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1
THERMAL PROPERTIES OF SOLIDSMeasurement Techniques
March 22nd, 2001
Presented by:Ileana ConstantinescuJamshid Sulaymonov
MatE 210, Experimental Methods in Mat. Eng., Spring 2001
In partial fullfillment of requirements for MatE 210Professor G. Selvaduray
2
THERMAL PROPERTIES - SOLIDS
• Introduction • Classification• Measurement Techniques • Thermal Conductivity• Axial Heat Flow Method - AHF• Calibration/Errors/Limitations of AHF• Conclusion
3
kkTo-Conductivity
SSTTThermal
Shock
ααTo-Diffusivity
CCppHeat
Capacity
ββvvThermal
Expansion
TECHNIQUES
INTRODUCTION/ BACKGROUNDINTRODUCTION/ BACKGROUND
Steady-State Non Steady-State
Hot WireHW
Radial HeatFlowRHF
GuardedHot Plate
GHP
Axial HeatFlowAHF
Laser Pulse(Flash)
ElectronBombardment
Heat Input
MonotonicHeating
Thermal Wave
4
INTRODUCTION
• THERMAL PROPERTIES OF SOLIDS– Interaction and propagation of thermal energy quanta (phonons)
through solid materials
• HEAT FLOW THROUGH SOLIDS– Initiated by ∆T across two sides of a solid
• HEAT CONDUCTION LAWS
First Order Fourier-Biot Equation Second Order Fourier-Biot Equation
dxAdTkq*
−=
5
Significance of Thermal Properties
• Design Applications– Material selection criteria– Thermo-mechanical
analysis for structural component design for extreme temperatures
– Prediction of alloy properties based on unalloyed metal properties (law of mixtures)
• Failure Analysis– Evaluation of thermally
induced stresses and degree of thermal cycling that led to material fracture (thermal shock resistance)
Fig. 1 – Orbiter Surface Isotherms (Solomon Musikant,"What Every Engineer Should Know about Ceramics", 1991, p. 148)
6
Heat Capacity
Fig.2 - Temperature Dependence of the MolarHeat Capacity (after Rolf E. Hummel, "ElectronicProperties of Materials”, 1985, p.269, fig. 19.1)
• Heat capacity,
• Specific heat,
• Molar heat capacity,
• Temperature dependence
• Dulong-petit value
• Cp ~ Cv
CvdQdT v
cv
Cv
m
7
• Debye temperature
• Total heat capacity
Ctot Cel Cph
Concept of Heat Capacity
Fig. 3 – Temperature Dependence of the Molar Heat Capacity; Experimental Values vs. Model predictions (Rolf E. Hummel, "Electronic Properties of Materials", 1985, p. 264)
8
1-10All100 – 1000 SCLim. In high temps.
Fast and EconomicalDifferential Scanning
2-10Electrical Conductor (Wire, rod, tube)
1000 - 7000EC Complex Instrumentation
SLSHigh Temps. MPM
Pulse
2-5All80 - 3000Solid SpecimenMulti-Property Measurement (MPM)
Modulation
2-5Electrical Conductor (sphere)
1000 - 2500Specimen:Electric Conductor (EC)ED
Solid & Liquid Specimen
Levitation
1-3All300 - 2000SCTime consumingED
Solid & Liquid Specimen
Drop
1-3All4 - 1300Specimen in Container (SC)Limitation in high temps. Based on enthalpy data (ED)
Very VersatileHigh SensitivitySolid and Liquid Specimen (SLS)
Adiabatic
Uncertainty (%)
Principal Specimen Materials
Temperature Range (K)
DisadvantagesAdvantagesMeasurement Technique
Table 1 - Specific Heat Measurement Techniques (after K.D. Maglic, “Compendium of ThermophysicalProperty Measurement Methods”, 1984, Volume 1, p.459)
Specific Heat Measurement Techniques
9
Thermal Expansion• Volumetric Expansion,
• Linear Expansion,
• Temperature Dependence
βm1
K
αm1
K
Fig. 4 - Thermal Expansion of Al and Pt from 0 Kto their melting temperature, from K.D. Maglic,“Compendium of Thermophysical PropertyMeasurement Methods”, 1992, Vol.2, p.551 fig2.)
βm
V2 V1
V1
T2
T1
.
αm
L2 L1
L1
T2
T1
.
