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Renaissance Man – Chasing Rainbows

Currently, there is general acceptance of the broad use of the newer popular group of contact transient measurement methods, to measure scientifically defined intrinsic thermal transport properties. As such it appears that we should also accept the claims of application and accuracy for some of the associated newer terms that have accompanied these methods. In particular, I refer to the term thermal effusivity now described and claimed by many supporters to be a thermal transport property of a material that can be measured by a “modified” form of one transient method. This term has been introduced more recently and has immediately gained “flavour of the era”. A “googled” search on the Internet obtained a multi-application response indicating that it now appears to have replaced thermal conductivity as the prime driving force in heat transfer applications at or across surfaces.


While according to the often-quoted axiom “if something looks like a duck, walks like a duck and sounds like a duck then it is a duck, the same reasoning does not apply to thermal effusivity where it can be seen more as a dead duck since it cannot be defined as thermal property per se. This is one of the more difficult examples that I illustrated by statements in previous Blogs that the subject of thermal conductivity and associated thermal properties is a highly complex one. Furthermore, now that it has become a subject for international standardization, via ASTM and possibly ISO, its popularity has become a cause of concern due to the deepening chasm in the contentious differences of opinion between those taking a factual purist approach and the many protagonist supporters of beliefs in the subject of heat transfer.

As I believe that one can obtain a better understanding of any subject from its history, examination of the approximate eighty-year background history of use and application of the term proved to be is most interesting while lacking factual consistency. It appears that there have been at least ten (10) synonymous descriptive, but often ambiguous, titles for the term. Initially the unambiguous favourite was thermal inertia but in the last ten years this has been usurped by the popular thermal effusivity.

Its existence is recognized as a discussion item found in many textbooks and publications addressing the complex subject of energy transfer involving perfect contact between homogeneous semi-infinite bodies at different temperatures. However, there is NO indication in any of these sources that the term is recognized or accepted especially as a thermal transport property. Even the computer I am using now questions its use every time it is included in the text. The definitive result from any and all of these investigations remains that unlike the property thermal conductivity NO strict IUPAC approved definition exists for thermal effusivity.

Protagonists indicate that, including its many synonymous terms, “thermal effusivity” is a concept which has had very wide use in many areas of heat transfer (apparently well over 10,000 citations) with more than 50% favouring the term being the most widely used unique one and thus establishing that it must be the correct term. To counter this claim of broad use I can only supply my personal experience with the observation that in my seventy-year history of providing measurements services to those involved in the field of thermal transport properties my first encounter and subsequent involvement in a subject relating to thermal inertia and much later thermal effusivity was some thirty years after I had started work in the late nineteen forties.

This lack of a definition changed in the early years of the present century, sometime about 2004, due to the sudden appearance of a “claimed definition” for the term. This appeared, as a short definitive statement without any supportive information on its provenance in Wikipedia the modern online form of “encyclopedia”

The initial definition that after over twenty remains the basis of that in the current and proposed ASTM standards is:

Thermal effusivity, e– a measure of a material’s ability to exchange thermal energy with its surroundings.

Discussion – Thermal effusivity, e, is related to thermal conductivity (λ), density (ρ), specific heat capacity (cp), and thermal diffusivity (a) by the following expression: e =

If two semi-infinite bodies initially at temperatures T1 and T2 are brought in perfect thermal contact, the temperature at the contact surface Tm will be given by their relative effusivities.

The materials are considered homogeneous and in a single thermodynamic phase with the thermal energy transfer conduction modes indicating relevance only to dense solids

Wikipedia publishes input information and technical data submitted from many sources worldwide. However, unlike the well-known and previously accepted Encyclopedia Britannica, such input is NOT technically reviewed first by experts before publication. Unfortunately, in this case, the lack of independent provenance of this input questions the validity of the subject since the total content of the short article consisted only of the definition coupled with a detailed description of a commercial measurement system claimed to be the means to measure thermal effusivity.

The practical explanation describing the function of the term is that it acts as a “quantifier” of the physiological haptic sensation (“feeling”) of hot, cold, warm etc. For example, when the human body in one environment enters another that is different in temperature there is an immediate corresponding change in feeling or when the human finger touches the surfaces of a metal and then a piece of a polymer and piece of balsa wood at the same lower temperature the response is a feeling of cold, cool and warm respectively. Such response is claimed to be the result of the temperature difference change caused by the exchange of thermal energy related directly, as in the latter case to the respective high to low values of thermal effusivity of the materials.

