In order to enhance the access to the suggested articles, I would like to add the web addresses of mentioned articles:

1- Journal of engineering physics & Thermophysics, October 1991, Volume 61, Issue 4, pp 1283-1284, Relationship between emissivity of metals and their thermophysical properties, I. P. Zhuk, N. I. Stetyukevich

http://link.springer.com/article/10.1007%2FBF00872600

2- British Journal of Applied Physics Volume 17, Number 4, S Atallah, 1966, Br. J. Appl. Phys. , A relationship between emissivity and thermal conductivity of metals. S. Atallah.

http://iopscience.iop.org/0508-3443/17/4/120

Dear Don,

let us know whether you have access to the measured experimental emissivity data of different metals at various temperatures or not? Can you measure these data in a lab? Or are you going to predict these data with reliable correlations? If you have access to large database of emissivity values at different temperatures, I think I can suggest you some solutions.

Dear Babak,

I may have posted my question too soon in my research. Here are my present responses to your very timely and discerning questions.

let us know whether you have access to the measured experimental emissivity data of different metals at various temperatures or not?

I have collected emissivity values for common materials from multiple industrial sources, such as infrared technology manufacturing and calibration companies with research and development units (FLIR, Mikron, Electrophysics, Raytheon, ISG, ASNT, ASTM, et cetera). As this information is considered reliable, the information also does not cover some important temperature ranges and does not cover multiple geometric types, I have set out to fill in some gaps experimentally and verify some data sets. I have completed these experiments.

I have multiple IR thermograms of heat exchangers, boilers, and combustion furnaces from which I am drawing data from known material surfaces with verified surface and interior temperatures. This data has been obtained by my performing in field infrared imaging evaluations, from over a decade of real world inspections.

Can you measure these data in a lab?

I have recently set up a NDT and chemical lab to measure emissivity values of various metals, refractory materials, and insulation. We, an engineer and I, are the process of constructing a full functioning model heat exchanger to run measurements in real time, though the operating temperature may be limited to 350C for safety reasons. The main purpose of the model heat exchanger is to observe and retrieve data for the effects of temperature gradients on steel shell, refractory, and insulation. The materials will be analyzed from ambient to a known high temperature, and material samples taken at well selected intervals.

Or are you going to predict these data with reliable correlations?

I have looked closely at Zhuk's and Atallah's mathematical approach and will utilize their assumptions and equations as a 'test' of results. Data on the thermal Conductivity of materials is readily available, including other variables such as diffusivity, specific heat. I have scoured thermodynamic information with the intent of forming correlations. This has taken me into sime diverse topics such as molecular transport phenomena, thermochemistry, and condensed matter physics.

I am looking at Caratheodory's axiomatic thermodynamics as an approach for establishing a general mathematical relationship. Even Angstrom, while developing a method of measurement of thermal conductivity, simplified a relationship between conductivity and radiation (Bouchard, 2000, Wooster Physics Department)

Dear Don,

Thanks for your extensive and comprehensive answers. As you have access to data from experimental measurements and also industrial observed data (which are really valuable), I can conclude that we have already a large database of experimental emissivity values and also reliable correlations to calculate thermal conductivity of different materials at various temperatures. From my own experience (once we had performed a similar research on simplified relations between gas emissivity and flue gas composition instead of using complicated spectral models) the first approach is accepting the previous developed correlations as a guideline for developing further extensions or even new approaches; as you have done so. But moving further needs clarifying two distinct approaches: 1- Are we looking forward to develop empirical or semi-empirical equations? or 2- Are we trying to develop new theoretical equations or even formulate a new theory for describing the phenomena? As any of this approaches means different ways of research as I know you are already aware of.

I think despite your final approach, the very first step is developing a mathematical relation between emissivity and thermal conductivity. One of the best approaches when you are handling large amount of data and no quit well comprehensive mathematical relation in hand, is using "Gene Expression Programming". With this method you would even be able to understand that which physical variable is important and which one has not very strong influence on equation. Also there is no need to have a predefined function, where GEP even can predict the equation form for you. Despite this benefits the predicted equation may not carry too much physical meaning which needs theoretical intervention and interpretation, but as a first step for understanding the whole phenomena, GEP is a very reliable tool. For more information on GEP and also getting to know one of the best softwares developed for it (GeneXproTools) visit : http://www.gepsoft.com/

Interesting paper for thermal/tactile vision transducer because Kenshalo measured same psychothermal impact of thermal conductance and emittance. Equating their classic formula suggests

1234 Kelvin^4 *5.67E-12W/cm^2= k* jndT/dz.=0.003 W/cmC* 0.0015C/3.4E-7cm

however our hypothesis about "hot dots" felt like cool pin pricks while seen on FLIR monitor.

John J Stapleton.

Thank you for insight about psycho-thermal or psycho-physical stimuli of the thermal properties of skin, et cetera. This field of inquiry is a bit beyond my expertise, yet I have begun an informal research/searching from your recommendation. It appears Dr. Dan Kenshalo is or has been a primary investigator for the application of temperature studies in the psycho-physical field of inquiry. However naively, I noticed that one researcher indicated that cool (cold) sensitivity receptor sites outnumber warm (hot) sensitivity receptor sites by 30:1, which could help explain or direct further analysis for your hypothesis. But then again my focus is experimentally limited to non-organic physical (physical chemistry) materials. Are you able to direct me to the documented source material for the "classic formula suggest ..."? Your initial Kelvin temperature appears too high for organic materials in my understanding.

I appreciate your recommendation for consideration.

Doctor Hargis,

Université Suisse Privée St Cléments, Lausanne, Switzerland

Department Engineering Science

Position Post-Doctoral Researcher - Thermal Physics

Thankyou for your quick, insightful comments.

KeyPublications [1] Kenshalo, D.R., Spatial Summation...Journal of Comparative Physiological Psychology 1967, Vol.63, No.3, 510-515; Warm & Cool Thresholds...Perception & Psychophysics, 1968, Vol.3 (2A); Temporal Course...Science, 4March1966 1095, 1096[1] , Holman:s Heat Transfer; Omnispectravision SPIE Vol 270, 1981, 3 Color IR...SID 1982 evoked 5-6 requests of SID Chair Stapleton to design for the blind,eg. VT patent 648999

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Yes I long wondered about Dr. Kenshalo’s seminal work. (ABC=dxdy(dT/dt)jndT= 0.48 akin to PV=kT combine Charles & Boyle) Using the Fick or Fourier equation with arguable skin depth & conductivity, the Watts/cm^2 fell in the range of blackbody emittance such as 1234.009 Kelvin which is very short duration, approximately 1 microsecond over 1/60 sec per 1mW/cm^2 FCC/FDA. MIT C Jones re-presented Kenshalo data but did not extrapolate as VT. Several documents on thermo-receptors are in the e-book available as PDF on Researchgate or MS Word email attachment. I suspect nociceptors.