# Combining thermal conductivity

• HalcyonicBlues

#### HalcyonicBlues

If thermal resistance is additive, then how can the thermal conductivity of two (or more) materials be combined? Can it? Eg. a wall filled with straw and air, a hollow brick, a mixture of polystyrene and fibreglass wool (just some random ideas off the top of my head).

It's quite easy for laminations such as walls because if you use the right units..

Thermal Resistance = 1/thermal conductivity

so if the total thermal conductivity of material n is TCn then

Total Thermal Cond. = 1/(1/TC1 + 1/TC2 + 1/TC3...+ 1/TCn)

Be careful about the units used for any source data. Many countries use R-Value or U-Value to mean different things. Sometime data is specified "per unit thickness" (eg per meter thickness) and sometimes the data is provided for the particular thickness of the product. It's not unknown for advertisers to try and confuse people by quoting the figure for the raw material used (eg per meter thickness) leaving you to work out how good (or bad) their 5mm thick product really is compared to thicker alternatives.

http://en.wikipedia.org/wiki/List_of_thermal_conductivities

is the value per meter thickness. You will need to scale the value to suit whatever thickness of lamination you have before working out the total for a combination. Not hard to do. If you have 100mm rather than 1 meter then the Thermal Conductivity goes up by a factor of 10.

For info I believe the best insulator is still Silica Aerogel which for any given thickness is about twice as good as PIR and PUR foams. Bit expensive though.

1 person
Example. Calculate total thermal conductivity of 100mm of concrete plus 150mm of polyeurathane.

From Wikipedia..

TC of 1m concrete is about 1 (eg a good conductor of heat)
TC of 1m Poly is about 0.02 (eg a good insulator)

both W.M-1.K-1

Scale..

TC of 100mm concrete = 1 * 1000/100 = 10
TC of 150mm Poly = 0.02 *1000/150 = 0.133

Total TC = 1(1/10 + 1/0.133) = 0.131

Which is quite close to that of the Poly alone.

Experts may say it's a bit more complicated than that. To do it accurately I think you need to take into account surface emissivity of the various layers but the above is usually good enough for designing houses.

1 person
The above works for laminations where heat goes through each one after the other in "series".

Something like a wall with a window or a brick with a hole in has two materials effectively in "parallel". You can work out the thermal resistance or thermal conductivity for the combination using area weighting.

Some objects will have a combination of materials in series and parallel. It's just a matter of breaking it down into manageable layers/bits. There is an analogy with electrical resistors which can be connected in any number of ways and combinations.

It's interesting to read how aerogel works. All to do with pore size and the mean free path of gas molecules.

I've no idea if it's possible to calculate the conductivity of mixtures like bread dough - I imagine it's best to measure it!

Andries Stucki and HalcyonicBlues