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.{{CRC90|page=2-65}} It is a measure of the rate of heat transfer inside a material and has SI units of m²/s. It is an intensive property. Thermal diffusivity is usually denoted by lowercase alpha ({{mvar|α}}), but {{mvar|a}}, {{mvar|h}}, {{mvar|κ}} (kappa),{{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}} {{mvar|K}},{{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}} {{mvar|D}}, $D\_T$ are also used.

The formula is{{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}}

$$$$

\alpha = \frac{k}{\rho c_p},

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/m³).

Together, {{mvar|ρc{{sub|p}}}} can be considered the volumetric heat capacity (J/(m³·K)).

Thermal diffusivity is a positive coefficient in the heat equation:{{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}}

$$$$

\frac{\partial T}{\partial t} = \alpha \nabla^2 T.

One way to view thermal diffusivity is as the ratio of the time derivative of temperature to its 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 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.{{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}}{{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}}

Thermal diffusivity is often measured with the flash method.{{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 }}

{{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 }} 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.

{{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

}}{{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}}