Rapid, in situ Thermal Conductivity Measurements—Even in Moist Insulating Materials

Dr. Gaylon Campbell shows how to measure the thermal conductivity of wet insulation with a 5-minute read time. These previously impossible measurements are now possible through advanced electronics and analytical methods.

Steady state methods for measuring thermal conductivity in insulation are painstakingly slow. The temperature gradient inherent to the method also induces moisture movement within moist samples, making it unsuitable for such measurements. This seminar describes a new algorithm, used with a line heat source, to measure thermal conductivity of insulating materials in one minute, even in the presence of moisture.

In this 30-minute webinar, Dr. Gaylon Campbell, world-renowned environmental measurement expert, describes:

  • The science behind the transient method, how to apply it, and how it performs on insulating materials
  • How moisture affects the thermal conductivity of insulation
  • Why only transient methods correctly measure the thermal conductivity of insulation when moisture is present
  • How to determine the volumetric specific heat of insulation, to use as input to the measurement

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Our scientists have decades of experience helping researchers and growers measure the soil-plant-atmosphere continuum.


Dr. Gaylon S. Campbell has been a research scientist and engineer at METER for 19 years following nearly 30 years on faculty at Washington State University.  Dr. Campbell’s first experience with environmental measurement came in the lab of Sterling Taylor at Utah State University making water potential measurements to understand plant water status.  Dr. Campbell is one of the world’s foremost authorities on physical measurements in the soil-plant-atmosphere continuum.  His book written with Dr. John Norman on Environmental Biophysics provides a critical foundation for anyone interested in understanding the physics of the natural world.  Dr. Campbell has written three books, over 100 refereed journal articles and book chapters, and has several patents.


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Today’s presentation will be about 30 minutes from our presenter Dr. Gaylon Campbell, who will discuss the new TEMPOS thermal properties analyzer installation mode. Dr. Campbell has been a research scientist and engineer at METER for over 20 years, following nearly 30 years on faculty at Washington State University. His first experience with environmental measurement came in the lab of Sterling Taylor at Utah State University, making water potential measurements to understand plant water status. Dr. Campbell is one of the world’s foremost authorities on physical measurements in the soil plant atmospheric continuum. His book written with Dr. John Norman on environmental biophysics provides a critical foundation for anyone interested in understanding the physics of the natural world. He has written three books, over 100 refereed journal articles and book chapters, and has several patents. So without further ado, I’ll hand it over to Gaylon to get us started.

Okay, thank you for being with us today to talk about rapid in situ thermal conductivity measurements in dry and moist insulating materials. We’ll start by defining the thermal conductivity and giving some background on how it’s measured. Then we’ll consider transient line heat source methods and show what we at METER have done to successfully modify that method to make it suitable for measuring thermal conductivity in insulation. We’ll show how the measurement is made. We’ll end by presenting some data from experiments that we’ve done here in our laboratory that show the moisture dependence of thermal conductivity in a couple of insulating materials.

We’ll start with defining some of the terms that we’ll use here. The thermal properties of a material have to do with its ability to transmit and store heat and the speed with which thermal disturbance can propagate through it. The thermal conductivity of the material is a measure of its ability to transmit heat. It’s equal to the flux density of heat across a plane in the material divided by the temperature gradient at that plane. The volumetric specific heat describes the quantity of heat that a unit volume of the material can hold per unit time and per unit temperature change. We write it as the product of a density of the material and the gravimetric specific heat. The thermal diffusivity of a material tells us how fast thermal disturbances will propagate in that material. And we compute it as the ratio of the conductivity to the volumetric specific heat. We’ll talk about the measurement of thermal conductivity in insulating materials today.

Instruments to measure thermal conductivity fall into two classes, a steady state methods and transient methods. Steady state methods are ones that are more typically used to measure thermal conductivity of insulating materials. Both guarded hot plates and heat flow meters are used for that. The transient methods like the line heat source are widely used for measuring thermal conductivity in materials that have higher thermal conductivities than insulation. But for reasons that I’ll discuss a little later, they haven’t worked well for insulation in the past. The basis for steady state methods is the establishment of a steady one dimensional heat flow through the material under test and then measuring the heat flux density H in the equations here, the thickness of the material Δ [delta] x in the equation and the temperature difference across it. The thermal conductivity is computed as shown in the equation by multiplying the heat flux density by the thickness and dividing by the temperature difference. The transient line heat source method uses a needle, inside which is a heater and a temperature sensor. You place the needle in the sample, you run a current through the heater for a short time and measure the temperature response of the needle, then find the conductivity that best matches a simulated temperature response with the measured device. The one that gives the best match will be the thermal conductivity of the material.

