Effusivity Smackdown or Standoff?

One of our engineers attended the short course “Thermal Management from an Industrial Point of View” at SEMI-THERM 25 last March presented by Clemens Lasance and Wendy Luiten.  One of the topics that I found really interesting from the course material was that related to contact temperatures.  More specifically, the contact temperature for two semi-infinite bodies, one of them being you.  After reading through their material I referred to my two heat transfer books to study it further but came away feeling disappointed.  My other source of education, besides talking to other engineers, is googling until I find what I am after.  I hit the mother lode when I googled “interfacial temperature when two semi-infinite objects at different temperatures touch”.  The key parameter is something called effusivity, which is a combination of the specific heat, density, and thermal conductivity.  It must be a new invention because it wasn’t in my heat transfer books, or maybe they had already used that greek letter for emissivity and therefore couldn’t include it.  For completeness, the equations for effusivity and contact temperature are below:

effusivity contact_temperature

When I think about transient conduction for those bodies that don’t have the distinction of being semi-infinite I see it as a smackdown between the two bodies in contact.  That body which is better able to absorb  heat  without changing temperature (high density, specific heat, and mass) and/or is more insulated (low k) is going to win.  The smaller one (thermally speaking) may put a chink in the armor of the larger but not much more.  When two bodies are considered to be semi-infinite the competition is a lot closer , a 15 round battle.  One will be more dominant than the other but it could be a long fight.  In the case of a human touching a surface we presumably have enough sense (both in the head and in the finger) to end the battle early if necessary.

It is interesting to me, and please correct me if my thinking is wrong, that the contact temperature is not a matter of opinion or pain tolerance.  When you touch something you are correctly detecting that temperature, the contact temperature. You are not properly detecting the surface temperature though.  So, to state it directly, there exists a contact temperature which is not the surface temperature of either body, unless both bodies are the same temperature.

Surface temperatures are a real product safety issue which Clemens and Wendy referenced from the link, found here, at the RoSPA website.  For consumer products it is also important from a perceived operation standpoint.  If the product feels hot, the consumer may think it is not operating normally or was poorly designed.  In either case the consumer will not be impressed.  There are some strategies for keeping things cool enough on the inside without sacrificing a “cool to the touch” enclosure temperature that I will discuss some time in the future.

Lastly, in all my googling it seemed to me that this topic was much better addressed by the physicists than the thermal engineers.  Draw your own conclusions.  Thanks to Clemens Lasance and Wendy Luiten for including this topic in their course.  Another great resource for further reading is from E. Marin’s paper, “Teaching thermal physics by touching”.  I found it here.

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Posted July 8th, 2009, by

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Commented on July 10, 2009 at 2:59 am
By Robin Bornoff

I find it fascinating that, if the two bodies are large enough, despite heat being transferred from the hotter one to the colder one on contact, the actual interface (touch) temperature remains constant. I suppose the pain to fingers occurs over time due to some kind of cooking (eurgh) as opposed to contact temperature itself increasing.

[…] not get bogged down with the temperature we feel when we are holding the device (that was discussed here).  Of the parameters mentioned, there are a couple of that won’t change significantly, T∞ […]

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