Thermal diffusivity and conductivity
-an introduction to theory -and practice
Utrecht, 02 October 2014 Dr. Hans-W. Marx Linseis Messgeräte GmbH Vielitzer Str. 43 D-95100 Selb / GERMANY www.linseis.com Phone: +49 9287 880-12 Fax: +49 9287 70488 France: +33 1 73 02 82 72 E-Mail: h.marx@linseis.de
Linseis Messgeräte GmbH
Linseis Messgeräte GmbH is a german medium sized company specialized in the production of instruments for thermal analysis since the 1950s.
Product range:
- Thermogravimetry TGA (under pressure; corrosive atmosphere) - Differential thermal analysis DTA
- Dynamic scanning calorimetry DSC
- Simultanous thermal analysis STA (TGA-DTA-DSC) - Dilatometry (piston or optical; with our without contact) - Thermomechanical analysis TMA
- Couplings for evolved gas analysis (EGA: MS – FTIR)
- Analysis for thermoelectrics (electrical resistivity and Seebeck coefficient) - Thermal diffusivity and thermal conductivity
Applications I
- Low thermal conductivity: insulations
- Building industry, instruments: thermal isolators (refrigerators, hot water tanks, heating pipes, brand protection…)
- Thermoelectrics: increasing figure of merit by decreasing thermal conductivity
Applications II
- High thermal conductivity: - Brake discs
- High performance alloys for tools: fast cooling of friction heat for longer lifetime and better performance (drills, tools for hot presses etc.)
- Electronics: dissipation of local heat avoiding overheating
- Knowledge of thermal conductivity:
- Simulation of casting and solidification processes
Thermal diffusivity – thermal conductivity
- Thermal diffusivity area/time (m²/s) - :
propagation of a temperature difference in a material
„how fast a temperature difference in a material is levelled out“ (German: Temperaturleitfähigkeit – “temperature conductivity”)
- Thermal conductivity power/(length * Kelvin) (W/m K) – : propagation of a heat difference in a material
„how good heat energy is conducted through a material“ (German: Wärmeleitfähigkeit – „heat conductivity“)
Heat (W) passing by a sample of 1 m thickness and a surface of 1 m² for a temperature gradient of 1 K during 1 sec
Thermal diffusivity and thermal conductivity are related through the following equation:
Transmitted heat = heat capacity * mass * temperature difference
All those properties (Cp, density) are temperature-dependent!
Thermal diffusivity – thermal conductivity
= Cp * density *
Material Thermal diffusivity in 10-6m²/s Thermal conductivity in W/m*K Water 0,15 0,56 Air 20 0,026 Wood 0,1-0,2 0,1-0,2 Glass 0,35-0,5 0,75-0,9 Iron 23 80 Steel 3,5-15 30-60 Copper 117 400 Diamond 1100 2300 Graphit 100-130 120-170 "Plexiglass„ PMMA 0,1 0,19 EPS 0,35-1,55 0,035-0,05
Methods
Stationary methods:
- A stable temperature gradient is installed through the material to be tested - Achieved when the heat flux in the sample equals the heat flux out of
the sample
- Advantage: simple theory and simple experimental set-up - Disadvantage: long measuring times
Transient (time dependant) methods:
- Sample is subjected by a thermal disturbance; this disturbance is observed as a function of time
- Advantage: rapid and simple measurement, small samples, measurement at different temperatures
Stationary methods
Heat Flow Meter – Guarded Hot Plate
Hot Plate
Heat flux sensor
Sample
Cold Plate
Heat flux sensor
Cold Plate Cold Plate Sample Hot Plate Cold Plate Sample
Guard Ring Guard Ring
Guard Plate
Sample
Hot Plate
Cold Plate
Guard Ring Guard Ring
Guard Insulation
Typical sample size: 30 x 30 x 10 cm Typical range: ca 0,001 to 1 W/mK
Transient methods – hot wire method
Typical range: 0.005 to 10 - 500 W/mK
Typical sample size: some cm x some cm x cm
thermocouple Hot wire Typical signal T ln(t) T1 T2 t1 t2
Thermal conductivity is inversely proportional to temperature increase. Thermal diffusivity is calculated from the time needed for maximum temperature rise
THB – Transient Hot Bridge: improved hot wire method (compensation of end effects)
Investigations of the PTB (National Metrology Institute of Germany) on the thermal conductivity of soils and sediments
Laser Flash Method - ASTM E 1461
Standard Test Method for Thermal
Diffusivity by the Flash Method
A small, thin disc specimen is subjected to a high intensity short duration
radiant energy pulse. The energy of the pulse is absorbed on the front surface of the specimen and the resulting temperature rise at the rear face is recorded. The thermal diffusivity value is calculated from the specimen thickness and the time required for the rear face temperature rise to reach half of its maximum value.
The Laser Flash Method
laser IR-detector sample 1 ms IR radiation lens d Zeit T TNorm(t) timeCalculation
- Determination of the baseline and the maximum
temperature rise => ∆T
max- Determination of the time required to reach half
maximum height ∆T
½; this is the “half time”, t
½- Calculation of thermal diffusivity from sample
thickness L and half time t
½:
= 0.13879 L
2/t
½Calculation
- Determine the baseline and maximum rise to give
the temperature difference, ∆T
max- Determine the time required from the initiation of the
pulse for the rear face temperature to reach ∆T
½.
This is the half time, t
½.
- Calculate the thermal diffusivity, a, from the
specimen thickness, L squared and the half time t
½,
as follows:
Α = 0.13879 L
2/t
½Detektor Iris Ofen Probenhalter Xenonlampe Detector Iris Furnace Sample holder Laser
LFA and XFA instrument
Detector furnace Pulse source Laser or Xenon Typical range: 0.1 up to 1000 W/mKThe Laser Flash Method – limits
Minimal sample thickness depends:
1. on acquisition rate of the instrument/detector: (limited number of measurement points)
2. On the duration of the laser pulse (overlay of temperature rise
Sample holder for thin films –”in-plane-adapter”
Sample holder for thin films of < 0,1 mm (depending on thermal diffusivity of the sample)
Thermal conductivity measurement –
A suitable method for nano structured materials:
Bulk ZnO: k2 ~ 100 W/m K
Z.X. Huang et. al. Physica B 406 (2011)
TDTR – example ZnO
thickness d2 (nm) k2 (W/(m*K)) 276 6.5 213 5.2 140 3.8 80 1.4Time domain thermoreflectance (TDTR) –
measurement principle
• Optical properties depend on temperature - e.g. reflectance of electromagnetic radiation:
Reflectance can be used as an indicator for temperature variation and thermal conductivity
R 1 ∂ R R R ∂ T
______
TDTR – experimental set-up
Rear heating / front detection Front heating / front detection
T. Baba, Japanese Journal of Applied Physics 48 (2009) 05EB04
„High speed laser flash method“ „Conventional Nanosecond thermoreflectance method“
TDTR – measurement principle
Choice of measurement method
HFM – heat flow meter: plates 30 x 30 cm; thickness up to 10 cm THB – transient hot bridge: solids, liquids, powders, pastes;
4 x 8 x < 1 cm
XFA and LFA - Xenon and Laser Flash Analyzer; solids and liquids; diameter 25,4 mm; thickness: some mm
0.001 0.010 0.100 1.00 10.0 100 1000
Thermal Conductivity (W/m-K)
Flash (-125 …2400°C) Hot Wire (RT…1500°C)
Guarded Heat Flow Meter (-150…300°C) Guarded Hot Plate (-180…650°C)
Heat Flow Meter (-20…100°C)
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