Here’s an approximate equation that usually use to get conductivity, as k in the equation, from the heat input, q in the equation, and the set of temperature measurements that we make. The graph on the right shows data. This is not for insulation, this is for soil that has a much higher conductivity than insulation does. And if we plot the temperature versus the logarithm of time, we typically get a straight line. If we divide the heat input q by four pi times the slope of that line, we get out a thermal conductivity for that material that works well for high thermal conductivity materials but doesn’t work well for insulation.

Both the steady and transient methods measure thermal conductivity. They each have their niche though and don’t typically compete much with each other. The steady state methods are direct with simple calculations. When they’re properly done, they can be very accurate for insulations. Measurements are made on relatively large samples in a laboratory, and this can have both advantages and disadvantages. Since a steady state needs to be established to get the measurement, it typically takes a long time to do that. And maybe a measurement or a few measurements a day is all that you can make. One major drawback of steady state methods is they don’t work for moist samples. And we’ll return to that point in a few minutes and discuss it more fully. Transient methods, on the other hand, are portable, fast, to take a reading only requires a couple of minutes with that method. The measurements can be made in situ without taking a sample, and the measurement doesn’t induce moisture movement. The measurements, however, are typically less accurate than steady state measurements. Measurements in heterogeneous materials are hard to interpret. A stable thermal environment is required for the measurements.

I want to spend a minute talking about thermally induced moisture flow in porous materials. The graph that I show here shows what happens in a moist soil when it’s subjected to a temperature gradient. As soon as the temperature gradient is applied, water moves away from the high temperature side and toward the low temperature side. The graph is for a 10 centimeter long soil column, and it’s subjected to a 10 degree C temperature difference. The initial water content of the soil is about 17.5%. But after about six hours, the water content at the cold face is 21% and at the hot face, it’s 10%. After four days, the left six centimeters of soil, the cold end, sit around 23% water content, and the right four centimeters is around 5% water content. This graph is for a soil, but the same thing happens to wet insulation or any other moist, porous material. The temperature gradient creates a vapor pressure gradient that results in water transport. This happens with moist insulation when we subject it to a temperature gradient in a steady state apparatus. Since the moisture affects the thermal conductivity of the insulation, steady state methods don’t give correct measurements of thermal conductivity in moist insulation. Transient methods inject only a short heat bolt to make the measurement. So moisture redistribution is negligible during the short bolts.

Now a few slides back I showed the equation that we normally use for the transient line heat source. They were developed assuming the heat source really is a line that doesn’t have any mass, doesn’t have any heat capacity. The needle we use in these measurements, of course, has both mass and heat capacity. For denser samples like soil, the needle heat capacity is similar to that of the sample. So the line heat source assumption works. But for insulation, the needle heat capacity can be 60 times that of the insulation. So those simple equations just don’t work. It’s possible to make a numerical model, however, that can correctly account for the heat capacity of the real needle. We can use that in an inverse calculation to determine thermal conductivity. Now, the analysis a lot more complicated, and we also need to know the volumetrics specific heat of the sample to get an accurate value for the conductivity.

The diagrams on the left here show different levels of complexity in the numerical model for the heat flow from the needle. The top diagram is for the line heat with no heat capacity. The second diagram, second one down, shows a simplified sensor with a heater and a thermometer. The bottom diagram takes into account the epoxy and stainless steel, as well as the heater and temperature sensor. The graph on the right compares the temperature responses of these three models and measurements in glycerin. We’ve conducted extensive testing of this method for determining thermal conductivity of insulating materials. And we’ve shown that an inverse method incorporating this numerical solution that the Fourier heat transfer equation does a good job of determining thermal conductivity in the insulation. However, it’s necessary to supply an independently measured volumetric specific heat to get good results with this. So the approach for this measurement is to insert the needle in the insulation, allow it to come to temperature equilibrium, then apply a constant current to the heater in the needle, and record the temperature at one second intervals for a minute. We then need to determine the volumetric specific heat in a separate experiment. We use the Levenberg–Marquardt nonlinear least-squares algorithm to find temperature offset and thermal conductivity that makes the model match the measurements. The conductivity that we find is the thermal conductivity of the insulation. Fortunately, the solution isn’t very sensitive to uncertainty in the volumetric specific heat. A 20% error in specific heat gives only a 5% error in conductivity. Some methods for finding thermal conductivity of insulation determine just the thermal diffusivity from the measurement that is made. These also require an independent measurement of volumetric specific heat to get the conductivity, but with those methods, a 20% error in specific heat would result in a 20% error in the conductivity.

