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Title: MAE 170 Lecture 5: Temperature Measurement


1
MAE 170 Lecture 5 Temperature Measurement
  • April 30, 2007

2
Todays schedule
  • In-class midterm
  • Discussion of thermocouple operation
  • Upcoming lab overview
  • Sample data and analysis ideas for upcoming week
  • Next weeks Labview listen carefully

3
Purpose of this weeks experiment
  • Learn how a thermocouple works
  • Use a thermocouple to take temperature
    measurements
  • Calibration
  • Measure heating / cooling rate of metal spheres
    in H2O
  • Use sets of data from a repeated experiment to
    assess experimental error

4
The Seebeck Effect
  • Generation of a voltage in a circuit containing
    two different metals, or semiconductors, by
    keeping the junctions between them at different
    temperatures.
  • Discovered by the German (Estonian) physician /
    physicist Thomas Seebeck (17701831) who
    (apparently accidentally) discovered the effect
    in 1821.
  • Seebeck, T.J., Ueber den magnetismus der
    galvenische kette, Abh. K. Akad. Wiss., Berlin,
    289, 1821.
  • Also called the thermoelectric effect.

The basis of the Seebeck effect is electron
mobility in conductors and semiconductors, which
is a function of temperature
5
So then, what is a thermocouple?
  • Electron mobility through a conductor changes as
    a function of temperature
  • When two different metals are joined, relative
    difference in electron mobility makes electrons
    from the more mobile metal jump to the less
    mobile metal
  • A potential difference is created between the two
    conductors
  • In the absence of a circuit, this causes charge
    to accumulate in one conductor, and charge to be
    depleted in the other conductor.

6
Example Type K thermocouple
  • Standard thermocouple gives 12.2 mV at 300 ºC
  • But we cant connect it like this as the
    measurement leads, which are metals, introduce
    secondary thermocouple junctions!
  • ? Voltage at secondary junctions would be
    erroneous if we put our DVM leads between the two
    sides of the TC here!

7
Wiring thermocouples Cold Junctions
  • As long as the connections of the measurement
    device with A are kept at the same temperature,
    the same voltage is generated at each measurement
    point and this cancels out
  • T2 must be a known temperature, historically, ice
    bath
  • Tabulated voltages assume T2 0 ºC

8
Thermocouple construction, continued
  • What about the joining of A to B, the two
    thermocouple leads? If I solder this will it
    create a new TC junction?
  • Law of intermediate metals states that a third
    metal, inserted between the two dissimilar metals
    of a thermocouple junction will have no effect
    provided that the two junctions (solder A) and
    (solder B) are at the same temperature
    practically this is always the case. So
    soldering TC junctions is OK.

???
A
B
9
Practical thermocouples
  • Today, thermocouples are almost always welded
    rather than soldered
  • Eliminates difficulties based on melting point of
    solder
  • Little TC welders are easy to find, cheap
  • Nobody wants to carry around a bucket of ice
    water when they use a TC, so
  • On-board thermocouple cold junctions sense the
    temperature at the point of connection of the
    thermocouple to the measurement device (room
    temperature) and provide the correct
    compensation voltage as if there were a TC in an
    ice bath connected

10
Thomas Seebeck (1770-1831)
  • Did not believe in his own effect denied that
    an electric current was generated!
  • Observed thermomagnetic currents (actually,
    magnetic field induced by the electric current)
    and wrote extensively on his observations.
  • Concludes (incorrectly) that the earth's magnetic
    field was produced by the temperature differences
    between the two poles and the equator.

11
Associated effect the Peltier Effect
  • A change in temperature at the junction of two
    different metals produced when an electric
    current flows through them
  • Opposite of the Seebeck effect
  • The extent of the change depends on what the
    conducting metals are, and the nature of change
    (rise or fall in temperature) depends on the
    direction of current flow
  • It is named after the French physicist Jean
    Charles Peltier (17851845) who discovered it in
    1834.
  • Basis of those 80 6-pack refrigerators that you
    can find at Target

12
Calibration of thermocouples
  • Typically nearly linear, but for accuracy modeled
    with a high-order polynomial
  • Calibrations available from manufacturer or
    www.nist.gov (National Institutes of Standards
    and Technology)
  • Want high sensitivity, linearity in the
    calibration curve for greater precision

Red Bad
(ºC)
Blue Good
(mV)
13
Types of thermocouples
  • Type K (Chromel / Alumel)
  • Type K is the 'general purpose' thermocouple. It
    is low cost and, owing to its popularity, it is
    available in a wide variety of probes.
    Thermocouples are available in the -200C to
    1200C range. Sensitivity is approx 41uV/C. Use
    type K unless you have a good reason not to.
  • Type E (Chromel / Constantan)
  • Type E has a high output (68uV/C) which makes it
    well suited to low temperature (cryogenic) use.
    Another property is that it is non-magnetic.
  • Type J (Iron / Constantan)
  • Limited range (-40 to 750C) makes type J less
    popular than type K. The main application is with
    old equipment that can not accept 'modern'
    thermocouples. J types should not be used above
    760C as an abrupt magnetic transformation will
    cause permanent decalibration.

