Editing Thermal diffusivity (section)

{{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>