Measuring the thermal conductivity of insulation

As I mentioned previously, I am currently obsessed with the thermal insulation I will be applying to the outside of my house.

I have checked that it should be safe from the point of view of flammability (link), but the question of how will it perform thermally still remains.

The insulation product I have chosen (Kingspan K5) has truly exceptional specifications. This allows me to clad the house with 100 mm thickness of K5 and achieve the same insulation level as 160 mm of expanded polystyrene (EPS).

In this article I describe the tests I have performed to show that the K5 insulation does in fact match the specified level of insulation in practice.

Conduction through Closed-Cell Foams

Heat travels through materials using three mechanisms: conduction, convection and radiation.

Closed-Cell Foams – in which sealed ‘cells’ of gas are surrounded by solid ‘walls’ – inhibit all three methods of heat transfer.

  • Conduction through the solid is reduced because the cross-sectional area of solid through which heat can travel is reduced.
    • Conduction is through the thin walls of the cells.
  • Conduction through the gas within the cells is very low
    • The thermal conductivity of gases is much less than that of solids.
  • Convection in the gas within the cells is inhibited because each cell has just a tiny temperature gradient across it
    • Smaller ‘cells’ inhibit convection more strongly.
  • Radiation across each cell is inhibited because each radiating surface sees a surface at almost the same temperature.
    • Smaller ‘cells’ inhibit radiation transfer more strongly

So a foam optimised for low heat transfer would have very little solid present and consist mainly of gas cells. But such  a foam would be very fragile.

So practical building materials balance cell size and wall thickness to produce materials that are sufficiently strong and not too expensive to manufacture.

This article (link) from the 10th International Conference on District Heating and Cooling summarises the properties of polyurethane (PU) foam that affect its thermal performance. I have summarised the calculations on the figure below.

  • The graph shows thermal conductivity on the vertical axis and foam density on the horizontal axis.
  • The red square shows the specified thermal conductivity of Kingspan K5 and the Blue Diamond shows the specified thermal conductivity of EPS.
  • Notice the low density of the foams compared to say bricks (~2000 kg/m^3)
  • The three solid lines show calculated contributions to the thermal conductivity of PU Foam as a function of density.
  • Notice that K5 has a specified thermal conductivity which is lower than that of still air.

All the data on the graph correspond to low thermal conductivities, but the differences are significant. The thermal conductivity of the K5 is around two thirds that of the EPS and so the same insulating effect can be achieved with just two thirds the thickness. Or alternatively, the same thickness of K5 can achieve one third less heat transfer than EPS.

The lowest achievable thermal conductivity that can be achieved is limited by thermal conduction through the gas in the cells. And so the K5 achieves its low conductivity by having cells filled with non-air gases – probably mainly carbon dioxide.

However I was sceptical…

These were just specifications. My erstwhile colleagues at NPL spoke often of the ‘optimism’ of many thermal transfer specifications. Could this material really have a thermal conductivity which is lower than that of still, non-convecting air!

…So I decided to do some tests…

I built two boxes out of 50 mm thick sheets of EPS and K5, sealing the joins with industrial glue.

I then heated a cylinder of concrete that I happened to have (100 mm diameter x 300 mm long weighing 5.14 kg) in the oven and heated it to around 50 °C – roughly 1 hour at the lowest gas setting.

I then placed the concrete in the box along with two data-logging thermometers – one at either end of the cylinder – and sealed the box with another piece of insulation.

I recorded the temperatures every minute for somewhere between 10 and 24 hours and measured the rate at which the concrete cooled.

The cooling curves for EPS and Kingspan K5 are shown in the figures below.

  • The two thin lines correspond to the readings from the two thermometers and the bold line corresponds to their average.
  • The (dotted red curve – – – –) shows a theoretical model of the data with the parameters optimised using the Excel solver.
  • The (dotted red line – – – –) shows a estimated time constant of the exponential temperature decay.
  • The (dotted blue line – – – –) shows a estimated background (room) temperature.

This data allowed me to establish two things.

  • Firstly, by simply comparing the time constants of the cooling curves (494 minutes and 801 minutes), it was clear that the K5 really does have a thermal conductivity which is about 40% lower than EPS.
  • Secondly, by assuming a value for the heat capacity of the concrete and that the heat flowed perpendicularly through the walls of the box I could estimate the thermal conductivity of the two materials. I found:
    • K5 thermal conductivity = 0.021 ± 0.001 W / m K
    • EPS thermal conductivity = 0.035 ± 0.001 W / m K
    • The uncertainties were estimated by analysing the data from each thermometer individually and then their average.
    • To my surprise, these figures agree closely with the specified properties of both EPS and K5

So my scepticism was – it seems – misplaced.

Summary

I am relieved. In my previous article I showed that the K5 has good flammability resistance and in this article I have shown that it really does have excellent thermal performance.

Being confident of these properties I am looking forward even more keenly to getting the material onto my house and snuggling in for a long cold winter.

By the way..

The Blue Maestro dataloggers that I used (link) are fantastically easy to use and come strongly recommended.

2 Responses to “Measuring the thermal conductivity of insulation”

  1. Richard O Hegarty Says:

    Great Article. I’m a researcher from a university in Ireland and we are carrying out in-situ u-value measurements. In one of our recent tests we found that the wall was performing a lot worse than as per design. The wall was constructed with k5 so I did what one does these days and went to Google….hence my presence here.

    How exactly did you calculate the conductivity values from the data you had: “by assuming a value for the heat capacity of the concrete and that the heat flowed perpendicularly through the walls of the box I could estimate the thermal conductivity of the two materials” Did you use the diffusivity equation?

    Hope to hear back. I’m now moving on to some of your other articles.

    • protonsforbreakfast Says:

      Richard

      Thank you for your kind comments. It is easier to explain what I did if I send you the spreadsheet. I will send it by e-mail to the logged e-mail address at UCD.

      In situ u-value tests are in reality the only ones that matter, but the heat flows are small and the real world environment complex that I can imagine that uncertainties are large. I did try making such a test myself but I made a very very basic error which was utterly humiliating. But being retired I no longer care!

      So I put my faith in just the crude assessment of the gas consumption within the house relative to the difference between the internal and external temperatures. I am confident of the overall figure (W/°C) from this analysis – but estimating the relative contributions of windows, doors, floors, rooves and air flow is highly model dependent.

      Anyway. I will annotate the spreadsheet now and send it shortly. If anyone else reads this and wants a copy, please drop me a line.

      Best wishes

      Michael

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