10
Thermal Expansion of Materials
Fig. 5 - Coefficients of thermal expansion at roomtemperature for various materials (from N.E. Dowling,Mechanical Behavior of Materials", 1999, p. 187)
11
Thermal Expansion Measurement Techniques
Accuracy(%)
Min. Coefficient of Thermal ExpansionTemperature
Range (C)CharacteristicsMeasurement
Techniques
3-12above 5-120 - 600Inconsistent precision
Thermomechanical Analysis
1-3below 5-150 - 700High accuracy Optical
Interference Techniques
5-7above 5-150 -2000Medium precision
Mechanical Dilatometer
αmµmmC.
Table 2 - Comparison of thermal expansion measurement techniques (ASTM Standards E831, E228, E-289)
12
• Thermal Conductivity, (Fourier’s Law)
• Principal Carriers of Heat
κJ
m s. K.
Fig. 6 - Heat flow in a solid state material (S. O.Kasap, "Principles of Electrical Engineering Materials And Devices”, 1997, p.137)
Fig. 7 - Heat flow in a metal rod heated at one end (after S.O. Kasap, “Principles of ElectricalEngineering Materials and Devices”, 1997, p.137)
Thermal Conductivity
dQdT
A κ.δTδx
.
κtot κel κph
Jq κdTdx
. J
m2 K.
• Fourier’s Law
13
• Thermal conduction in metals and alloys
Fig. 8 - Thermal Conductivity vs. temperature for two puremetals (Cu and Al) and two alloys (brass and Al-14%Mg)(S.O. Kasap, “Principles of Electrical EngineeringMaterials and Devices”, 1997, p.139)
Fig. 9 - Thermal Conductivity vs. electrical conductivity forvarious metals at 20C (after (after S.O. Kasap, “Principles ofElectrical Engineering Materials and Devices”, 1997, p.139)
Thermal Conductivity Mechanism
14
Thermal Conductivity Measurement Techniques
150.05 – 15Refractory Materials
600 – 1600 High temp. gradients Slow
SimplicityPanel Test
5 - 150.02 – 2Refractory Materials
RT – 1800Low conductivity materials
Small Temperature Drop in specimen
Hot Wire Method
2 - 5<1.0Thermal Insulators
80 – 1500ComplexCostly
Slow (3 – 12 h)
Wide Range of MaterialsHigh Accuracy
Guarded Hot Plate
2 - 510 – 200Wires, rods, tubes of elec. Conductors
400 – 3000Complex Equipment
High Temps.FastElect.Properties
Direct Electrical Heating
3 - 150.01- 200Solids and powders in cylindrical form
RT – 2600Large specimensAccuracy High Temps.
Radial Heat Flow
0.5 - 2.010 – 500Metals & Alloys, Cylindrical Shape
90 – 1300heat losses above ~ 500K
High AccuracyElectrical Resistivity
Axial Heat Flow
Uncertainty (%)
Conductivity Range,
Principal Specimen Materials
Temperature Range (K)
DisadvantagesAdvantagesMeasurement Technique
Table 3 - Specific Heat Measurement Techniques (K.D. Maglic, “Compendium of Thermophysical Property Measurement Methods”, 1984, Volume 1, p.6)
Wm K.
15
Thermal Diffusivity
• Definition– Rate at which a temperature
disturbance on one side of the body travels to another part of the body
• Classical Measurement Techniques:– Pulse Method (Laser)– Temperature Wave– Electron bombardment– Monotonic heating
2nd Order Fourrier Law:
k = α * cp * ρ
k – thermal conductivityα – thermal diffusivityCp – heat capacityρ - density
α
16
THERMAL DIFFUSIVITY MEASUREMENT TECHNIQUES
2 – 1210-8 – 10-5Ceramics, plastics, composites
4.2 - 3000Inappropriate for good thermal conductors Low precision
Simple ApparatusSimple MeasurementWide T Range
Monotonic Heating Regime Method
2 – 1010-7 – 10-5Metals, nonmetals, liquid metals
330 – 3200High Vacuum;Complex Experimental apparatus
High T coverageSmall specimenAC techniques applicable
Electron Bombardment Heat Input Method
1 – 910-7 – 10-4
Solids, liquid metals, gasesSpecimens: rods, cylinders
60 – 1300Complex Math AnalysisComplex Error Analysis
Wide Materials RangeMulti-property Measurement
Temperature Wave Method
1.5 – 5 10-7 – 10-3
solids, liquid metalsSpecimen disks 6- 16 mm in diameter
100 – 3300Not convenient for translucent materialsComplex Error Analysis
Wide T rangesSimple, rapidmeasurement
Pulse Method
Uncertainty%
