Why Do We Use the Term “Thermal Effusivity”?

Written by Lab Manager, Sarah Ackermann, MSc.

Thermal effusivity is a measure of the ability of a material to exchange heat with its immediate surroundings at a surface. If you touch upholstered chair or a metal chair with your hand – the heat will transfer more efficiently between the metal chair and your hand owing to the higher thermal effusivity of the metal, and it will feel colder. This is why asphalt will feel hotter to bare feet than a black towel, even though both can reach a similar surface temperature due to solar irradiation on a hot summer day.  Thermal effusivity as a parameter is defined with the following equation:

Where:

• e is the Thermal Effusivity
• k is the Thermal Conductivity
• ρ is the Density
• c_p is the Mass Specific Heat Capacity

It can also be defined by the thermal relaxation of a surface which as absorbed a Dirac pulse of energy (Q):^[i]

Where:

• Q is the Dirac Heat Pulse
• ΔT(t) is the Temperature Change as a Function of Time
• t is Time

The concept today known as thermal effusivity has been in use since the early days of heat transfer research as a convenient property for studying scenarios of one-dimensional heat transfer. The earliest use of the term “thermal effusivity” traceable with scientific indexing tools was in 1955.^[ii] The term itself is likely older, as contemporary publications do not use the term as if it is new. Since the 1950s, the term has amassed over 5400 citations in the literature.^[iii] However, thermal effusivity isn’t the only term for this thermophysical property– nor is it the most widely used term for it. Why, then do we use the term thermal effusivity?

Let’s explore the other terms for the same property:

Thermal Inertia

The property is sometimes known under the ambiguous term of “thermal inertia”, which has approximately 93,000 citations in the literature.^[iv] However, it is not always used to refer to what we would call thermal effusivity, but has four different definitions in common use:

1. Use synonymous with common use of the term “thermal effusivity”, that is described by the equation:^[v]
   
2. Equal to the square of “thermal effusivity”, which is to say:^[vi]
   
3. As a more complicated property which accounts for the time lag of temperature response of a region of a complex body (e.g. a building envelope) to a change in heat flow associated with a system, primarily in the PCM and building materials industry.^[vii]
4. Equivalent to the thermal mass (in units of J/m²K) of the sample, mainly in geosciences.^[viii]

Due to the variation in how “Thermal Inertia” has been defined in the past, it is not commonly the preferred term by industry today.

Thermal Accumuluation

Thermal accumulation, another term, has about the same number of mentions in the literature as thermal effusivity.^[ix] Like thermal inertia, thermal accumulation is an ambiguous term with two different definitions in common use:

1. The amount of heat that accumulates or is stored within a material exposed to discontinuous heat pulses, or alternatively referring to the phenomenon of heat build-up within materials.^[x]
2. Synonymous with what we term thermal effusivity.^[xi]

For the same reason as above, thermal accumulation is not common in today’s work.

Other Terms

Other terms in use include thermal capacitance coefficient, thermal product, thermal impedance coefficient, heat transfer coefficient, thermal absorption coefficient, thermal responsivity, thermal absorptivity, and heat storage capacity. All of these terms are either less well used than thermal effusivity are ambiguous terms, or both, and for these reasons should be deprecated.

Thermal Effusivity

Thermal effusivity, with over 5400 unique mentions in the literature, has more literature mentions than the two other competing specific and unambiguous terms (thermal absorptivity, thermal responsivity, with roughly 1200 mentions^[xii] and roughly 705 mentions,^[xiii] respectively, in the literature). Some terms less common than thermal effusivity are furthermore not unique (see thermal product, which can be synonymous with thermal effusivity but also can be used to refer to a number of context-dependent things such as the result of thermal degradation on biomolecules and has roughly 2900 mentions in the literature even including biosciences applications of the term, or “thermal property value”, which can be synonymous with thermal effusivity in some publications but in most cases refers to a generic value of a generic thermal property and has 145 mentions in the literature).

