Editing Thermal diffusivity

{{Short description|Rate at which heat spreads throughout a material}}

In [[thermodynamics]], '''thermal diffusivity''' is the [[thermal conductivity]] divided by [[density]] and [[specific heat capacity]] at constant pressure.<ref>{{CRC90|page=2-65}}</ref> It is a measure of the rate of [[heat transfer]] inside a material and has [[SI|SI units]] of m<sup>2</sup>/s. It is an [[intensive property]]. Thermal diffusivity is usually denoted by lowercase [[alpha]] ({{mvar|α}}), but {{mvar|a}}, {{mvar|h}}, {{mvar|κ}} ([[kappa]]),<ref>{{cite book |last1=Hetnarski |first1=Richard B. |last2=Eslami |first2=M. Reza |title=Thermal Stresses – Advanced Theory and Applications |year=2009 |publisher=Springer Netherlands |location=Dordrecht |isbn=978-1-4020-9247-3 |pages=170 |edition=Online-Ausg. |doi=10.1007/978-3-030-10436-8}}</ref> {{mvar|K}},<ref name = AJP>{{cite journal |last1=Unsworth |first1=J. |last2=Duarte |first2=From. J. |author2-link=F. J. Duarte |title=Heat diffusion in a solid sphere and Fourier Theory |journal=Am. J. Phys. |pages=891–893 |doi=10.1119/1.11601 |volume=47 |bibcode=1979AmJPh..47..981U |issue=11 |year=1979}}</ref> {{mvar|D}}, <math>D_T</math> are also used.

The formula is<ref>{{cite book |first1=R. Byron |last1=Bird |first2=Warren E. |last2=Stewart |first3=Edwin N. |last3=Lightfoot |title=Transport Phenomena |publisher=John Wiley and Sons, Inc. |year=1960 |isbn=978-0-471-07392-5 |at=Eq. 8.1-7 |url-access=registration |url=https://archive.org/details/transportphenome00bird}}</ref>
<math display="block">
 \alpha = \frac{k}{\rho c_p},
</math>
where
: {{mvar|k}} is [[thermal conductivity]] (W/(m·K)),
: {{mvar|c{{sub|p}}}} is [[specific heat capacity]] (J/(kg·K)),
: {{mvar|ρ}} is [[density]] (kg/m<sup>3</sup>).
Together, {{mvar|ρc{{sub|p}}}} can be considered the [[volumetric heat capacity]] (J/(m<sup>3</sup>·K)).

Thermal diffusivity is a positive [[coefficient]] in the [[heat equation]]:<ref>{{cite book |last1=Carslaw |first1=H. S. |author1-link=Horatio Scott Carslaw |last2=Jaeger |first2=J. C. |author2-link=John Conrad Jaeger |year=1959 |title=Conduction of Heat in Solids |edition=2nd |publisher=Oxford University Press |isbn=978-0-19-853368-9}}</ref>
<math display="block">
 \frac{\partial T}{\partial t} = \alpha \nabla^2 T.
</math>

One way to view thermal diffusivity is as the ratio of the [[time derivative]] of [[temperature]] to its [[Second derivative#Generalization to higher dimensions|curvature]], quantifying the rate at which temperature concavity is "smoothed out". In a substance with high thermal diffusivity, heat moves rapidly through it because the substance conducts heat quickly relative to its energy storage capacity or "thermal bulk".

Thermal diffusivity and [[thermal effusivity]] are related concepts and quantities used to simulate [[non-equilibrium thermodynamics]]. Diffusivity is the more fundamental concept and describes the [[stochastic process]] of heat spread throughout some ''[[local property|local]] volume'' of a substance. Effusivity describes the corresponding transient process of heat flow through some ''local area'' of interest. Upon reaching a [[steady state]], where the stored energy distribution stabilizes, the thermal conductivity ({{mvar|k}}) may be sufficient to describe heat transfers inside solid or rigid bodies by applying [[Fourier's law]].<ref>{{cite book |last=Dante |first=Roberto C. |title=Handbook of Friction Materials and Their Applications |year=2016 |publisher=Elsevier |doi=10.1016/B978-0-08-100619-1.00009-2 |pages=123–134}}</ref><ref>{{cite book |last=Venkanna |first=B. K. |title=Fundamentals of Heat and Mass Transfer |url=https://books.google.com/books?id=IIIVHRirRgEC&pg=PA38 |access-date=1 December 2011 |year=2010 |publisher=PHI Learning |location=New Delhi |isbn=978-81-203-4031-2 |page=38}}</ref>

