Thermal diffusivity

In thermodynamics, 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 and has SI units of m²/s. It is an intensive property. 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)).

Thermal diffusivity is a positive coefficient 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". 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 ( $k$ ) may be sufficient to describe heat transfers inside solid or rigid bodies by applying Fourier's law.^[6]^[7]

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, From. 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.
^ Bird, R. Byron; Stewart, Warren E.; Lightfoot, Edwin N. (1960). Transport Phenomena. John Wiley and Sons, Inc. Eq. 8.1-7. ISBN 978-0-471-07392-5. {{cite book}}: ISBN / Date incompatibility (help)
^ Carslaw, H. S.; Jaeger, J. C. (1959). Conduction of Heat in Solids (2nd ed.). Oxford University Press. ISBN 978-0-19-853368-9. {{cite book}}: ISBN / Date incompatibility (help)
^ 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, From. 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] Bird, R. Byron; Stewart, Warren E.; Lightfoot, Edwin N. (1960). Transport Phenomena. John Wiley and Sons, Inc. Eq. 8.1-7. ISBN 978-0-471-07392-5. {{cite book}}: ISBN / Date incompatibility (help)

[5] Carslaw, H. S.; Jaeger, J. C. (1959). Conduction of Heat in Solids (2nd ed.). Oxford University Press. ISBN 978-0-19-853368-9. {{cite book}}: ISBN / Date incompatibility (help)

[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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