Diffusivity Range
Principal Specimen Material
Temperature Range (K)
DisadvantagesAdvantagesMeasurement Technique
Table 4 – Thermal Diffusivity Measurement Techniques (K.D. Maglic, “Compendium of Thermophysical Property MeasurementMethods”, 1984, Volume 1, p.302)
17
Thermal Shock
The tendency of ceramicmaterials to fracture as a resultof rapid temperature changeduring rapid cooling:
σ * dxST = -------------
Q
σ = stress developed (psi)Q = unit flux of heat (J)dx = solid thickness (in)
The thermal shock coefficient, ST, can be calculated from CTE and thermal conductivity measurements:
β * EST = -------------
k
β − coefficient of thermal expansion (CTE)E - Young's Modulusk – thermal conductivity
18
Heating Method Advantages Disadvantages Materials Studied
Induction (5-40 kW capacity)
rapid heating; complex sample geometries
coil design experience;electric noise due to high magnetic field; high cost
Al, Cu, Steels, Ni-superalloys
Quartz Lamp (radiation)
inexpensive; uniform T; screening materials
slow cooling rates; enforced cooling needed
Ni, Co alloys, metallic composites
Fluidized Bed good for screening TF resistance
surface oxidation, calculation of σ-ε T transients
Ni-base superalloys
Burner Heating (Flame)
screening of TF; surface corrosion representative of service
oxidation, T transients
Ni-superalloys, steels
Dynamometer (friction heating)
very high T on surface reached; representative of service
oxides are wedged into cracks; friction changes with time
0.5 to 0.7% C steels
THERMAL SHOCK / THERMO-MECHANICAL METHODS
Table 5 – Thermal Shock, Thermo-mechanical Measurement Techniques (ASM Metals Handbook, vol. 19, "Fatigue and Fracture", 1996, p. 529)
19
Guarded Hot PlateSummary of the Test Method
Fig. 10a - Components of the Guarded-Hot-Plate Apparatus Fig. 10b – Measurement Principle for a Guarded Hot Plate
(ASTM Standard C-177, 2000, p.21)
20
Hot Wire MethodSummary of the Test Method
Fig.11a - Components of the Hot Wire Apparatus Fig. 11b - Hot Wire Sample Setup
(ASTM Standard C 177, 2000, p.21)
21
Axial Heat Flow – Comparative Method
• Summary
• Requirements – Meter bars (standards)– Insulation materials– Temperature sensors– Guard cylinder– Sampling
• Calculation
Fig. 12 (Axial Heat Flow Apparatus - http://www.umr.edu/)
22
Summary
± 5% to ± 10%depending on sample and
conductivityAccuracy
± 2% Reproducibility
Customized size Sample Size
-180 to 600°CMean Sample Temp. Range
0.02 to 250 W/(m*K) Thermal Conductivity Range
23
Requirementsλ M T( )
λMtop
λMbm
λ S T( )
λ S 1( ) T( )
λ I T( )
-Conductivity of meter bars as a function of T
- Conductivity of top bar
- Conductivity of bottom bar
- Conductivity of specimen
- Conductivity of specimen
- Conductivity of insulation
rA
rB
• Specimen radius
• Guard cylinder inner radius
•Guard temperature as a function of position
Tg z( )Fig. 13 - Schematic of a Comparative-Guarded-Axial Heat
Flow System. (ASTM Standards 1999, E 1225, p.437)
rA rB
T1
T2
T3
T4T5
T6
24
Reference Materials for Use As Meter Bars
NISTNIST specification2To 1000Electrolytic Iron SRM 734
Manufacturer……90 to 1200Pyroceram Code 9606
ManufacturerDependent on T (K)< 8 up to 900(K)1300Fused Silica
Manufacturer6 90 to 600Pyrex 7740
ManufacturerDependent on T (K)< 290 to 1250Copper
…Dependent on T (K)2 80 to 1200Iron
NISTCalculated from measured values
< 54 to 1200Austenitic SS SRM 735
NISTDependent on T (K)2 to 84 to >2000Tungsten SRM 730
Material Source Percent Uncertainty in λ
(%)
Temperature Range (K)
Material λm
Wm K.
Table 6 - Reference Materials for Use as Meter Bars (ASTM Standards 1999, E 1225, p. 420)
25
0.250.090.039Zirconia 60 – 90 (kg/m3)
0.330.130.044Aluminosilicate 60 – 120 (kg/m3)
…0.170.05Perlite
…0.160.07Vermiculite
0.370.330.19Bubbled Zirconia
0.410.370.21Bubbled Alumina
1300K800K300K
Typical Thermal Conductivity, Material
λmW
m K.