Thermal diffusivity is often measured with the [[Laser flash analysis|flash method]].<ref>{{Cite web |url=http://www.netzsch.com/en/home/ |title=NETZSCH-Gerätebau, Germany |access-date=2012-03-12 |archive-url=https://web.archive.org/web/20120311084633/http://www.netzsch.com/en/home/ |archive-date=2012-03-11 |url-status=dead }}</ref><ref name="Parker">
{{cite journal
 |author1=W. J. Parker |author2=R. J. Jenkins |author3=C. P. Butler |author4=G. L. Abbott
 |title=Method of Determining Thermal Diffusivity, Heat Capacity and Thermal Conductivity
 |journal=Journal of Applied Physics
 |volume=32 |issue=9 |page=1679
 |year=1961
 |doi=10.1063/1.1728417
 |bibcode=1961JAP....32.1679P }}</ref> It involves heating a strip or cylindrical sample with a short energy pulse at one end and analyzing the temperature change (reduction in amplitude and phase shift of the pulse) a short distance away.<ref>
{{cite journal
 |author1=J. Blumm |author2=J. Opfermann
 |title= Improvement of the mathematical modeling of flash measurements
 |journal=High Temperatures – High Pressures
 |volume=34 |issue=5 |page=515
 |year=2002
 |doi=10.1068/htjr061 
}}</ref><ref>{{cite conference |last=Thermitus |first=M.-A. |editor=Gaal, Daniela S. |editor2=Gaal, Peter S. |title=New Beam Size Correction for Thermal Diffusivity Measurement with the Flash Method |conference=30th International Thermal Conductivity Conference/18th International Thermal Expansion Symposium |conference-url=https://web.archive.org/web/20100128105338/http://www.thermalconductivity.org/ |book-title=Thermal Conductivity 30/Thermal Expansion 18 |url=https://books.google.com/books?id=F9row3bxLuYC&pg=PA217 |access-date=1 December 2011 |date=October 2010 |publisher=DEStech Publications |location=Lancaster, PA |isbn=978-1-60595-015-0 |page=217}}</ref>