14
Types of thermocouples, continued - High
temperature thermocouples
  • Type N (Nicrosil / Nisil)
  • High stability and resistance to high temperature
    oxidation makes type N suitable for high
    temperature measurements without the cost of
    platinum (B,R,S) types. Designed to be an
    'improved' type K, it is becoming more popular.
  • Thermocouple types B, R and S are all 'noble'
    metal thermocouples and exhibit similar
    characteristics. They are the most stable of all
    thermocouples, but due to their low sensitivity
    (approx 10uV/0C) they are usually only used for
    high temperature measurement (gt300C).
  • Type B (Platinum / Rhodium)
  • Suited for high temperature measurements up to
    1800C. Unusually type B thermocouples (due to
    the shape of their temperature / voltage curve)
    give the same output at 0C and 42C. This makes
    them useless below 50C.
  • Type R (Platinum / Rhodium) and Type S
  • Suited for high temperature measurements up to
    1600C. Low sensitivity (10uV/C) and high cost
    makes them unsuitable for general purpose use.

15
Some sources of error in thermocouples
  • Electrical
  • Common mode noise
  • These things are long wires big antennas!
  • Common mode voltage
  • Inductive pick up by measurement device swamps
    your small signal
  • Grounded system (e.g. water pipe) measured with a
    unsheathed thermocouple
  • Unintended metals creating extra TC junctions in
    circuit
  • Thermal (next slide)

16
Errors common in high temperature measurements
(like 1000K and higher)
17
Must do a heat balance on the TC bead to get the
actual temperature
  • Conduction down the wires and catalysis can be
    minimized, but requires thought. Then

18
Thermocouple cousins Thermoelectrics
  • What if we add heat to one thermocouple junction,
    cool the other?
  • Electric current flows in the circuit!
  • 2-4 efficient, currently

19
Thermoelectric Fundamentals (slide courtesy of
Prof. G.S. Jackson, Univ. of Maryland)
  • Thermoelectrics are couples of n- and p-type
    semiconductors
  • generated voltage ? (TH TC) across the
    junctions
  • generated current as a function of heat flux
    through couples
  • ideally with low thermal conductivity and high
    electrical conductivity
  • Fraction of energy converted hTE is
    function of Z and TH TC

20
Motivation for Exploring Waste Heat Recovery
(courtesy G.S. Jackson, Univ. of Maryland)
  • 65-85 of fuel energy is lost as waste heat in a
    typical automobile
  • another 2-10 may be used for alternator to meet
    electrical loads.
  • If accessory loads are met via waste heat
    recovery, more fuel energy is converted directly
    to propulsion (an increase of 2 to 10)

21
MEASUREMENT OF HEAT TRANSFER COEFFICIENTS
T?
Ts
Q - h AS?T - h AS(Ts-T?)
22
BROAD OBJECTIVE INVESTIGATE THE PROBLEM OF

HOW DO SPHERES COOL?
23
Consider
  • An engineer, a psychologist, and a physicist were
    asked to make recommendations to improve the
    productivity of an under-producing dairy farm
  • Engineer more technology
  • Psychologist improve environment
  • Physicist

24
Consider a spherical cow
T(t)
  • Great engineers and physicists are able to
    appropriately simplify problems to extract the
    physics!

25
Heat transfer background - Temperature
  • Remember temperature is the manifestation of
    molecular motion (typo last time)
  • Translational motion is one of the primary forms
    of molecular energy storage
  • Others are electronic energy (electrons),
    vibrational energy (bonds), rotational energy
  • Translation is not quantized like the other
    energy forms
  • so

k Boltzmann constant 1.38 x 10-23 J/moleculeK
26
Heat transfer background Heat Capacity
  • The ability of a substance to store energy in
    various modes is called the heat capacity of the
    substance
  • In gases, we have a heat capacity at constant
    volume Cv, and at constant pressure Cp ? Cp gt Cv
  • For incompressible solids and liquids there is
    generally just one value of C
  • Units C J/kgK
  • For a particular volume V m3 of an
    incompressible solid (or liquid) with a density ?
    kg/m3

27
Energy moves around in different ways
  • Random molecular motion conduction
  • Organized motion convection
  • Electromagnetic waves radiation
  • ? Today we focus on conduction and convection

