Thermal conductivity

Physical size
Surname Thermal conductivity
Formula symbol ${\ displaystyle \ lambda, \, \ kappa, \, k}$
Size and
unit system
unit dimension
SI W / ( m · K ) M · L · T −3 · Θ −1

The thermal conductivity , and the coefficient of thermal conductivity is a material property that the heat flow through a material because of the heat conduction determined. The thermal conductivity shows how well a material conducts heat or how well it is suitable for thermal insulation . The lower the value of the thermal conductivity, the better the thermal insulation. In the SI system, the thermal conductivity has the unit watt per meter and Kelvin.

The thermal conductivity of most materials increases slightly with increasing temperature. At a phase transition or physical state transition (. Eg fixed <> liquid <> gas), the conductivity changes, however, usually strongly and abruptly.

From the thermal conductivity can by dividing the volume- heat capacity , the thermal diffusivity are calculated. The reciprocal of thermal conductivity is the (specific) thermal resistance .

definition

Thermal conduction is understood to mean the transport of heat in a medium without material transport (such as with convection ).

To define the “thermal conductivity” parameter, imagine two heat reservoirs that have the temperatures and (it applies ), and are separated from each other by a flat wall of a certain material. The properties of the material are the same at every location inside and have no preferred direction; the material is therefore homogeneous and isotropic . The wall has a thickness and is infinitely extensive. (In practice it is sufficient that the wall is much wider and higher than it is thick.) There is a constant flow of heat between the two reservoirs. The heat flow then flows through any part of the wall with the surface . ${\ displaystyle T_ {1}}$${\ displaystyle T_ {2}}$${\ displaystyle T_ {1}> T_ {2}}$${\ displaystyle l}$${\ displaystyle A}$${\ displaystyle {\ dot {Q}}}$

Under the conditions mentioned, the temperature gradient is constant over the entire thickness of the wall. The heat flow is then proportional to

• the area ${\ displaystyle A}$
• the temperature difference ${\ displaystyle \ Delta T = T_ {1} -T_ {2}}$
• and inversely proportional to the wall thickness${\ displaystyle l}$

and otherwise only depends on the thermal conductivity of the medium (wall material). This gives the definition equation for the thermal conductivity:

${\ displaystyle \ lambda = {\ frac {{\ dot {Q}} \ cdot l} {A \ cdot \ Delta T}}}$

This connection is also called Fourier's law . The unit of thermal conductivity immediately follows from the definition:

${\ displaystyle [\ lambda] = {\ frac {[{\ dot {Q}}] \ cdot [l]} {[A] \ cdot [\ Delta T]}} = {\ frac {\ mathrm {1W \ cdot 1m}} {\ mathrm {1m ^ {2} \ cdot K}}} = \ mathrm {1 {\ frac {W} {m \ cdot K}}}}$

In the general case it is not enough to consider only one dimension . In particular, the temperature profile is linear only in exceptional cases . The more general formulation is therefore:

${\ displaystyle {\ dot {\ mathbf {q}}} = - \ lambda \ cdot \ mathrm {grad} T}$

In this equation is the (vectorial) heat flux density . The negative sign is due to the fact that heat always flows along the temperature gradient, i.e. against the temperature gradient. ${\ displaystyle {\ dot {\ mathbf {q}}}}$

Tensor representation

In the general anisotropic case, the thermal conductivity is a tensor of the second order . B. described by a 3 × 3 matrix . So lead z. B. Wood and slate in the grain direction and a quartz crystal in the direction of the c-axis heat better than across it. If the temperature gradient runs at an angle to the material axes, the direction of the heat flow deviates from that of the gradient.

example
Dry pine wood with a density of 0.45 g / cm³ has a thermal conductivity of 0.26 W / (m · K) parallel to the fiber and 0.11 W / (m · K) perpendicular to it. If you choose the fiber direction as the z-axis and the x- and y-axes perpendicular to it, you can write the tensor of the thermal conductivity as a diagonal 3 × 3 matrix:
${\ displaystyle \ lambda = {\ begin {pmatrix} 0 {,} 11 & 0 & 0 \\ 0 & 0 {,} 11 & 0 \\ 0 & 0 & 0 {,} 26 \ end {pmatrix}} \, {\ frac {\ mathrm {W}} { \ mathrm {m} \ cdot \ mathrm {K}}}}$

Mechanisms of heat conduction

In addition to thermal conduction, thermal energy can also be transmitted through thermal radiation and convection . In the case of substances with high thermal conductivity, these mechanisms can be neglected in some cases.

