# How to calculate the thermal conductivity of a composite material

Very new to thermal conductivity calculations, so I'm aware there are already queries on here that may cover this, but I'm struggling to apply them to this instance.

I'm trying to calculate the U-Value of a composite material. The data I have is the thickness of the materials used, and their thermal conductivity in W/mK. How do I use these to calculate the thermal conductivity of the material as a whole?

My attempt so far has been to calculate the individual R-Values by dividing the thickness of the material in metres by the W/mK, and then sum those R-Values, and then divide 1 by that sum to get a U-Value. I'm sure I'm off somewhere though, as the U-Value has ended up huge!

Appreciate any assistance, fairly sure it's a simple answer for someone familiar with the topic!

• Think about them like parallel resistances. Commented Feb 23, 2023 at 10:22
• First result of a google search; kingspan.com/tr/en/knowledge-articles/… Commented Feb 23, 2023 at 10:23
• Thanks, does that mean that the method I've described above is actually correct? Commented Feb 23, 2023 at 10:27
• Anything divided by 1 stays the same so no. Commented Feb 23, 2023 at 10:29
• Sorry, typo! Edited now - I'm dividing 1 by the sum of the individual element's R-Values to arrive at a U-Value Commented Feb 23, 2023 at 10:34

## 1 Answer

The answer depends on the configuration of your composite material.

If the materials are arranged such that heat must transfer through each and every material in sequence, you would treat those material elements as a circuit in series: the total resistance to thermal conductivity is equal to the sum of the thermal resistances (R total = R1 + R2 +... Ri). In addition, the thermal "current" is your heat flow (Q) and the thermal "voltage" is the temperature difference (T2-T1 = Delta T). Simply solve the equation using the equation I = V / R or Q = Delta T / R total

If, however, the materials are arranged such that heat may transfer through one material or another, you would treat those material elements as a circuit in parallel: the inverse of the total resistance to thermal conductivity is equal to the sum of inverses of the thermal resistances (1 / R total = 1 / R1 + 1 / R2 +... 1 / Ri). The thermal "current" and "voltage" are the same as shown above.

If you have a combination of the two, you will solve for an R at whatever locations are arranged in parallel and then use them in conjunction with the sections that are in series in the Q = Delta T / R Total equation.