Use Thermal Conduction Value to Find Apparent Temperature of Material if Touched

I'd like to calculate the "apparent temperature" of a material if you touched it, using the material's thermal conductions value (k).

I've found tables listing the thermal conduction of different materials (http://www.physicsclassroom.com/class/thermalP/Lesson-1/Rates-of-Heat-Transfer, and a small table here: http://cfbt-us.com/wordpress/?p=1110). How can I calculate what it might feel like to touch a block of Copper vs a brick or wood, all at the same temperature, such as 50 degrees fahrenheit.

Everything I've found either mentions in vague terms that "metal feels colder" (or hotter, given specific circumstances), or talks about finding the rate of the transfer between two substances. I'd love to be able to calculate "Touching cast iron at 40 degrees will feel like __ degrees to your fingers".

I'm guessing finding a precise value would be difficult because factors such as the thickness of the material, the pressure which you're touching, etc, would have an impact... but if there's a way to find a relatively accurate answer, that would be incredibly interesting!

• It probably isn't possible to find precise values because, as you suggested, the apparent temperature would depend on the pressure with which you're touching. But for a starting point for any analysis, I think that you really want to look up the "thermal diffusivities" of various materials rather than their thermal conductivities. Thermal diffusivity is a better measure of how cold an object will feel to the touch because it involves not only the thermal conductivity of the object, but also its heat capacity.
– user93237
Commented Jun 14, 2017 at 17:36
• Thanks Samuel. I'll research "thermal diffusivities". Not familiar with that term. Thanks!
– bzle
Commented Jun 14, 2017 at 19:06

It has to be relative to something else.

The "apparent temperature" (at least in a very strict sense) is still the temperature that metal is at. That is because people feel heat not temperature.

It takes more heat, so it feels colder but its temperature could be the same as the surrounding air.

You could compare it to non-moving air at the same temperature; to which it would feel colder, and you could determine the equivalent temperature of stagnant air that would take that much heat from your body.

To do that first you would need to find the heat lost to the object you want the equivalent temperature of. Then you calculate what temperature the air (or whatever you are using for a comparison) would need to be at to get the same amount of heat transfer.

To your body, it would feel like the equivalent temperature of the metal; because the body can only measure heat flux, not temperature directly.

• Thanks JMac! I think you understand what I'm trying to find here. Perhaps "perceived temperature" would have been a better phrasing. I like your idea of comparing the feeling to stagnant air, but I'm not sure how to perform that calculation either! I do appreciate you describing what the calculation would need to do. Anyone know what the equation for achieving this would be?
– bzle
Commented Jun 14, 2017 at 18:50

This is a good intuitive question, to which the answer is that it does not make sense.

Because: We do not feel temperature!

A sentence like...

Touching cast iron at 40 degrees will feel like __ degrees to your fingers

... doesn't make any sense.

What we feel is heat transfer. How much energy that passes into our fingers per second.

And heat transfer $\dot q$ can be large or small depending on different parameters. It depends on temperature $T$, yes, and also on thermal conductivity $\kappa$ and contact area $A$ and any contact resistance $R$ and the heat capacity of the material $c$ and it's density $\rho$...

See for example the heat conduction equation (Fourier's law):

$$\dot q=A\kappa \frac{\Delta T}{\Delta x}$$

... which transfers heat as long as there is contact and a temperature difference, and the heat transfer equation:

$$\dot T=\frac{\kappa}{c\rho} \frac{dT^2}{dx^2}$$

... which in more details looks at how the temperature changes along the way.

So unfortunately, saying that something will feel like a specific temperature makes just as little sense as saying that it feels like a specific heat capacity or a specific contact area. All these parameters are involved and together cause heat flow.

• The contact area is something you can approximately account for in the math. You can solve for heat transfer per unit area, which is really to some extent what your body will feel (you can tell approximately if something is extremely hot and extremely localized, or warm over a larger area); it's not like you just have 1 nerve in your body that says "you have this much heat going in". Assuming you want the temperature at the exact moment, and it's relative to something else (like stagnant air), you could come up with something. You just need to make it clear what you're talking about.
– JMac
Commented Jun 14, 2017 at 18:42
• Thanks Steeven. I know my terms aren't accurate for describing what's going on, but there's got to be a way to give a general estimation for what you can expect. For example: An average person that walks into their basement (with an assumed temperature and moisture content of __) and puts their finger on __ material at a normal/reasonable pressure for 1 second, can expect to experience a feeling similar too __ degrees f. You probably still think this doesn't make any sense... The forecast has a "feels like" temp instead of the actual temp, just to help people. I want to find that for objects.
– bzle
Commented Jun 14, 2017 at 19:04