Overall, what is known as “thermal effusivity” is a concept which has wide use in the literature (well over 10,000 papers published using the concept) and thermal effusivity appears to be the most widely used unique term for the concept and therefore thermal effusivity is the correct term.

With all these competing terms – some have argued, why have a term at all? My response would be that as at least 10 terms have been coined to describe the same concept across different fields, it’s obviously a useful tool in describing certain types of heat transfer geometries and phenomena. On the other hand, scientific jargon should clarify meaning rather than obscure it – so, where possible, an unambiguous and widely used term should be the preferred term for a concept. Ultimately, this is why I use the term thermal effusivity, even though the same concept is in fact known through other terms in the literature.

Why is Thermal Effusivity Important?

The concept of the thermal effusivity parameter is widely used in fields where a one-dimensional heat transfer is the important or dominant heat-transfer mechanism, where surface heat gain or loss is an important consideration, and where thermal impedance between dissimilar materials or structures is of interest. This section will highlight applications in 3 specific fields.

Modelling Heat Gain in Building Envelopes

In the field of construction and architecture, it’s important to understand the effect of construction choices in the responsiveness of a building environment to environmental pressures. Good engineering choices can stabilize interior temperatures of buildings, reducing the effect of environment fluctuations on people inside the building – and therefore reducing the cost associated with room environmental conditioning.

However, many simplified models which treat thermal inertia effects as a function of a constant heat capacitance overestimate the responsiveness of known structures an underestimate the effect of high mass construction materials on interior temperature stability. Thermal effusivity’s unique utility in predicting surface temperature responsiveness of building envelopes has made it important in predicting the responsiveness of building envelope design to environment. Starting with Van der Maas et al in 1997, effusivity based models have become standard in the field of human ecology. It is integral to the models which inform design choices such as selection of insulation system, examining the effect of material choices in design for challenging environments, studying the effects of all heat-transfer mechanisms within a building, and specifically in looking at the effect of novel materials and construction systems on building heat management.

Studying Heat Transfer in Phase Change Processes (including Phase Change Material Applications and Optimizing PCM Performance)

In a phase change process, how quickly the material can absorb or reject heat to and from its environment is the key performance attribute dictating how quickly the system can cycle. For this reason, thermal effusivity has been used in the modeling of boiling processes since the 1970s and is also used in modelling melting and solidification processes.

Because of this, optimization of thermal effusivity is a key research aim for designing phase change materials with efficient performance in harvesting of ambient thermal energy, and thermal effusivity as a parameter is a key input for models which seek to inform rational design of these systems in construction and battery thermal management applications for electric vehicles and consumer electronics, among others.  

Thermal Studies for Thermal PPE Clothing Applications and Studying Heat Transfer Between the Human Body and its Environment

When temperature hazards exist – for example, in extreme cold weather or in fire fighting applications – how much heat penetrates or is removed from a surface over a short time frame can mean the difference between discomfort and injury to the wearer. Quantitatively understanding of heat flow and temperature response under changing conditions is a key safety factor for design.

Thermal effusivity is in these applications a key input parameter for thermal analysis of the skin-environment system. This sees application in designing evaluation systems for performance assessment of thermal PPE, in evaluation of the heat exchanged between the human body and its environment under different work conditions, and in considering the effect of thermal radiation on human temperature regulation. It is also key in considering heat transfer between the human body and furniture like seating, and in studying the heat transfer dynamics of clothing systems.