In a vacuum there is no heat conduction and no convection, only heat radiation. High vacuum is therefore the best insulator against heat flows.

In metals , the conduction electrons can transport not only charge (= electrical current ) but also thermal energy, see Wiedemann-Franz's law . Therefore, metals with high electrical conductivity usually also have good thermal conductivity. One example is silver, which of all pure metals is both the best electrical conductor and the best thermal conductor.

Measurement

Measuring devices for determining the thermal conductivity of thermal insulation materials , so-called heat flow meters and other heat flow calorimeters , measure the electrical power of a heating element corresponding to the heat flow , the thickness of a sample and the temperature difference on a defined measuring surface ( Peltier element ). Furthermore, so-called heat flow sensors enable the non-invasive measurement of heat flows due to the Seebeck effect . Measured quantities are the heat flow and the absolute temperature. On the basis of these measurement principles, the thermal radiation of materials that are transparent to thermal radiation and the thermal convection due to gases trapped in the insulation material are also determined. The result is therefore the sum of the heat flows of the three types of heat transfer and not just a heat flow due to heat conduction .

The thermal conductivity of a substance can be determined using thermal conduction or Fourier's law .

Thermal conductivity in construction

In the construction industry, since the introduction of the European Construction Products Regulation in 2013, three different sizes have been used in parallel to identify thermal insulation materials and for calculation.

• ${\ displaystyle \ lambda _ {D}}$, Nominal value of thermal conductivity according to CE marking
• ${\ displaystyle \ lambda _ {B}}$, Rated value of thermal conductivity according to DIN 4108-4
• ${\ displaystyle \ lambda _ {\ text {limit}}}$, Limit value of the thermal conductivity according to the general building authority approval (ABZ) of a building product

They differ from one another in the way they are identified and used. Only the rated value of the thermal conductivity according to DIN 4108-4 can be used directly to verify the physical properties of building components; the other thermal conductivity values ​​require a safety margin.

Norms

• DIN 4108-4 Thermal insulation and energy savings in buildings - Part 4: Thermal and moisture-proof rated values
• ÖNORM B 8110-7 Thermal insulation in building construction - Part 7: Tabulated thermal insulation design values

Sample values

The thermal conductivity values ​​of various substances can vary by many orders of magnitude. For example, high values ​​are required for heat sinks , which are supposed to dissipate heat well , whereas thermal insulation materials should have low values.

The thermal conductivity is a material constant at a defined ambient conditions ( temperature and humidity ) and therefore is partially provided with an index: , or . Unless otherwise stated, the following numerical values ​​apply to 0 ° C. A higher thermal conductivity means a greater heat transfer per period. ${\ displaystyle \ lambda}$${\ displaystyle \ lambda _ {20/50}}$${\ displaystyle \ lambda _ {23/80}}$${\ displaystyle \ lambda _ {\ mathrm {dry}}}$

