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]

Thermal diffusivity of selected materials and substances

Thermal diffusivity of selected materials and substances^[12]
Material	Thermal diffusivity (mm²/s)	Refs.
Pyrolytic graphite, parallel to layers	1220
Diamond	1060–1160
Carbon/carbon composite at 25 °C	216.5	^[13]
Helium (300 K, 1 atm)	190	^[14]
Silver, pure (99.9%)	165.63
Hydrogen (300 K, 1 atm)	160	^[14]
Gold	127	^[15]
Copper at 25 °C	111	^[13]
Aluminium	97	^[15]
Silicon	88	^[15]
Al-10Si-Mn-Mg (Silafont 36) at 20 °C	74.2	^[16]
Aluminium 6061-T6 Alloy	64	^[15]
Molybdenum (99.95%) at 25 °C	54.3	^[17]
Al-5Mg-2Si-Mn (Magsimal-59) at 20 °C	44.0	^[18]
Tin	40	^[15]
Water vapor (1 atm, 400 K)	23.38
Iron	23	^[15]
Argon (300 K, 1 atm)	22	^[14]
Nitrogen (300 K, 1 atm)	22	^[14]
Air (300 K)	19	^[15]
Steel, AISI 1010 (0.1% carbon)	18.8	^[19]
Aluminium oxide (polycrystalline)	12.0
Steel, 1% carbon	11.72
Si₃N₄ with CNTs 26 °C	9.142	^[20]
Si₃N₄ without CNTs 26 °C	8.605	^[20]
Steel, stainless 304A at 27 °C	4.2	^[15]
Pyrolytic graphite, normal to layers	3.6
Steel, stainless 310 at 25 °C	3.352	^[21]
Inconel 600 at 25 °C	3.428	^[22]
Quartz	1.4	^[15]
Sandstone	1.15
Ice at 0 °C	1.02
Silicon dioxide (polycrystalline)	0.83	^[15]
Brick, common	0.52
Glass, window	0.34
Brick, adobe	0.27
PC (polycarbonate) at 25 °C	0.144	^[23]
Water at 25 °C	0.143	^[23]
PTFE (Polytetrafluorethylene) at 25 °C	0.124	^[24]
PP (polypropylene) at 25 °C	0.096	^[23]
Nylon	0.09
Rubber	0.089–0.13	^[3]
Wood (yellow pine)	0.082
Paraffin at 25 °C	0.081	^[23]
PVC (polyvinyl chloride)	0.08	^[15]
Oil, engine (saturated liquid, 100 °C)	0.0738
Alcohol	0.07	^[15]

References

^ 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.
^ ^a ^b 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.
^ Brown; Marco (1958). Introduction to Heat Transfer (3rd ed.). McGraw-Hill. and Eckert; Drake (1959). Heat and Mass Transfer. McGraw-Hill. ISBN 978-0-89116-553-8. {{cite book}}: ISBN / Date incompatibility (help) cited in Holman, J.P. (2002). Heat Transfer (9th ed.). McGraw-Hill. ISBN 978-0-07-029639-8.
^ ^a ^b V. Casalegno; P. Vavassori; M. Valle; M. Ferraris; M. Salvo; G. Pintsuk (2010). "Measurement of thermal properties of a ceramic/metal joint by laser flash method". Journal of Nuclear Materials. 407 (2): 83. Bibcode:2010JNuM..407...83C. doi:10.1016/j.jnucmat.2010.09.032.
^ ^a ^b ^c ^d Lide, David R., ed. (1992). CDC Handbook of Chemistry and Physics (71st ed.). Boston: Chemical Rubber Publishing Company. cited in Baierlein, Ralph (1999). Thermal Physics. Cambridge, UK: Cambridge University Press. p. 372. ISBN 978-0-521-59082-2. Retrieved 1 December 2011.
^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l Jim Wilson (August 2007). "Materials Data". Electronics Cooling.
^ P. Hofer; E. Kaschnitz (2011). "Thermal diffusivity of the aluminium alloy Al-10Si-Mn-Mg (Silafont 36) in the solid and liquid states". High Temperatures – High Pressures. 40 (3–4): 311.
^ A. Lindemann; J. Blumm (2009). Measurement of the Thermophysical Properties of Pure Molybdenum. 17th Plansee Seminar. Vol. 3.
^ E. Kaschnitz; M. Küblböck (2008). "Thermal diffusivity of the aluminium alloy Al-5Mg-2Si-Mn (Magsimal-59) in the solid and liquid states". High Temperatures – High Pressures. 37 (3): 221.
^ Lienhard, John H. Lienhard, John H. (2019). A Heat Transfer Textbook (5th ed.). Dover Pub. p. 715.{{cite book}}: CS1 maint: multiple names: authors list (link)
^ ^a ^b O. Koszor; A. Lindemann; F. Davin; C. Balázsi (2009). "Observation of thermophysical and tribological properties of CNT reinforced Si₃ N₄". Key Engineering Materials. 409: 354. doi:10.4028/www.scientific.net/KEM.409.354. S2CID 136957396.
^ J. Blumm; A. Lindemann; B. Niedrig; R. Campbell (2007). "Measurement of Selected Thermophysical Properties of the NPL Certified Reference Material Stainless Steel 310". International Journal of Thermophysics. 28 (2): 674. Bibcode:2007IJT....28..674B. doi:10.1007/s10765-007-0177-z. S2CID 120628607.
^ J. Blumm; A. Lindemann; B. Niedrig (2003–2007). "Measurement of the thermophysical properties of an NPL thermal conductivity standard Inconel 600". High Temperatures – High Pressures. 35/36 (6): 621. doi:10.1068/htjr145.
^ ^a ^b ^c ^d J. Blumm; A. Lindemann (2003–2007). "Characterization of the thermophysical properties of molten polymers and liquids using the flash technique" (PDF). High Temperatures – High Pressures. 35/36 (6): 627. doi:10.1068/htjr144.
^ J. Blumm; A. Lindemann; M. Meyer; C. Strasser (2011). "Characterization of PTFE Using Advanced Thermal Analysis Technique". International Journal of Thermophysics. 40 (3–4): 311. Bibcode:2010IJT....31.1919B. doi:10.1007/s10765-008-0512-z. S2CID 122020437.

