final temperature, and T1 is the initial temperature.

Example 10.11

What is the length of a copper rod at 420K, if the rod was 93m long at 10°F?

New length = L1[1 + (T2 − T1)] = 93{1 + 16.9 × 10−6 [147 − (−12)]}m New Length = 93[1 + 16.9 × 10−6 × 159] = 93 × 1.0027m = 93.25m

Volume thermal expansion is the change in the volume () per degree temperature change due to the linear coefficient of expansion. The thermal expansion coefficients for linear and volume expansion for some common materials per °F (°C) are given in Table 10.5. The volume expansion in a material due to changes in temperature is given by:

where V2 is the final volume, V1 is the initial volume, is the coefficient of volumetric thermal expansion, T2 is the final temperature, and T1 the initial temperature.

Example 10.12

Calculate the new volume for a silver cube that measures 3.15 ft on a side, if the temperature is increased from 15°to 230°C.

Old Volume = 31.26 ft3

New volume = 3.153[1 + 57.6 × 10−6 × (230 − 15)]

= 3.153(1 + 0.012) = 31.63 ft3

In a gas, the relation between the pressure, volume, and temperature is given by:

Table 10.5 Thermal Coefficients of Expansion per °F (°C)

where P1 is the initial pressure, V1 is the initial volume, T1 is the initial absolute temperature, P2 is the final pressure, V2 is the final volume, and T2 is the final absolute temperature.

10.3Temperature Measuring Devices

The methods of measuring temperature can be categorized as follows:

1.Expansion of materials;

2.Electrical resistance change;

3.Thermistors;

4.Thermocouples;

5.Pyrometers;

6.Semiconductors.

Thermometer is often used as a general term for devices for measuring temperature. Examples of temperature measuring devices are described below.

10.3.1Expansion Thermometers

Liquid in glass thermometers using mercury were, by far, the most common direct visual reading thermometer (if not the only one). Mercury also has the advantage of not wetting the glass; that is, the mercury cleanly traverses the glass tube without breaking into globules or coating the tube. The operating range of the mercury thermometer is from −30° to +800°F (−35° to +450°C). The freezing point of mercury −38°F (−38°C). The toxicity of mercury, ease of breakage, the introduction of cost-effective, accurate, and easily read digital thermometers, has brought about the demise of the mercury thermometer for room and clinical measurements. Other liquid in glass devices operate on the same principle as the mercury thermometer. These other liquids have similar properties to mercury (e.g., have a high linear coefficient of expansion, are clearly visible, are nonwetting), but are nontoxic. The liquid in glass thermometers are used to replace the mercury thermometer, and to extend its operating range. These thermometers are inexpensive, and have good accuracy (<0.1°C) and linearity. These devices are fragile, and used for local measurement. The operating range with different liquids is from −300° to +1,000°F (−170° to +530°C). Each type of liquid has a limited operating range.

A bimetallic strip is a relatively inaccurate, rugged temperature-measuring device, which is slow to respond and has hysteresis. The device is low cost, and therefore is used extensively in On/Off-types of applications, or for local analog applications not requiring high accuracy, but it is not normally used to give remote analog indication. These devices operate on the principle that metals are pliable, and different metals have different coefficients of expansion, as shown in Table 10.5. If two strips of dissimilar metals, such as brass and invar (copper-nickel alloy), are joined together along their length, then they will flex to form an arc as the temperature changes. This is shown in Figure 10.1(a). Bimetallic strips are usually configured as a spiral or helix for compactness, and can then be used with a pointer to make an inexpensive, compact, rugged thermometer, as shown in Figure 10.1(b).

In a resistance thermometer, the variation of resistance with temperature is given by:

where RT2 is the resistance at temperature T2, and RT1 is the resistance at temperature

T1.

Example 10.15

What is the resistance of a platinum resistor at 480°C, if its resistance at 16°C is 110Ω?

Resistance at 480° C = 110[1+ 000385.(480 − 16)]Ω

=110(1+ 17864.)Ω

=306.5Ω

Resistance devices are normally measured using a Wheatstone bridge type of system, or are supplied from a constant current source. Care should be taken to prevent the electrical current from heating the device and causing erroneous readings. One method of overcoming this problem is to use a pulse technique (i.e., by passing a current through the resistor only when a measurement is being made), keeping the average power very low so that the temperature of the resistor remains at the ambient temperature.

10.3.3Thermistors

Thermistors are a class of metal oxide (semiconductor material) that typically has a high negative temperature coefficient of resistance. They also can be positive. Thermistors have high sensitivity, which can be up to a 10% change per degree Celsius, making it the most sensitive temperature element available, but thermistors also have very nonlinear characteristics. The typical response time is from 0.5 to 5 seconds, with an operating range typically from −50° to +300°C [3]. Devices are available with the temperature range extended to 500°C. Thermistors are low cost, and are manufactured in a wide range of shapes, sizes, and values. When in use, care has to be taken to minimize the effects of internal heating. Thermistor materials have a temperature coefficient of resistance () given by:

Constant temperature enclosure

(b)

Figure 10.6 (a) Thermocouple with the reference junction held at a fixed temperature, and (b) the temperature of the reference junction measured, and a correction applied to the output signal.

2.The Peltier effect states that if a current flows through a thermocouple, then one junction is heated (outputs energy), and the other junction is cooled (absorbs energy).

3.The Thompson effect states that when a current flows in a conductor along which there is a temperature difference, heat is produced or absorbed, depending upon the direction of the current and the variation of temperature.

In practice, the Seebeck voltage is the sum of the electromotive forces generated by the Peltier and Thompson effects. There are a number of laws to be observed in thermocouple circuits. First, the law of intermediate temperatures states that the thermoelectric effect depends only on the temperatures of the junctions, and is not affected by the temperatures along the leads. Second, the law of intermediate metals states that metals other than those making up the thermocouples can be used in the circuit, as long as their junctions are at the same temperature. Other types of metals can be used for interconnections, and tag strips can be used without adversely affecting the output voltage from the thermocouple. Letters designate the various types of thermocouples. Tables of the differential output voltages for different types of thermocouples are available from manufacturers’ thermocouple data sheets [4]. Table 10.7 lists some thermocouple materials and their Seebeck coefficients. The operating range of the thermocouple is reduced to the figures in parentheses if the given accuracy is required. For operation over the full temperature range, the