Building materials
material Thermal conductivity λ in W / (m K)
EPS plaster 0.07
Perforated brick made of pore clay 0.07 ... 0.45
Aerated concrete ( aerated concrete) 0.08 ... 0.25
Wood perpendicular to the grain 0.09 ... 0.19
Thermal plaster 0.11
bitumen 0.16
rubber 0.16
Clay , clay plaster 0.47 ... 0.93
Brickwork ( solid brick ) 0.50 ... 1.40
Sand-lime brick (KS) 0.56 ... 1.30
Sand , dry 0.58
Lime plaster 0.70
Glass 0.76
Lime cement plaster 1.0
Epoxy resin mortar with 85% quartz sand 1.2
Cement screed 1.4
concrete 2.1
limestone 2.2
Sandstone 2.3; 2.1-3.9
granite 2.8
marble 2.8
High-alloy steel (austenitic; e.g. X5CrNi18-10) 15th
Low alloyed ferritic steel (e.g. 42CrMo4) 42
Unalloyed steel 48 ... 58
Insulation materials
material Thermal conductivity λ in W / (m K)
Vacuum insulation board 0.004 ... 0.006
Airgel 0.017 ... 0.021
Resole resin 0.021
Polyurethane (PUR) 0.021 ... 0.035
Expanded polystyrene with graphite ( gray EPS ) 0.030 ... 0.035
Extruded Polystyrene (XPS) 0.032 ... 0.040
Mineral wool 0.032 ... 0.050
Polyethylene foams 0.034 ... 0.040
Wool 0.035
Sheep wool 0.035 ... 0.045
cork 0.035 ... 0.046
Expanded polystyrene (EPS) 0.035 ... 0.050
cellulose 0.037 ... 0.045
Wood fiber insulation board 0.037 ... 0.060
jute 0.038
Bales of straw 0.038 ... 0.067
Hemp insulation mats 0.042
flax 0.040
Foam glass 0.040
hemp 0.040 ... 0.045
Seaweed 0.040 ... 0.049
Wood fiber 0.040 ... 0.060
Perlite (rock) 0.040 ... 0.070
Reed plate 0.045 ... 0.055
straw 0.052 ... 0.072
Glass foam granulate 0.080
Wood wool lightweight panel 0.090
Expanded clay 0.100 ... 0.160
Metals
material Thermal conductivity λ in W / (m K)
silver 429
Copper (pure) 401
Copper (commodity) 240 ... 380
Copper alloys ( Sn , Zn , Ni , Pb ) 30 ... 110
Gold (pure) 314
Aluminum (99.5%) 236
beryllium 201
Calcium 201
tungsten 173
magnesium 156
silicon 163
Aluminum alloys 75 ... 235
potassium 135
molybdenum 138
Brass 120
zinc 110
magnesium 170
tungsten 167
sodium 133
nickel 85
iron 80.2
Chrome steel 1.400 30th
platinum 71
tin 67
Tantalum 54
titanium 22nd
Bismuth 8.4
mercury 8.3
Gases ( standard condition )
material Thermal conductivity λ in W / (m K)
hydrogen 0.186
Ammonia at 25 ° C 0.024
helium 0.1567
argon 0.0179
krypton 0.00949
xenon 0.0055
air 0.0262
oxygen 0.0263
nitrogen 0.0260
Steam 0.0248
carbon dioxide 0.0168
Methane (20 ° C, 1 bar) 0.0341
Sulfur hexafluoride 0.012
Plastics
material Thermal conductivity λ in W / (m K)
Polyethylene terephthalate (PET) 0.24
Polyurethane compact (PUR) 0.245
Polyimide (PI) 0.37 ... 0.52
Polyetherimide (PEI) 0.24
Polytetrafluoroethylene (PTFE) 0.25
Polyvinyl chloride (PVC) 0.17
Polyamides (nylon, perlon) 0.25 ... 0.35
Polypropylene (PP) 0.23
Polycarbonate 0.20
Epoxy resin (EP) 0.20
Polymethyl methacrylate (PMMA, plexiglass) 0.19
Polyethylene (PE) 0.33 ... 0.57
Polystyrene (PS) 0.17
Polysiloxane (silicone) 0.2 ... 0.3
Polyetheretherketone (PEEK) 0.25
Liquids and other substances
material Thermal conductivity λ in W / (m K)
oil 0.13 ... 0.15
petrol 0.140
Snow (0.25 g / cm³) 0.16
alcohol 0.173
sulfur 0.269
Ammonia under pressure 0.521
sulfuric acid 0.544
Water (0 ° C) 0.5562
chalk 0.92
Silicon dioxide (quartz) 1.2 ... 12
humus 1.26
Ice (−10 ° C) 2.33
Thermal paste 4… 12.5
Alumina 28
Carbon ( graphite ) 119 ... 165
Silicon 148
Aluminum nitride 180 ... 220
Silicon carbide 350
diamond 2300
Graph 5300
Corundum (Al 2 O 3 ~ 99%) 41.9