Other Applications

The highlights above are just three of the many application areas of thermal effusivity. Other applications include:

• Flaw detection in composites[xiv]
• Evaluation of photoacoustic phenomena in pure[xv] heterogenous materials.[xvi]
• Food science, including quality assessment and production process design[xvii] and investigation of the dependence of thermal properties on water content of food products.[xviii]
• Photopyroelectric thermal properties analysis.[xix]
• In studying of pool boiling.[xx]
• Modeling of heat gain and passive cooling in building envelopes.[xxi]
• Corrosion modelling of metals.[xxii]
• Determining thermal performance of construction materials[xxiii]
• Characterization of thin films[xxiv]
• Photothermal depth profiling[xxv]
• Studying wear of metals[xxvi] and brake pad materials[xxvii]
• Modelling heat transfer between the human body and its environment,[xxviii] understanding the thermal behavior of the human body[xxix]
• Modelling the thermal performance of textile materials.[xxx]
• Thermal impedance problems in electronics and other fields.[xxxi]
• Understanding heat and mass transfer in geological sediments and deposits,[xxxii] with application to underground power cables, oil and gas pipelines, underground infrastructure design, and geothermal heat capture.
• Characterizing the preservation state and condition of precious cultural artefacts such as mosaics.[xxxiii]
• Studying the solidification from melt of eutectics and metals.[xxxiv]
• In the engineering and design of thermal imaging systems often used as portable temperature detectors (a field of particular relevance in the COVID-19 pandemic)[xxxv]
• Design of medical devices for continuous health monitoring.[xxxvi]
• Studying battery and electronics thermal management with application to electric vehicles, among others.[xxxvii]
• In heat exchanger design.[xxxviii]
• In semiconductor research,[xxxix] where it’s found that thermal effusivity dictates out of phase signal
• In studying photovoltaic window performance[xl]

In short – anywhere that one-dimensional heat-transfer predominates, or where thermal impedance is important, thermal effusivity is a key thermal parameter for understanding the thermodynamics of the process at play.

Measuring Thermal Effusivity

There are several ways to measure thermal effusivity – my favorite is the Modified Transient Plane Source (MTPS) method for its speed, versatility, and simple setup. The MTPS method is available on C-Therm’s Tx Thermal Effusivity Touch Tester and Trident Thermal Conductivity Analyzer properties platforms, and C-Therm  also offers thermal effusivity testing according to ASTM D7984 through our Thermal Analysis Labs division. If you have a need for fast and accurate thermal effusivity testing, contact us and one of our experts can help you move your project forward with a solution that’s right for you.

Recommended Reading / Works Cited

[i] C. Fort. Characterization of materials and structures by the photothermal method. Journal de Physique IV Proceedings, EDP Sciences, 1994, 04 (C7), pp.C7-287-C7-290. ff10.1051/jp4:1994768ff. ffjpa-00253297

[ii] Krischer, O. and Esdorn, H. VDI Forsch.-H 1955.

[iii] Google Scholar search, excluding patents, dated May 21, 2021. Searched for exact matches to the term “thermal effusivity”

[iv] Google Scholar search, excluding patents, dated May 21, 2021. Searched for exact matches to the term “thermal inertia”

[v] Mellon, M.T.; Jakosky, B.M.; Keiffer, H.H.; and Christiansen, P.R. Icarus 148, 437– 455 (2000)

[vi] Hendler, E; Crosbie, R; and Hardy, J.D. Journal of Applied Physiology. 1958. 12(2). 177-185.

[vii] Ramakrishnan, S; Wang, X; Sanjayan, J; Petinakis, E; and Wilson, J. Solar Energy 158 (2017) 626–635.

[viii] Gouttevin, I; Lehning, M; Jonas, T; Gustafsson, D; Mölder. Geosci. Model Dev., 8, 2379–2398, 2015

[ix] Google Scholar search, excluding patents, dated May 21, 2021. Searched for exact matches to the term “thermal accumulation”

[x] Juodkazis, S.; Misawa, H.; and Maksimov, I. Appl. Phys. Lett., Vol. 85, No. 22, 29 November 2004

[xi] Krajewski, P. K.; Magda, K.; Stojecki, P.,. Archives of Foundry Engineering 2013. Vol. 13, iss. 3. 89–94

