MAE 170 Lecture 5: Temperature Measurement

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MAE 170 Lecture 5 Temperature Measurement

• April 30, 2007

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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

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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

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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
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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.

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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!

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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

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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
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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

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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.

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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

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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)
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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.

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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.

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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)

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Errors common in high temperature measurements
(like 1000K and higher)
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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

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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

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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

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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)

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

HOW DO SPHERES COOL?
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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

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Consider a spherical cow
T(t)

• Great engineers and physicists are able to
  appropriately simplify problems to extract the
  physics!

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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
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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

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Energy moves around in different ways

• Random molecular motion conduction
• Organized motion convection
• Electromagnetic waves radiation
• ? Today we focus on conduction and convection

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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

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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
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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

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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

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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

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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)

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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
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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

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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

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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!
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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
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Lab 5 Measurement of Temperature
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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?

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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

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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.
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This weeks experiment
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BEFORE YOU START

• check if thermocouple is working

Thermocouple with conversion CJ.vi
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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.

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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.

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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.

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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

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

Thermocouple with conversion CJ.vi
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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

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Heat the spheres to 1000C
Repeat for brass sphere.
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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

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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!

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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

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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!
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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

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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