28
Conduction Introduction to Fouriers Law
  • Direct exchange of energy between molecules,
    analogous to species diffusion
  • Empirically-determined Fouriers Law
  • Heat that flows between two surfaces is
    proportional to conductivity k W/mK, area
    A and gradient of temperature
  • Flow is in direction opposite to temperature
    gradient, i.e. heat flows from HOT to COLD

29
Convection Introduction to Newtons Law
  • Packets of flowing fluid (gas or liquid) can
    typically transfer heat more efficiently than
    conduction alone
  • Increases thermal gradient at surface by sweeping
    in new fluid

Stagnant fluid with no convection
Fluid with convection
Thermal gradient
Hot surface
30
Heat transfer coefficient Newtons Law
  • h is called the heat transfer coefficient
  • Geometry and flow-dependent
  • A is area, Thot and Tcold are temperatures
  • If q WJ/s then h W/m2K

31
Our problem this week Fluid cooling of a metal
sphere (thermocouple in the middle)
  • Flowing fluid cools the outside of the sphere
  • Newtons law
  • Heat transfer occurs inside sphere
  • Fouriers law of conduction


32
Are conduction and convection equal for our
sphere?
  • Electrical analogy to heat transfer (A.K.
    Oppenheim, 1950s)
  • ?V IR ? ?T QR
  • Fouriers law Q -kA dT/dx -kA ?T/ ?x
  • Resistance to conduction ?x / kA
  • Newtons law Q hA(Th Tc)
  • Resistance to convection 1/hA
  • Define Biot number Conduction R / Convection R
  • Bi (?x / kA) / (1/hA) h?x/k
  • In spherical geometry, proper ?x is radius
  • Bi hr/k

33
Simplified lumped heat transfer model
(remember the spherical cow?)
  • Can we simplify? Experience tells us that
    conduction in a metal is VERY FAST compared with
    other kinds of heat transfer
  • Propose if k/r gtgt h, neglect conduction in the
    solid
  • Equivalent simplification
  • ? Metal is at a constant temperature
  • If Bi lt 0.1, there is a 5 error or less in
    estimating temperature throughout body as a
    single-valued function of time T(t)

34
Lumped analysis
  • Energy leaving the fluid volume through
    convection is reflected in reduced solid
    temperature (energy storage)

Energy balance equation
  • 1st order ODE in time needs just an initial
    condition
  • Solution

Knowing T0,T, Rs, C and r, a measure of Ts versus
t will yield h
35
Time constant, applicability of lumped analysis
  • T-T? is reduced 63.2 (1/e) when t ?
  • Condition for lumped analysis (conduction fast
    compared with convection)
  • Evaluate with nondimensional Biot number

36
Recap, remember 1st Major Assumption
  • Temperature is uniform throughout sphere.
  • - Temperature gradients are small inside
    sphere.
  • - Resistance to conduction within solid much
    less than
  • resistance to convection across fluid
    boundary layer.
  •   Resistance to conduction /
    Resistance to convection Biot Number

37
Recap, remember 2nd Major Assumption

Heat transfer coefficient is assumed not to be a
function of ?T.
Rate of heat energy passing through sphere
Q - h As (Ts - T?) (W)
(W/m2-Ko)(m2)(Ko)
Not changing in time!
38
CAN WE ASSUME h TO BE A CONSTANT? h will
depend on (Ts - T?) for free convection, boiling,
condensation, large temperature differences


h(a) gt h(b)
h(free convection) more dependent on ?T
Note as h goes up 1st approximation is worse
(hR/klt0.1), but 2nd approximation
better
39
Lab 5 Measurement of Temperature
40
Pre-lab write-up and questions
  • Do the pre-lab write-up in your lab notebook as
    usual
  • How does a thermocouple work? Why is it made of
    two metals?
  • Temperature is the manifestation of what
    molecular property? MOTION!!!
  • What does a cold junction do? Why is it
    necessary?

41
Objectives of this weeks laboratory experiment
  • Calibrate a thermocouple with a reference
    junction in an ice bath
  • To obtain free and forced convection heat
    transfer coefficients from transient temperature
    measurements of heating and cooling of metal
    spheres

42
This weeks experiment
  • K-type thermocouples have been placed in
  • the center of aluminum and brass spheres
  • Measure the voltage output from aluminum
  • ball at room temperature
  • Hold the aluminum ball in your hand and
  • notice change of voltage

Check that thermocouples in both spheres are
working.
43
This weeks experiment
44
BEFORE YOU START
  • check if thermocouple is working

Thermocouple with conversion CJ.vi
45
Step 1 Obtain Calibration for TC
  • Get a beaker of ice water with enough ice to last
    a little while.
  • Get a beaker or pan of water and put it on the
    hot plate. Dont put too much water in the pan,
    youll want to not take all day heating the
    water.
  • Youre going to create a calibration with the
    help of an alcohol thermometer. You and your
    partner(s) will take measurements separately,
    this will add to the mystery and the error of the
    experiment! To make this work, you and your
    partner(s) must not reveal to each other the
    numbers youre writing until the end of the
    calibration experiment.
  • Put the cold junction in the ice water, suspend
    it so that it is happy.
  • Put the measurement junction in the
    room-temperature water in the pan. Dont let the
    thermocouple bead rest on the bottom of the pan,
    bend the leads or something to make sure that it
    is suspended.
  • Put the alcohol thermometer in the pan as well.