Table 7 - Suitable Thermal Insulation Materials (ASTM Standards 1999, E 1225, p. 420)
Suitable Thermal Insulation Materials
26
Thermocouple Attachments
Fig. 14 - Thermocouple Attachments (ASTM Standards 1999, E 1225, p. 421)
1 2
3 4
27
Calculations
qtop
λ M T2 T1
.
Z2
Z1
qbottom
λ M T6
T5
.
Z6
Z5
λs
qtop qbottom Z4
Z3
.
2 T4
T3
.
Fig. 15 - Schematic of a Comparative-Guarded-AxialHeat Flow System. (ASTM Standards 1999, E 1225, p.437)
28
AXIAL HEAT FLOW TECHNIQUESources of Error
• Equipment• Operator• Material Tested• Experimental Plan
– Absolute or Comparative Technique– Need for NIST traceable standards– Number of samples tested– Number of readings per sample– Precision/ Accuracy of Method
(matching desired value?)– Propagation of Errors
29
AHF - Equipment Design to Minimize Measurement Errors
• Selection of suitable low 'k' insulation material to prevent lateral heat losses
• Determination of optimum attachment method of to-probe to sample surface to reduce the interfacial thermal resistance
• Selection of appropriate thermocouple temperature probes
– 'T' (Copper-Constantan)– 'K' (Chromega-Alomega)– 'J' (Iron-Constantan)– 'E' (Chromega-Constantan)
• Fit the equipment with heated guards to achieve better temperature control along bars in the axial direction
Fig. 16 - Schematic of a Comparative-Guarded-AxialHeat Flow System. Use of Guard Heaters and Insulation to Minimize Lateral Heat Losses (ASTM Standards 1999, E 1225, p.437)
30
AHF - Instrumentation
• Sensor Measurement Precision– combination of T sensor and instrument used for measuring sensor output
should ensure a T measurement precision of +/- 0.04 K and an absolute error less than +/- 0.5%
• Temperature Control– instrumentation should be adequate to maintain required T control and
measure all output voltages with accuracy comparable with the system capability (reported in the OEM manual)
• Calibration and Verification Required:– if ratio of meter bar to sample ‘k’ values is below 0.3 or above 3.0, and
thermal conductance match is not possible to attain – if specimen geometry is complex– if unusual test conditions or modifications of the setup are required
31
SAMPLE INFORMATION
• Chemical composition (impurity, alloying element content) • Crystal structure• Porosity (concentration of voids)• Processing history• Sample preparation (e.g. mechanical polishing)
32
?Which Is The Best Technique ??
Fig. 17 – Thermal Conductivity Measurement Techniques for Titanium (L- Longitudinal Heat Flow Method, C- Comparative Method, E- Direct Electrical Heating Method. Y.S. Touloukian, "THERMAL CONDUCTIVITY- Metallic Elements and Alloys", vol. 1, 1970, p. 410)
33
CONCLUSION
• Knowledge of materials' thermal properties allows their correct evaluation and selection as thermal conductors or insulators for a specific application
• Selection of the optimum measurement technique must be done based on:– Previous knowledge of expected TC value for that material– Desired accuracy– Temperature of interest
• The AHF Comparative method (steady-state) – Advantages:
• Relatively simple equipment• Precise method for TC measurements of good conductors (e.g. metals, alloys)• Flexible geometries of specimen and standard• High accuracy at temperatures between 298 and 400 K
– Disadvantages:• Slow measurement times (requires thermal equilibrium)• ~ 10 % Uncertainty in TC values at temperatures > 400 K• Requires standards (meter bars) with TC values similar to that of specimen
34
List of References
• ASTM Standards 1999, C 1113, E 1225, E 831, E 228, E 289• ASTM Standards 2000, C 177• N. E. Dowling “Mechanical Behavior of Materials”, 1999• R. E. Hummel, “Electronic Properties of Materials”, 1985• S.O. Kasap “Principles of Electrical Engineering Materials
and Devices”, 1997• K.D. Maglic “Compendium of Thermophysical Property Measurement
Methods”, Vol1. and Vol2., 1984• S. Musikant "What Every Engineer Should Know About Ceramics",
1991• Y. S. Touloukian "Thermal Conductivity – Metallic Elements and
Alloys", vol. 1, 1970• L. H. Van Vlack “ Materials Science for Engineers”, 1975