[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.

[12] Brown; Marco (1958). Introduction to Heat Transfer (3rd ed.). McGraw-Hill. and Eckert; Drake (1959). Heat and Mass Transfer. McGraw-Hill. ISBN 978-0-89116-553-8. {{cite book}}: ISBN / Date incompatibility (help) cited in Holman, J.P. (2002). Heat Transfer (9th ed.). McGraw-Hill. ISBN 978-0-07-029639-8.

[Casalegno2010-13] V. Casalegno; P. Vavassori; M. Valle; M. Ferraris; M. Salvo; G. Pintsuk (2010). "Measurement of thermal properties of a ceramic/metal joint by laser flash method". Journal of Nuclear Materials. 407 (2): 83. Bibcode:2010JNuM..407...83C. doi:10.1016/j.jnucmat.2010.09.032.

[baierlein-14] Lide, David R., ed. (1992). CDC Handbook of Chemistry and Physics (71st ed.). Boston: Chemical Rubber Publishing Company. cited in Baierlein, Ralph (1999). Thermal Physics. Cambridge, UK: Cambridge University Press. p. 372. ISBN 978-0-521-59082-2. Retrieved 1 December 2011.

[eleccool-15] ^ ^a ^b ^c ^d ^e ^f ^g ^h ⁱ ^j ^k ^l Jim Wilson (August 2007). "Materials Data". Electronics Cooling.

[16] P. Hofer; E. Kaschnitz (2011). "Thermal diffusivity of the aluminium alloy Al-10Si-Mn-Mg (Silafont 36) in the solid and liquid states". High Temperatures – High Pressures. 40 (3–4): 311.

[17] A. Lindemann; J. Blumm (2009). Measurement of the Thermophysical Properties of Pure Molybdenum. 17th Plansee Seminar. Vol. 3.

[18] E. Kaschnitz; M. Küblböck (2008). "Thermal diffusivity of the aluminium alloy Al-5Mg-2Si-Mn (Magsimal-59) in the solid and liquid states". High Temperatures – High Pressures. 37 (3): 221.

[19] Lienhard, John H. Lienhard, John H. (2019). A Heat Transfer Textbook (5th ed.). Dover Pub. p. 715.{{cite book}}: CS1 maint: multiple names: authors list (link)

[Koszor2009-20] O. Koszor; A. Lindemann; F. Davin; C. Balázsi (2009). "Observation of thermophysical and tribological properties of CNT reinforced Si₃ N₄". Key Engineering Materials. 409: 354. doi:10.4028/www.scientific.net/KEM.409.354. S2CID 136957396.

[21] J. Blumm; A. Lindemann; B. Niedrig; R. Campbell (2007). "Measurement of Selected Thermophysical Properties of the NPL Certified Reference Material Stainless Steel 310". International Journal of Thermophysics. 28 (2): 674. Bibcode:2007IJT....28..674B. doi:10.1007/s10765-007-0177-z. S2CID 120628607.

[22] J. Blumm; A. Lindemann; B. Niedrig (2003–2007). "Measurement of the thermophysical properties of an NPL thermal conductivity standard Inconel 600". High Temperatures – High Pressures. 35/36 (6): 621. doi:10.1068/htjr145.

[HTHP3536pp627-23] J. Blumm; A. Lindemann (2003–2007). "Characterization of the thermophysical properties of molten polymers and liquids using the flash technique" (PDF). High Temperatures – High Pressures. 35/36 (6): 627. doi:10.1068/htjr144.

[24] J. Blumm; A. Lindemann; M. Meyer; C. Strasser (2011). "Characterization of PTFE Using Advanced Thermal Analysis Technique". International Journal of Thermophysics. 40 (3–4): 311. Bibcode:2010IJT....31.1919B. doi:10.1007/s10765-008-0512-z. S2CID 122020437.

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Thermal diffusivity

Thermal diffusivity of selected materials and substances

See also

References

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