Returning to the basics, the term is expressed as the complex quantity of the square root of the product of the three intrinsic bulk defined physical properties with simple units, yet the combination of terms results in an unusual form of unit. As defined, the material is a semi-infinite body and in a single thermodynamic phase such that thermal energy will be transported by conduction modes only. This is due to it being based solely on the assumptions represented in the basic heat transfer equation that the energy transfer is uniform and transferred in homogeneous materials by conduction processes only.

If it is considered a physical property, the most direct effect of the thermal effusivity is to govern the transmission and reflection coefficients of heat traveling between materials. Thus, when the subject of heat transfer is viewed in terms of thermal waves, surface effects become important for high frequency components (radiation, etc) and have to be included, whereas it is only the reflection of low frequency (conduction) thermal waves that depend solely on bulk properties that are considered in the current definition.

Non-equilibrium, thermophysical properties of homogeneous materials are correctly defined only by their occurrence within a differential equation that defines a transport process of some kind within that material that is strictly homogeneous and in a single thermodynamic phase. Examples are Fourier’s Laws that define thermal conductivity and thermal diffusivity respectively or Fick’s Law which defines self-diffusion coefficient

Therefore, the so-termed thermal effusivity is NOT a thermophysical transport property in the same sense since there is no differential equation in which it occurs as the proportionality between a flux and a gradient of a thermodynamic variable. It is evaluated as   a quantity consisting of a transport property combined with two equilibrium properties. Thus, in that sense, it could be considered a material property but that becomes questionable since there is no differential equation in which it occurs as the proportionality between a flux and a gradient of a thermodynamic variable and the way in which this combination occurs in physical problems and other possible uses,

An examination of the various situations where this combination can arise indicates that the only totally successful one is that involving a horizontal rectangular slab of homogeneous material subjected to a constant point heat flux. This results in an immediate rise in temperature at the surface only at the instant of contact. For any other point in the solid, the thermal effusivity is not the only relevant combination of properties so it is highly doubtful that the concept is useful even in an idealised 1D-heat conduction with no surface effects. Other situations indicate that the dependence on the thermal effusivity as a property is even more restricted as is it confined to the surface of the material and to small times, which depend upon the material itself.

One very popular application of thermal effusivity is the quasi-qualitative measurement of coolness or warmth feel of non-uniform or anisotropic materials of textiles and fabrics. When a textile or fabric or similar type of non-uniform or anisotropic material is measured at the surface with short test times by a transient method or instrument, the measured value will include the transfer mechanisms, conduction, convection, and radiation heat, plus contact resistance between the sensor and specimen.

As the dominant property of the specimen in the thermal effusivity expression is the thermal conductance, which is valid for solids only, the most appropriate term used to describe the measured value correctly for these inhomogeneous materials will be thermal effusance comparable to thermal conductance. It is interesting that note that in 2018 I had discussions on this issue with a member of the ASTM D-13 Committee for Fabrics. Following these, I later discovered that significant changes drawing attention to and addressing the issue had been made in the Wikipedia definition. However, these revisions have not yet been replicated in the ASTM versions. Furthermore, with this understanding, thermal conductivity can never be derived from the thermal effusivity expression. This becomes an important consideration when considering qualitative use of the term when testing materials other than dense homogeneous solids.

In principle, therefore, any belief in the validity of the thermal effusivity being considered and used as an equivalent property to other established well defined transport properties is distinctly very weak. It is not universally applicable to all applications since it has real impact only at surfaces and/or at extremely short times. With many competing terms coined to describe the same concept across different fields, plus the numerous uncertainties in its understanding and application the often asked question is “what is the purpose so why have such a term at all?”

My response is that while it may appear to be a useful tool it cannot be applied universally as it addresses ONLY in subjects describing certain specific types of heat transfer geometries and phenomena. Scientific jargon should clarify rather than obscure applications and meanings so, where possible, unambiguous and accepted used terms should be the answer especially in the development of standards related to its measurement and use.


Renaissance Man.


A short footnote: I have just “Googled” the term today only to find that there are many more sources of information available but now there is an excess of 80% that addresses only the subject of the thermal effusivity of FABRICS!

It really is a funny old complex world!


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