On the Search for New Solutions of the Single-Pass Crossflow Heat Exchanger Problem, Int.J.Heat Mass Transfer, 28, 1965–1976.. Mean Temperature Difference in Old Tube Pass Heat Exchangers
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T temperature gradient
total transitional correction factor
t tube or number oftubes
tube-to-baffle leakage path transverse
tw number oftubes in one window
volumetric equivalent diameter void void volume
Wf wetted perimeter for friction
Wh wetted perimeter for heat transfer
W1 wetted perimeter ofone channel
wall window
we end-space condition
wg gross window area
y tube pitch factor
2 inlet or outlet
Superscripts
m exponent, dimensionless
n exponent, dimensionless
y exponent, dimensionless
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CHAPTER 12
Experimental Methods
JOS ´E L LAGE Mechanical Engineering Department Southern Methodist University Dallas, Texas
12.1 Fundamentals 12.1.1 Measurement 12.1.2 Sensing 12.1.3 Calibration 12.1.4 Readability 12.2 Measurement error 12.2.1 Uncertainty: bias and precision errors 12.2.2 Mean and deviation
12.2.3 Error distribution 12.2.4 Chauvenet’s criterion and the chi-square test 12.3 Calculation error
12.4 Curve fitting 12.5 Equipment 12.5.1 Glass thermometers 12.5.2 Thermocouples 12.5.3 Resistance temperature detectors 12.5.4 Liquid crystals
12.5.5 Pyrometers 12.5.6 Heat flow meters Nomenclature
References
12.1 FUNDAMENTALS 12.1.1 Measurement
Measurement is one of the most important activities in science and engineering
Validation of new theories, determination of material property values, classification of new materials, performance evaluation of new and existing devices, and monitoring and control of existing and new processes are activities that depend on measurements
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Measurement, or measuring, is also the most important part of an experiment.
Measuring is not absolute, as it does not define a quantity (standard) to be measured.
Measuring is a relative effort and is made to compare and to evaluate To be indepen-dent, a comparison requires a measure, a standard unit.
The art of measuring is at least as old as humanity itself The human body performs measurements all the time One of the most basic quantities continuously measured by
the human body is the environment temperature Feeling hot or cold is a consequence
of this measuring Although not descriptive (not quantified with a parameter such as temperature), the natural measuring of the environmental temperature by the human body is nevertheless a relative process This process is based on a comparison of the environmental temperature with a certain standard, in this case the temperature at
which the body feels neitherhot norcold—the null point of human thermal control.
In heat transfer, temperature and heat flow are unquestionably the most important quantities to be measured Other quantities of interest to heat transfer include fluid speed, pressure (force), mechanical stress, electric current, voltage, length, surface area, volume, and displacement In this chapter the focus is on temperature and heat flow measurements
General measuring concepts such as sensitivity, hysteresis, calibration, accuracy, and readability are presented first Then the discussion turns to statistical concepts such as mean, deviation, standard deviation, normal distribution, Chauvenet’s crite-rion, and the chi-square test, related to the determination of precision, bias error, and
measuring uncertainty The final section of this chapter is devoted to a brief discussion
of some common instruments for measuring temperature or heat flow
12.1.2 Sensing
Among the two possible alternatives for sensing devices, the most common are the
contact sensing devices such as thermocouples that measure by physical contact In
general, contact sensing devices are rugged, economical, relatively accurate, and easy
to use Disadvantages commonly associated with contact sensing devices include susceptibility to wear (e.g., breaking of thermocouple junction) They also require
accessibility forphysical contact Because of the contact nature of these devices,
they tend to interfere with the medium where measurement is to be taken, frequently affecting the state and the value of the quantity to be measured The last disadvan-tage can be a serious problem For instance, the conductive wires of a thermocouple will always provide a heat path when in contact with the medium where tempera-ture is to be measured This heat path can modify the state of the medium where temperature is to be measured by adding energy to, or extracting energy from, the medium
Anotheralternative is a non-contact sensing device such as an infrared sensor or pyrometer This type of sensing device is advantageous because it does not require
physical contact; that is, the measurement can be made remotely They are more convenient than the contact sensing devices for measuring quantities from surfaces
in movement without contact with the surface In addition, they do not interfere with the quantities being measured (no heat sink/source), are generally faster in
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obtaining the measurement (because of the smaller thermal inertia), and are less prone
to wear
Some disadvantages include cost (generally more expensive than contact sensing devices), difficult calibration, and the effect of the environment on the measurement (e.g., dust and smoke in the field of view will affect the measurement of surface temperature using an infrared detector)
Most measuring devices do not measure the quantity of interest directly In the case of thermocouples, for instance, what is measured is a voltage across the open-circuit terminals of the thermocouple wires This voltage emanates from the electrical effect that temperature has on the electrical potential (EMF) along two distinct but connected conductive wires By knowing how the voltage read by the electrical instrument relates to the temperature at the connection of the two thermocouple wires,
the voltage can be translated into temperature The same is true in relation to the
more common mercury thermometers The mercury thermometer does not measure the temperature directly but the variation caused by the temperature on the volume
of mercury inside the thermometer The scale printed on the thermometer glass, translating the mercury volume variation into temperature, allows the measurement
of volume to be translated into temperature These are types of indirect measurement.
The sensitivity of measuring devices is a very important characteristic for
measur-ing Sensitivity can be understood as the relation between cause and consequence
Thermocouples have sensitivities listed in mV/°C because the consequence of mea-suring an increase in temperature is a change in voltage across the thermocouple terminals
Suppose that a thermocouple for measuring a temperature variation of 60°C is needed, and a multimeterhaving a scale from 0 to 100 mV is available Unless the thermocouple has a sensitivityS smallerthan 100 mV per60°C, orequivalently,
S < 1.67 mV/°C, measurement cannot be performed within the available voltage
range It should be kept in mind that small quantities are, in general, more difficult and expensive to be measured; that is, thermocouples with small sensitivities tend to
be more costly
The sensitivity of an instrument might not be uniform along the entire range avail-able for measurement In such cases, translation from the quantity actually measured
to the quantity of interest is not linear Moreover, the sensitivity of an instrument might depend on the direction of variation of the quantity being measured For in-stance, when increasing the temperature, a certain thermocouple device might have a uniform sensitivity equal to 1.5 mV/°C But when the temperature to be measured de-creases, the sensitivity might be nonuniform; for exampleS(T ) = 1.5α(T ) (mV/°C),
whereα(T ) is a certain function of temperature T In this case, the temperature value
corresponding to a certain voltage when the temperature increases will differ from the temperature value at the same measured voltage when the temperature decreases
The instrument is then said to exhibit hysteresis Figure 12.1 demonstrates this
phe-nomenon considering a thermocouple with uniform sensitivity equal to 1.5 mV/°C when measuring an increase in temperature (continuous line) from 0°C to 20°C, and nonuniform sensitivity equal to 1.5(2.33 − 0.133T + 0.0033T2) mV/°C when mea-suring a decrease in temperature from 20°C to 0°C