[xii] Google Scholar search, excluding patents, dated May 21, 2021. Searched for exact matches to the term “thermal absorptivity”

[xiii] Google Scholar search, excluding patents, dated May 21, 2021. Searched for exact matches to the term “thermal responsivity”

[xiv] Maldague, X.; Krapez, J. C. ; Cielo, P. ; Poussart, D. “Processing of thermal images for the detection and enhancement of subsurface flaws in composite materials” 1988. Signal Processing and Pattern Recognition in Nondestructive Evaluation of Materials. Springer Berlin Heidelberg. p. 257-285

[xv] Sanchez, Ruben R.; Rieumont, Jacques B.; Cardoso, Sergio L.; da Silva, Marcelo G.; Sthel, Marcelo S.; Massunaga, Marcelo S. O.; Gatts, Carlos N.; Vargas, Helion. Photoacoustic Monitoring of Internal Plastification in Poly(3-hydroxybutyrate-co-3-hydroxyvalerate) Copolymers: Measurements of Thermal Parameters. Journal of the Brazilian Chemical Society. 1999. 10(2). 97-103.

[xvi] Aamodt, L.C. and Murphy, J.C. “Thermal effects in materials with continuously varying optical and thermal properties in one dimension.” 1986. Canadian Journal of Physics. 64(9). 1221-1229.

[xvii] Bicanic, Dane ; Chirtoc, Mihai ; Dadârlat, Dorin ; Bovenkamp, Pieter Van ; and Schayk, Heidi Van. “Direct Determination of Thermophysical Parameter Kuprhoc in Mayonnaise, Shortening, and Edible Oil.” Applied Spectroscopy. 1992. 46(4). 602-605.

[xviii] Frandas, A; Paris, D; Bissieux, C; Chirtoc, M; Antoniow, J.S.; and Egée, M. “Classical and photopyroelectric studies of optical and thermophysical properties of starch sheets: dependence on water content and temperature.” Applied Physics B. 2000. 71(1). 69-75.

[xix] Dadarlat, Dorin; Bicanic, Dane; Visser, Henk; Mercuri, Fulvio; and Frandas, Angela. “Photopyroelectric method for determination of thermophysical parameters and detection of phase transitions in fatty acids and triglycerides. Part I: Principles, theory, and instrumentational concepts.” Journal of the American Oil Chemists’ Society. 1995. 72(3). 273-79.

[xx] Magrini, U., and Nannei, E. (May 1, 1975). “On the Influence of the Thickness and Thermal Properties of Heating Walls on the Heat Transfer Coefficients in Nucleate Pool Boiling.” ASME. J. Heat Transfer. May 1975; 97(2): 173–178. https://doi.org/10.1115/1.3450337; Watwe, A. A. and Bar-Cohen, Avram. THE ROLE OF THICKNESS AND THERMAL EFFUSIVITY IN POOL BOILING CHF IN HIGHLY-WETTING LIQUIDS. Proceeding of International Heat Transfer Conference 10. 1994. https://www.ihtcdigitallibrary.com/conferences/791db5793b1c5bfd,1898885d7f299db1,65a4aac76ba20ffa.html  ; “Influence of wall material on nucleate pool boiling of liquid nitrogen.” International Journal of Heat and Mass Transfer. Volume 94, March 2016, Pages 1-8

[xxi] J. VAN DER MAAS∗ & E. MALDONADO (1997) A NEW THERMAL INERTIA MODEL BASED ON EFFUSIVITY, International Journal of Solar Energy, 19:1-3, 131-160, DOI: 10.1080/01425919708914334

[xxii] L. Veleva, S.A. Tomás, E. Marín, A. Cruz-Orea, I. Delgadillo, J.J. Alvarado-Gil, P. Quintana, R. Pomés, F. Sánchez, H. Vargas, L.C.M. Miranda, On the use of the photoacoustic technique for corrosion monitoring of metals: Cu and Zn oxides formed in tropical environments. Corrosion Science. 1997. 39(9). 1641-1655.

