Thermal diffusivity

In heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure.^[1] It is a measure of the rate of heat transfer inside a material. It has units of m²/s. Thermal diffusivity is usually denoted by lowercase alpha ( $α$ ), but $a$ , $h$ , $κ$ (kappa),^[2] $K$ ,^[3] , $D$ , $D_{T}$ are also used.

The formula is:^[4] $\alpha ={\frac {k}{\rho c_{p}}}$ where

$k$ is thermal conductivity (W/(m·K))
$c p$ is specific heat capacity (J/(kg·K))
$ρ$ is density (kg/m³)

Together, $ρc p$ can be considered the volumetric heat capacity (J/(m³·K)).

As seen in the heat equation,^[5] ${\frac {\partial T}{\partial t}}=\alpha \nabla ^{2}T,$ 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". Thermal diffusivity is a contrasting measure to thermal effusivity.^[6]^[7] In a substance with high thermal diffusivity, heat moves rapidly through it because the substance conducts heat quickly relative to its volumetric heat capacity or 'thermal bulk'.

Thermal diffusivity is often measured with the flash method.^[8]^[9] 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.^[10]^[11]

^ Lide, David R., ed. (2009). CRC Handbook of Chemistry and Physics (90th ed.). Boca Raton, Florida: CRC Press. p. 2-65. ISBN 978-1-4200-9084-0.
^ Hetnarski, Richard B.; Eslami, M. Reza (2009). Thermal Stresses - Advanced Theory and Applications (Online-Ausg. ed.). Dordrecht: Springer Netherlands. p. 170. doi:10.1007/978-3-030-10436-8. ISBN 978-1-4020-9247-3.
^ Unsworth, J.; Duarte, F. J. (1979), "Heat diffusion in a solid sphere and Fourier Theory", Am. J. Phys., 47 (11): 891–893, Bibcode:1979AmJPh..47..981U, doi:10.1119/1.11601
^ Lightfoot, R. Byron Bird, Warren E. Stewart, Edwin N. (1960). Transport Phenomena. John Wiley and Sons, Inc. Eq. 8.1-7. ISBN 978-0-471-07392-5.{{cite book}}: CS1 maint: multiple names: authors list (link)
^ Carslaw, H. S.; Jaeger, J. C. (1959), Conduction of Heat in Solids (2nd ed.), Oxford University Press, ISBN 978-0-19-853368-9
^ Dante, Roberto C. (2016). Handbook of Friction Materials and Their Applications. Elsevier. pp. 123–134. doi:10.1016/B978-0-08-100619-1.00009-2.
^ Venkanna, B.K. (2010). Fundamentals of Heat and Mass Transfer. New Delhi: PHI Learning. p. 38. ISBN 978-81-203-4031-2. Retrieved 1 December 2011.
^ "NETZSCH-Gerätebau, Germany". Archived from the original on 2012-03-11. Retrieved 2012-03-12.
^ W.J. Parker; R.J. Jenkins; C.P. Butler; G.L. Abbott (1961). "Method of Determining Thermal Diffusivity, Heat Capacity and Thermal Conductivity". Journal of Applied Physics. 32 (9): 1679. Bibcode:1961JAP....32.1679P. doi:10.1063/1.1728417.
^ J. Blumm; J. Opfermann (2002). "Improvement of the mathematical modeling of flash measurements". High Temperatures – High Pressures. 34 (5): 515. doi:10.1068/htjr061.
^ Thermitus, M.-A. (October 2010). "New Beam Size Correction for Thermal Diffusivity Measurement with the Flash Method". In Gaal, Daniela S.; Gaal, Peter S. (eds.). Thermal Conductivity 30/Thermal Expansion 18. 30th International Thermal Conductivity Conference/18th International Thermal Expansion Symposium. Lancaster, PA: DEStech Publications. p. 217. ISBN 978-1-60595-015-0. Retrieved 1 December 2011.

[1] Lide, David R., ed. (2009). CRC Handbook of Chemistry and Physics (90th ed.). Boca Raton, Florida: CRC Press. p. 2-65. ISBN 978-1-4200-9084-0.

[2] Hetnarski, Richard B.; Eslami, M. Reza (2009). Thermal Stresses - Advanced Theory and Applications (Online-Ausg. ed.). Dordrecht: Springer Netherlands. p. 170. doi:10.1007/978-3-030-10436-8. ISBN 978-1-4020-9247-3.

[AJP-3] Unsworth, J.; Duarte, F. J. (1979), "Heat diffusion in a solid sphere and Fourier Theory", Am. J. Phys., 47 (11): 891–893, Bibcode:1979AmJPh..47..981U, doi:10.1119/1.11601

[4] Lightfoot, R. Byron Bird, Warren E. Stewart, Edwin N. (1960). Transport Phenomena. John Wiley and Sons, Inc. Eq. 8.1-7. ISBN 978-0-471-07392-5.{{cite book}}: CS1 maint: multiple names: authors list (link)

[5] Carslaw, H. S.; Jaeger, J. C. (1959), Conduction of Heat in Solids (2nd ed.), Oxford University Press, ISBN 978-0-19-853368-9

[6] Dante, Roberto C. (2016). Handbook of Friction Materials and Their Applications. Elsevier. pp. 123–134. doi:10.1016/B978-0-08-100619-1.00009-2.

[7] Venkanna, B.K. (2010). Fundamentals of Heat and Mass Transfer. New Delhi: PHI Learning. p. 38. ISBN 978-81-203-4031-2. Retrieved 1 December 2011.

[8] "NETZSCH-Gerätebau, Germany". Archived from the original on 2012-03-11. Retrieved 2012-03-12.

[Parker-9] W.J. Parker; R.J. Jenkins; C.P. Butler; G.L. Abbott (1961). "Method of Determining Thermal Diffusivity, Heat Capacity and Thermal Conductivity". Journal of Applied Physics. 32 (9): 1679. Bibcode:1961JAP....32.1679P. doi:10.1063/1.1728417.

[10] J. Blumm; J. Opfermann (2002). "Improvement of the mathematical modeling of flash measurements". High Temperatures – High Pressures. 34 (5): 515. doi:10.1068/htjr061.

[11] Thermitus, M.-A. (October 2010). "New Beam Size Correction for Thermal Diffusivity Measurement with the Flash Method". In Gaal, Daniela S.; Gaal, Peter S. (eds.). Thermal Conductivity 30/Thermal Expansion 18. 30th International Thermal Conductivity Conference/18th International Thermal Expansion Symposium. Lancaster, PA: DEStech Publications. p. 217. ISBN 978-1-60595-015-0. Retrieved 1 December 2011.

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