literature

• Landolt-Börnstein - database for almost all physical properties, including thermal conductivity values

Commons : Thermal Conductivity  - Collection of images, videos and audio files

Individual evidence

1. a b David R. Lide (Ed.): CRC Handbook of Chemistry and Physics . 87th edition. (Internet version: 2006–2007), CRC Press / Taylor and Francis, Boca Raton, FL, Properties of Solids, pp. 12-204 ( limited preview in Google Book Search).
2. ^ Walter J. Moore: Physical chemistry. Walter de Gruyter, 1986, ISBN 978-3-11-010979-5 , p. 47 ( limited preview in the Google book search).
3. Confusion about thermal conductivity . In: Deutsches Architektenblatt , October 1, 2013.
4. Handbook of concrete protection through coatings, Expert Verlag 1992, page 413
5. ^ Sven Fuchs, Andrea Förster: Rock thermal conductivity of Mesozoic geothermal aquifers in the Northeast German Basin . In: Chemistry of the Earth - Geochemistry . tape 70 , Supplement 3, August 2010, p. 13–22 , doi : 10.1016 / j.chemer.2010.05.010 ( edoc.gfz-potsdam.de [PDF]).
6. Leaflet 821 (PDF; 877 kB); Stainless Steel - Properties; Publisher: Informationsstelle Edelstahl Rostfrei Table 9; Status: 2014.
7. Data sheets Trocellen PE insulation materials, accessed on July 30, 2010 ( Memento from August 21, 2010 in the Internet Archive )
8. Guidelines for ecological insulation materials (PDF) from BENZ GmbH & Co. KG Baustoffe, accessed on March 1, 2017.
9. Product information Thermosafe-homogen® from GUTEX Holzfaserplattenwerk H. Henselmann GmbH & CO. KG, accessed on May 29, 2016.
10. Product information THERMO HEMP PREMIUM from THERMO NATUR GmbH & Co. KG, accessed on February 22, 2020.
11. ^ Hans-Jürgen Bargel, Hermann Hilbrans: Material science . Springer, 2008, ISBN 978-3-540-79296-3 , pp. 275 ( limited preview in Google Book Search).
12. Material properties of cast alloys (PDF) and pipe materials (PDF) from Wieland-Werke AG, accessed in August 2014.
13. Thermal conductivity . ( Memento from March 11, 2016 in the Internet Archive )
14. David R. Lide (Ed.): CRC Handbook of Chemistry and Physics . 90th edition. (Internet version: 2010), CRC Press / Taylor and Francis, Boca Raton, FL, Fluid Properties, pp. 6-184. Values ​​apply at 300 K.
15. schweizer-fn.de
16. Horst Czichos (ed.): The basics of engineering, D materials, thermal conductivity of materials . 31st edition. Springer, 2000, ISBN 3-540-66882-9 , pp. D 54 .
17. a b
18. entry in makeitfrom.com
19. a b c d schweizer-fn.de
20. ↑ Material
21. David R. Lide (Ed.): CRC Handbook of Chemistry and Physics . 90th edition. (Internet version: 2010), CRC Press / Taylor and Francis, Boca Raton, FL, Fluid Properties, pp. 6-220.
22. Lecture documents hydroscript. - PTB Braunschweig ( memento from September 24, 2015 in the Internet Archive ).
23. geizhals.eu
24. oskar-moser.de: Technical data for synthetic sapphire