In most geometry inverse problem, information like the temperature measurement on the surface is use to detect the shape and location of a defect. My question is: is it possible to measure the temperature distribution or temperature gradient of a material up to certain depth? What kind of device is used for this kind of problem? Can you recommend a study that deals with such kind of problem?

  • $\begingroup$ You can google 'Thermographic impact damage on composite' to get some ideas. $\endgroup$ Oct 6 '18 at 8:32
  • $\begingroup$ How deep are you thinking? And what kind of material? $\endgroup$
    – user190081
    Oct 6 '18 at 13:33
  • $\begingroup$ I am not actually interested on how deep it could but only on the possibility of measuring the temperature up to some depth. $\endgroup$ Oct 8 '18 at 3:57
  • $\begingroup$ Theoretically it's possible, it is called differential energy equation but it's just an approximation, I think you need at least two boundary condition to solve the DE. $\endgroup$ Oct 8 '18 at 14:08
  • $\begingroup$ @SamFarjamirad can you recommend a book or article that tackles such topic. I would be glad to explore more on the subject. $\endgroup$ Oct 9 '18 at 14:08

Yes, in material engineering they call it Thermography. By Radiating heat on the surface or infrared radiation we can map the temperature distribution.

The heat transport throughout the material is affected by defects (holes, fracture ...). Also the heat that produce during the fracture of material can be detected in this technic.

Usually a laser puls is used to send the energy throughout the material and a thermographic camera to visualise the temperature gradient.

This technic is very popular to find delimitation in fiber re-infocred plastics, or defects in welding connections between metals and composites.

I had a brief course in college, named fracture mechanics, which deals with this kind of problem but not concentrated. I think material engineering and science is the right field. Also the basic knowledge of heat transport and thermodynamic is indispensable to understand what is happening.

  • $\begingroup$ Thermography will only help you with surface (or near surface) measurements. As I understand the question OP is interested in measuring the temperature distribution inside the material. $\endgroup$
    – user190081
    Oct 6 '18 at 13:47
  • $\begingroup$ I am familiar with thermography, but, can you explain what do you mean by `near-surface'? $\endgroup$ Oct 8 '18 at 4:00
  • $\begingroup$ @JulienneFranz I was thinking of examples like hot steam running thru pipes or something like that, where you are able to detect the steam thru the thin wall of the pipe...in retrospective, I would exclude that "near surface" part form my previous comment. $\endgroup$
    – user190081
    Oct 8 '18 at 13:27
  • $\begingroup$ @user190081 do you have any particular reference for such kind of study or experiments? I am really interested to know more about the problem and how it is dealt with theoretically, numerically and experimentally. $\endgroup$ Oct 9 '18 at 14:13

Use infrared.

"Contactless measuring infrared thermometers are well known for temperature measurements. This also applies for the measurement of metals"

"Next to time, temperature is the most frequently measured physical property. Infrared temperature measurement devices define temperatures through the infrared radiation delivered by the object - without contacting the object."

See the linked article for further explanation of this method, which seems meeting your interest. Non-contact temperature measurement on metal surfaces via infrared


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