== Thermal diffusivity of selected materials and substances ==
{| class="wikitable sortable"
|+Thermal diffusivity of selected materials and substances<ref>{{cite book| title=Introduction to Heat Transfer|edition= 3rd|publisher=McGraw-Hill| year=1958| last1=Brown |last2= Marco}}  and {{cite book| last1=Eckert |last2=Drake| title=Heat and Mass Transfer| publisher=McGraw-Hill| year=1959| isbn=978-0-89116-553-8}} cited in {{cite book| first=J.P. |last=Holman| title=Heat Transfer| edition=9th| publisher=McGraw-Hill|year= 2002| isbn=978-0-07-029639-8}}</ref>
! Material !!Thermal diffusivity<br>(mm<sup>2</sup>/s)!!Refs.
|-
| [[Pyrolytic carbon|Pyrolytic graphite]], parallel to layers ||1220|| 
|-
| [[Diamond]] ||1060–1160|| 
|-
|Carbon/carbon  composite at 25&nbsp;°C
|216.5
|<ref name="Casalegno2010" />
|-
|Helium (300 K, 1 atm)
|190
|<ref name="baierlein">{{cite book|title=CDC Handbook of Chemistry and Physics|publisher=Chemical Rubber Publishing Company|year=1992|editor-last=Lide|editor-first=David R.|edition=71st|location=Boston}} cited in {{cite book|last=Baierlein|first=Ralph|url=https://archive.org/details/thermalphysics00ralp|title=Thermal Physics|publisher=Cambridge University Press|year=1999|isbn=978-0-521-59082-2|location=Cambridge, UK|page=[https://archive.org/details/thermalphysics00ralp/page/372 372]|access-date=1 December 2011|url-access=registration}}</ref>
|-
| Silver, pure (99.9%) ||165.63||
|-
|Hydrogen (300 K, 1 atm)
|160
|<ref name="baierlein" />
|-
| [[Gold]]  ||127||<ref name="eleccool">{{cite journal|url=http://www.electronics-cooling.com/2007/08/thermal-diffusivity/|title=Materials Data|author=Jim Wilson|journal=Electronics Cooling|date=August 2007}}</ref>
|-
| [[Copper]] at 25&nbsp;°C  || 111||<ref  name="Casalegno2010">{{cite journal|title= Measurement of thermal properties of a ceramic/metal joint by laser flash method |journal= Journal of Nuclear Materials |volume=407 |issue=2|page=83 |author1=V. Casalegno |author2=P. Vavassori |author3=M. Valle |author4=M. Ferraris |author5=M. Salvo |author6=G. Pintsuk | year= 2010 |doi=10.1016/j.jnucmat.2010.09.032|bibcode = 2010JNuM..407...83C }}</ref>
|-
| [[Aluminium]] || 97|| <ref name="eleccool"/> 
|-
|Silicon
|88
|<ref name="eleccool" />
|-
| Al-10Si-Mn-Mg (Silafont 36) at 20&nbsp;°C   || 74.2|| <ref>{{cite journal  |author1=P. Hofer |author2=E. Kaschnitz | title= Thermal diffusivity of the aluminium alloy Al-10Si-Mn-Mg (Silafont 36) in the solid and liquid states  |journal= High Temperatures – High Pressures | volume=40  |issue=3–4 |page=311 | year= 2011|url= http://www.oldcitypublishing.com/HTHP/HTHPcontents/HTHP40.3-4contents.html }}</ref>
|-
| Aluminium 6061-T6  Alloy  || 64||<ref name="eleccool"/>
|-
|[[Molybdenum]] (99.95%) at 25&nbsp;°C || 54.3||<ref>{{cite conference|conference=17th [[PLANSEE|Plansee]] Seminar |title= Measurement of the Thermophysical Properties of Pure Molybdenum |author1=A. Lindemann |author2=J. Blumm | year= 2009 |volume=3 }}</ref>
|-
| Al-5Mg-2Si-Mn (Magsimal-59) at 20&nbsp;°C  || 44.0|| <ref>{{cite journal |author1=E. Kaschnitz |author2=M. Küblböck |title=Thermal diffusivity of the aluminium alloy Al-5Mg-2Si-Mn (Magsimal-59) in the solid and liquid states|journal=High Temperatures – High Pressures |volume= 37 |issue=3 |page= 221 | year= 2008 |url= http://www.oldcitypublishing.com/HTHP/HTHPcontents/HTHP37.3contents.html }}</ref> 
|-
|Tin
|40
|<ref name="eleccool" />
|-
|Water vapor (1 atm, 400 K)
|23.38
|
|-
| Iron || 23||<ref name="eleccool" />
|-
|Argon (300 K, 1 atm)
|22
|<ref name="baierlein" />
|-
|Nitrogen (300 K, 1 atm)
|22
|<ref name="baierlein" />
|-
|Air (300 K)
|19
|<ref name="eleccool" />
|-
