Units of thermal conductivity

[Carl Wilson 4Participant @carlwilson4]

Assistance required please:-

I'm currently looking at a reference that gives thermal conductivity of a material as a variable in a design equation. The units used are imperial.

Now, there is often a lot of argy bargy about metric/SI versus imperial units…there is an ongoing series in the SMEE journal based on this. Personally, I'm easy and I often have to use both and am happy with that.

That said, this next thing has me flummoxed somewhat. I know that in SI the unit of thermal conductivity is the watt per metre kelvin (W/m-K). In imperial units this is expressed as British thermal units per hour per foot deg Fahrenheit (or deg Rankine) (Btu/hr ft deg F or deg R).

So far so fine…but I'm currently looking at a reference that is telling me that a certain material has a thermal conductivity measured in Btu/in^2-degF/in

Whats that all about? Be grateful if someone could throw me a bone.

[Carl Wilson 4Participant @carlwilson4]

[Neil WyattModerator @neilwyatt]

The brain understands the area as different from the thickness (of the wall etc.) but as doubling the area an doubling the thickness cancel out, the units are given in feet, inches or metres.

The odd formula doesn't do this so has square inches divided by inches, which cancel out to inches.

Other than that, the unit of time seems to have been lost from the formula, as a BTU is an amount of energy, rather than a rate of doing work (like a Watt).

Try here for a conversion table

Neil

[Carl Wilson 4Participant @carlwilson4]

Yes. That is why I could not understand the units;- no unit of time. A watt is one joule per second. So it should be Btu/sec or Btu/hr…

Thank you for the advice.

[CabengParticipant @cabeng]

Time isn't missing, Neil, what's wrong is that the equation is for thermal conductance, not conductivity.

Thermal conductance is the heat transfer per unit time, per unit area, per unit temperature, per unit thickness . If you see what I mean!

A.k.a. how much heat (Btu) flows in one hour through one square inch (cross section) of material, one inch thick, with one degree F of temperature difference across it.

IN SI units, Joules/sq.m./degC/m/sec. I think.

Thermal conductivity is a property of the material itself, independant of the structure of the object through which the heat is passing.

Thermal conductance depends on thermal conductivity of the material, but in conjunction with the dimensions of the object through which the heat is passing..

Thermal conductance is the reciprocal of thermal resistance.

Caveat – I'm rusty, having given up heat transfer calculations 3 years ago when I retired, and although I'm bilingual (well, more than that, but I'm not sure that quadlingual is a word – I can (or could) work in fps, cgs, mks, and SI) in most units, I haven't used imperial units for heat transfer in over 40 years! So any errors in the above are down to atrophy of the relevant brain cells!

[Carl Wilson 4Participant @carlwilson4]

Hello Cabeng,

Thanks for that – thermal conductance, of course. I am also having to look at thermal resistance in the numbers I'm crunching. I was wondering if I might get in touch with you by email? I have a few questions that would definitely benefit from your experience, but which may not be of much interest to the rest of the posters here.

Carl.

[Neil WyattModerator @neilwyatt]

Thanks Cabeng – I was just extrapolating from a-level physics, many years ago!

Presumably thermal resistance is just the reciprocal of thermal conductivity?

Neil

[CabengParticipant @cabeng]

Carl: yes, ok, send me a PM. But that's with some reluctance as a) I really am rusty these days, b) my experience of heat transfer calcs is in a rather narrow speciality, and c) forget the Btu, I'll have to talk in Watts etc.

I doubt I'll be of any assistance, so don't get too hopeful!

Neil: see my response above, thermal conductance is the reciprocal of thermal resistance.

[Carl Wilson 4Participant @carlwilson4]

Hello Cabeng and Neil,

Well, I finally got to the bottom of the mystery. The reference I'm working from is one of the NASA special publications, SP125. The section in question was talking about the properties of Alloy X750, which is a type of Inconel.

I tried as best I could to work around the idea that they were talking about thermal conductance, as we'd said, but it just wasn't making any sense. So, reading ahead a bit, I found the same units referring to thermal conductivity, but this time with a time dimension (seconds). So it was a simple misprint – they were referring to thermal conductivity after all. So instead of Btu/in^2-degF/in it should have read Btu/in^2 – s -degF/in. Alloy X750 was shown to have a value of 3.2 x 10^-4 in these units, at a temperature of 1200 deg Rankine, i.e. ~ 740 degF.

Normally in imperial units thermal conductivity is given in Btu/in/hr/ft^2/degF. In these units, Alloy X750 has a value of ~ 122 at 740 deg F. In order to convert, if this value is "X" and the value in Btu/in^2-s-degF/in is "Y", then:-

Y= 144/(X * 3600)

Using the above example, 144/(122 * 3600) = 3.2 x 10^-4. Mystery solved.

Cabeng, will PM you in the next few days, would be very good to add you to my small band of experts whom I turn to for support and counselling. Thanks in advance and thanks again for your interest in my original post.

 

Edited By Carl Wilson 4 on 19/12/2014 09:26:21

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