Thermal diffusivity

In heat transfer analysis, thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure.<ref>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.</ref> 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),<ref>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.</ref> K,<ref name = AJP>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</ref> and D are also used.

The formula is:<ref>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)</ref>

<math>\alpha = \frac{ k }{ \rho c_{p} }</math>

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

<math>\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 curvature, quantifying the rate at which temperature concavity is "smoothed out". Thermal diffusivity is a contrasting measure to thermal effusivity.<ref>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.</ref><ref>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.</ref> 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.<ref>"NETZSCH-Gerätebau, Germany". Archived from the original on 2012-03-11. Retrieved 2012-03-12.</ref><ref name="Parker"> 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.</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> J. Blumm; J. Opfermann (2002). "Improvement of the mathematical modeling of flash measurements". High Temperatures – High Pressures. 34 (5): 515. doi:10.1068/htjr061.</ref><ref>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.</ref>

Thermal diffusivity of selected materials and substances

Thermal diffusivity of selected materials and substances<ref>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. cited in Holman, J.P. (2002). Heat Transfer (9th ed.). McGraw-Hill. ISBN 978-0-07-029639-8.</ref>

Material	Thermal diffusivity (mm2/s)	References
Pyrolytic graphite, parallel to layers	1,220
Diamond	1,060 - 1,160
Carbon/carbon composite at 25 °C	216.5	<ref name="Casalegno2010" />
Helium (300 K, 1 atm)	190	<ref name="baierlein">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.</ref>
Silver, pure (99.9%)	165.63
Hydrogen (300 K, 1 atm)	160	<ref name="baierlein" />
Gold	127	<ref name="eleccool">Jim Wilson (August 2007). "Materials Data". {{cite journal}}: Cite journal requires |journal= (help)</ref>
Copper at 25 °C	111	<ref name="Casalegno2010">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.</ref>
Aluminium	97	<ref name="eleccool"/>
Silicon	88	<ref name="eleccool" />
Al-10Si-Mn-Mg (Silafont 36) at 20 °C	74.2	<ref>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.</ref>
Aluminium 6061-T6 Alloy	64	<ref name="eleccool"/>
Molybdenum (99.95%) at 25 °C	54.3	<ref>A. Lindemann; J. Blumm (2009). Measurement of the Thermophysical Properties of Pure Molybdenum. 17th Plansee Seminar. Vol. 3.</ref>
Al-5Mg-2Si-Mn (Magsimal-59) at 20 °C	44.0	<ref>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.</ref>
Tin	40	<ref name="eleccool" />
Water vapor (1 atm, 400 K)	23.38
Iron	23	<ref name="eleccool" />
Argon (300 K, 1 atm)	22	<ref name="baierlein" />
Nitrogen (300 K, 1 atm)	22	<ref name="baierlein" />
Air (300 K)	19	<ref name="eleccool" />
Steel, AISI 1010 (0.1% carbon)	18.8	<ref>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)</ref>
Aluminium oxide (polycrystalline)	12.0
Steel, 1% carbon	11.72
Si3N4 with CNTs 26 °C	9.142	<ref name="Koszor2009">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.</ref>
Si3N4 without CNTs 26 °C	8.605	<ref name="Koszor2009" />
Steel, stainless 304A at 27 °C	4.2	<ref name="eleccool"/>
Pyrolytic graphite, normal to layers	3.6
Steel, stainless 310 at 25 °C	3.352	<ref>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.</ref>
Inconel 600 at 25 °C	3.428	<ref>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.</ref>
Quartz	1.4	<ref name="eleccool"/>
Sandstone	1.15
Ice at 0 °C	1.02
Silicon dioxide (polycrystalline)	0.83	<ref name="eleccool"/>
Brick, common	0.52
Glass, window	0.34
Brick, adobe	0.27
PC (polycarbonate) at 25 °C	0.144	<ref name="HTHP3536pp627">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.</ref>
Water at 25 °C	0.143	<ref name="HTHP3536pp627" />
PTFE (Polytetrafluorethylene) at 25 °C	0.124	<ref>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.</ref>
PP (polypropylene) at 25 °C	0.096	<ref name="HTHP3536pp627"/>
Nylon	0.09
Rubber	0.089 - 0.13	<ref name="AJP" />
Wood (yellow pine)	0.082
Paraffin at 25 °C	0.081	<ref name="HTHP3536pp627"/>
PVC (polyvinyl chloride)	0.08	<ref name="eleccool"/>
Oil, engine (saturated liquid, 100 °C)	0.0738
Alcohol	0.07	<ref name="eleccool"/>

See also

• Heat equation
• Laser flash analysis
• Thermophoresis
• Thermal effusivity
• Thermal time constant