[xxiii] Bouguerra, A.; Ledhem, A.; Laurent, J. P.; Diop, M. B.; and Queneudec, M. J. Phys. D: Appl. Phys. (1998). 31(17). 2184–2190.

[xxiv] Martinsons, Christophe and Heuret, Michel. “Recent progress in the measurement of the thermal properties of hard coatings.” Thin Solid Coatings. 1998. 317. 455-7.

[xxv] Krapez, Jean-Claude. “Thermal effusivity profile characterization from pulse photothermal data.” Journal of Applied Physics. 2000. 87(9). 4514-24.

[xxvi] Abdel-Aal, Hisham A. “The correlation between thermal property variation and high temperature wear transition of rubbing metals.” Wear. 2000. 237. 147-151.

[xxvii] W. A. D. N. Gunathilake, M. S. M. Perera and M. A. Wijewardane, “Mathematical Modelling and Analysis of Wear Characteristics of Vehicle Brakes with TEGs,” in 113th Annual Sessions, Institute of Engineers Sri Lanka, Colombo, Sri Lanka, 2019.

[xxviii] D C Agrawal 1999 Phys. Educ. 34 220

[xxix] Otsuka, Kimio, et al. “Imaging of skin thermal properties with estimation of ambient radiation temperature.” IEEE engineering in medicine and biology magazine 21.6 (2002): 49-55.

[xxx] Mangat, Asif Elahi, et al. “Model of thermal absorptivity of knitted rib in dry state and its experimental authentication.” Comparative analysis of siro yarn properties spun on ring and pneumatic compact spinning systems (2017): 263.

[xxxi] Ernesto Marin-Moares. “Time Varying Heat Conduction In Solids” In: Heat Conduction – Basic Research. Ed: Vyacheslav S. Vikhrenko. InTech Open. P. 177-202.

[xxxii] Seward, Anya. “THERMAL ROCK PROPERTIES – COMPARISONS OF APPARENT VALUES DETERMINED FROM IN-SITU TEMPERATURE PROFILES, AND VALUES DETERMINED BY LABORATORY MEASUREMENTS.” Proceedings 38th New Zealand Geothermal Workshop. 23 – 25 November 2016. Auckland, New Zealand.

[xxxiii] P Theodorakeas et al 2015 J. Phys.: Conf. Ser. 655 012061

[xxxiv] Kamal, Mustafa, et al. “A study of eutectic indium-bismuth and indium-bismuth-tin Field’s metal rapidly solidified from melt.” Journal: JOURNAL OF ADVANCES IN PHYSICS 7.2 (2015).

[xxxv] Abdelrahman, Yomna, et al. “Stay cool! understanding thermal attacks on mobile-based user authentication.” Proceedings of the 2017 CHI Conference on Human Factors in Computing Systems. 2017.

[xxxvi] Selem, Enas, et al. “THE (temperature heterogeneity energy) aware routing protocol for IoT health application.” IEEE Access 7 (2019): 108957-108968.

[xxxvii] SCIENTIA SINICA Technologica, Volume 50 , Issue 10 : 1298-1315(2020) https://doi.org/10.1360/SST-2020-0083

[xxxviii] International Journal of Heat and Mass Transfer Volume 148, February 2020, 119162. https://doi.org/10.1016/j.ijheatmasstransfer.2019.119162

[xxxix] Koh, Yee Kan, and David G. Cahill. “Frequency dependence of the thermal conductivity of semiconductor alloys.” Physical Review B 76.7 (2007): 075207.

[xl] ALRASHIDI, H., GHOSH, A., ISSA, W., SELLAMI, N., MALLICK, T.K. and SUNDARAM, S. 2020. Thermal performance of semitransparent CdTe BIPV window at temperate climate. Solar energy [online], 195, pages 536-543. Available from: https://doi.org/10.1016/j.solener.2019.11.084