46
Step 1 Obtain TC Calibration, continued
  • Starting at room temperature, record the
    thermometer reading and the voltage on the
    thermocouple (use either the DMM or the
    oscilloscope).
  • Now turn on the heat, at the rate that you desire
    (maybe not full blast at first). As the
    temperature rises, you and your partner(s) should
    take independent measurements of the water
    temperature with the thermometer and the
    corresponding thermocouple voltage. Ramp it up
    all the way to boiling. Record your data in your
    laboratory notebook.
  • At this point you have data to construct
    independent calibration curves of the
    thermocouple with an ice bath reference.

47
What to do with Step 1 data?
  • In the report for this week each of you should
    plot your own data, and make the appropriate fit
    (linear, exponential, log, power, you-name-it) of
    your data to a calibration curve. Report the
    corresponding equation and the error associated
    between your data and your calibration curve
    (including how you determined the error).
  • Then, combine forces.
  • Compare the calibration curves that you and your
    partner(s) have made. Are the fits different?
    How different? Can you determine the error
    between the two (i.e. at a voltage V, what is the
    temperature difference between the two curves)?
  • Combine your temperature data and derive a new
    best-fit curve. Does the error between the fit
    and the measurement improve when you combine
    data? Is the combined data better than both of
    your sets of original data (or is one of you a
    better data-taker than the other)? Discuss.

48
Step 2 Take transient temperature data,
determine heat transfer coefficients
  • Find the Thermocouple with Conversion CJ.vi on
    the lab computer.
  • This vi is set to take data from the thermocouple
    and save it on the computer, with the help of the
    proto board.
  • On the green proto board, put the W1 jumper into
    the pins marked TEMP.
  • Channel 0 will output a voltage equivalent to
    room temperature, which will be compared (with
    the vi) to the thermocouple voltage on Channel 6.
  • National Instruments has kindly provided an
    eighth-order polynomial fit to determine
    temperature from Channel 6 voltage, using the
    compensation this is programmed into the vi.
  • Test the VI, compare it with your calibration in
    ice water and boiling water

49
Adjust offset by reading temperature of sphere at
steady state in boiling water

Thermocouple with conversion CJ.vi
50
EXPERIMENTAL CONDITIONS
  • Vary the magnitude of the heat transfer
    coefficient h by using a stirrer in one set of
    experiments and no stirrer in the other set of
    experiments

51

Heat the spheres to 1000C
Repeat for brass sphere.
52

Measure temperature decay to 00C
  • Perform experiment in still water
  • Repeat for forced convection
  • Make sure that the sphere is not
  • touching base and walls of the tank

53
ANALYSIS
  • In your analysis to solve for the heat transfer
    coefficient, assume that the lumped analysis
    applies
  • Bi lt 0.1
  • Youre also assuming that h is constant over the
    temperature range from 0 lt T lt 100 ºC
  • As Re goes up h goes up
  • 1st and 2nd assumptions may not hold as well as
    you would like!

54
Analysis and Details
  • Repeat each experiment (brass/aluminum,
    free/forced) 2 or 3 times so that you can do an
    error analysis
  • Plot ln q (left hand side of this equation) to
    determine h using known properties
  • Please thoroughly dry the spheres when youre
    done
  • Dont forget to record the diameter

55

Things to talk about in Lab 6

For each of the four cases plot T as a function
of t over a suitable range. Repeat in
dimensionless coordinates (?,?). Make suitable
comments per class discussion Make table of h
and Bi for four cases, commenting on which
cases you would expect to be more accurate. Do
an error analysis!
56
Acknowledgements / Sources
  • Basic physics texts
  • http//encyclopedia.thefreedictionary.com/thermoco
    uple
  • http//en.wikipedia.org
  • Christopher R. Shaddix, Practical Aspects of
    Correcting Thermocouple Measurements for
    Radiation Loss, Western States Section / The
    Combustion Institute paper 98F-24, Seattle, WA,
    October 1998.
  • Prof. G.S. Jackson, University of Maryland,
    College Park

57
NEXT WEEK
Measurement of Pressure and Acceleration
  • OBJECTIVES
  • Calibrate pressure transducer
  • Calibrate accelerometer
  • Compare spring constant values calculated
  • from F kx and ? (k/m)1/2
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