| [[Steel]], AISI 1010 (0.1% carbon)  || 18.8|| <ref>{{cite book|last=Lienhard|first=John H. Lienhard, John H. |title=A Heat Transfer Textbook|year=2019|publisher=Dover Pub|page= 715|edition=5th}}</ref>
|-
|Aluminium oxide (polycrystalline)
|12.0
|
|-
| [[Steel]], 1% carbon ||11.72|| 
|-
|Si<sub>3</sub>N<sub>4</sub> with [[carbon nanotube|CNTs]] 26&nbsp;°C
|9.142
|<ref name="Koszor2009">{{cite journal|author1=O. Koszor|author2=A. Lindemann|author3=F. Davin|author4=C. Balázsi|year=2009|title=Observation of thermophysical and tribological properties of CNT reinforced Si<sub>3</sub> N<sub>4</sub>|journal=Key Engineering Materials|volume=409|page=354|doi=10.4028/www.scientific.net/KEM.409.354|s2cid=136957396}}</ref>
|-
|Si<sub>3</sub>N<sub>4</sub> without [[carbon nanotube|CNTs]] 26&nbsp;°C
|8.605
|<ref name="Koszor2009" />
|-
| Steel, stainless 304A at 27&nbsp;°C   || 4.2|| <ref name="eleccool"/>
|-
|Pyrolytic graphite, normal to layers
|3.6
|
|-
| Steel, stainless 310 at 25&nbsp;°C   || 3.352||<ref>{{cite journal  |author1=J. Blumm |author2=A. Lindemann |author3=B. Niedrig |author4=R. Campbell |title=Measurement of Selected Thermophysical Properties of the NPL Certified Reference Material Stainless Steel 310  |journal=[[International Journal of Thermophysics]]  |volume=28 |page=674  |year=2007  |doi= 10.1007/s10765-007-0177-z |issue=2 |bibcode = 2007IJT....28..674B |s2cid=120628607 }}</ref>
|-
| [[Inconel 600]] at 25&nbsp;°C  || 3.428|| <ref>{{cite journal |author1=J. Blumm |author2=A. Lindemann |author3=B. Niedrig |title= Measurement of the thermophysical properties of an NPL thermal conductivity standard Inconel 600|journal= High Temperatures – High Pressures |volume=35/36 |issue=6 |page=621 | year= 2003–2007 |url=http://www.perceptionweb.com/abstract.cgi?id=htjr145 |doi=10.1068/htjr145|url-access=subscription }}</ref> 
|-
| Quartz   || 1.4|| <ref name="eleccool"/>
|-
|Sandstone
|1.15
|
|-
|Ice at 0&nbsp;°C
|1.02
|
|-
| Silicon dioxide (polycrystalline)  || 0.83||<ref name="eleccool"/> 
|-
|Brick, common
|0.52
|
|-
|Glass, window
|0.34
|
|-
|Brick, adobe
|0.27
|
|-
| [[Polycarbonate|PC]] (polycarbonate) at 25&nbsp;°C  || 0.144||  <ref  name="HTHP3536pp627">{{cite journal |author1=J. Blumm |author2=A. Lindemann |title= Characterization of the thermophysical properties of molten polymers and liquids using the flash technique |journal=High Temperatures – High Pressures |volume= 35/36 |issue=6 |page= 627 | year= 2003–2007 |doi=10.1068/htjr144 |url=http://www.eyoungindustry.com/uploadfile/file/20151027/20151027211034_96662.pdf}}</ref> 
|-
|Water at 25&nbsp;°C
|0.143
|<ref name="HTHP3536pp627" />
|-
|[[PTFE]] (Polytetrafluorethylene) at 25&nbsp;°C
|0.124
|<ref>{{cite journal|author1=J. Blumm|author2=A. Lindemann|author3=M. Meyer|author4=C. Strasser|year=2011|title=Characterization of PTFE Using Advanced Thermal Analysis Technique|journal=International Journal of Thermophysics|volume=40|issue=3–4|page=311|bibcode=2010IJT....31.1919B|doi=10.1007/s10765-008-0512-z|s2cid=122020437}}</ref>
|-
| [[polypropylene|PP]] (polypropylene) at 25&nbsp;°C  || 0.096|| <ref  name="HTHP3536pp627"/> 
|-
|Nylon
|0.09
|
|-
|Rubber
|0.089–0.13
|<ref name="AJP" />
|-
|Wood (yellow pine)
|0.082
|
|-
| Paraffin at 25&nbsp;°C  || 0.081||<ref  name="HTHP3536pp627"/> 
|-
| [[PVC]] (polyvinyl chloride)   || 0.08|| <ref name="eleccool"/>
|-
| Oil, engine (saturated liquid, 100&nbsp;°C) || 0.0738||
|-
| Alcohol 	 || 0.07||<ref name="eleccool"/> 
|}

==See also==
* [[Diffusion]]
* [[List of thermodynamic properties]]

==References==
{{Reflist}}

{{Authority control}}

{{DEFAULTSORT:Thermal Diffusivity}}
[[Category:Thermodynamic properties]]
[[Category:Heat transfer]]
[[Category:Physical quantities]]
[[Category:Heat conduction]]