The volumetric specific heat is the product of a density and a gravimetric specific heat. The density is easily measured, and that’s often the largest source of uncertainty in the calculation. The couple of points here talk about how to make that measurement that you cut a piece material to make a right rectangular prism. You determine its length, width and height, unless it’s volume, you could weigh that then and get the density by weight divided by the volume. The table here is from the internet. It gives gravametric specific heat values for some of the common materials from which insulation is made. The calculation at the bottom shows the volumetric specific heat calculated for a styrofoam sample where we know the density and the gravametric specific heat.

Now let’s go through the procedure that we follow to make measurement with this method. Of course the probe can be inserted anywhere one might want to make a measurement, but it has a somewhat blunt end, so if you directly push it into a foam, you can tear the foam and leave gaps that will adversely affect your thermal conductivity measurement. It’s advisable to pre-punch or pre-drill tight fitting holes for the probe to go in as we did here. Here, we put two slabs together — the material we had was thin enough that we were concerned about the heat from the heat bolt going outside the boundary. So we put two slabs together, and then we put some additional insulation on the outside of that, just to provide better thermal stability for the measurement. The TEMPOS that we use to make the measurement supplies the power to do the measurement and records the temperatures at every second. This instrument is capable of resolving about a millikelvin in temperature, and record the temperatures when we make this measurement for a minute. For each material that you measure, you enter the volumetric specific heat before you start the measurement. And you just use the keyboard of the instrument to enter the number that you determined earlier. Now the TEMPOS does the simulations, and it finds the conductivity and the offset that best fit the data obtained in the reading to that model. Here’s an example of a set of data obtained on a styrofoam sample. The standard error of estimate for this data set is about eight millikelvins. And so we can tell from that that the TEMPOS does a good job of measuring, and that the model does a good job of fitting the data.

I hope it’s clear now from what I’ve presented the transient line heat source method that we use with the TEMPOS and our new algorithm that we put in the TEMPOS does a good job of measuring the thermal conductivity of insulation. I’d like to finish up with results of an experiment we did to compare the performance of two types of insulating materials in the presence of high ambient humidity. The two insulating materials are fiberglass and cellulose, which differ a lot in their ability to take up moisture. Now besides the TEMPOS for measuring thermal properties, METER makes and sells a vapor absorption analyzer that is shown in this picture on the right. And that instrument provides data that are useful for comparing these two materials. The graph on the left compares isotherms for the two materials. The horizontal axis is the water activity of the sample, or the relative humidity of air in equilibrium with the sample. The vertical axis is the water content of the material. Fiberglass takes up very little moisture until the humidity is above about 80%. And even at 95%, the water content is only about 7%. Cellulose, on the other hand, takes up a significant amount of water over the whole range of humidity, and at 95% humidity the water content is about 40%. Two lines that are shown here are for adsorption and desorption. Now we dried both insulation samples over desiccant, and then we placed them in a chamber that was maintained at a constant relative humidity of 90% for two days. We set the TEMPOS up to take repeated measurements every hour.

At the end of the experiment, we measured the water activity and water content of the samples, and final water contents and water activities are shown in the table at the bottom of the graph. Both samples have low conductivities when dry, the fiberglass around 3.2 kilowatts per meter Kelvin, and the cellulose around 3.4. Both increase as they take up water. The fiberglass reaches a stable conductivity around four milliwatts per meter Kelvin, but the cellulose continues to increase and as above five milliwatts per meter Kelvin after two days. The water contents we measured are consistent with the predictions from water activity in the isotherms that we showed in the last slide. Qualitatively, these results are about what we would have expected, insulation conductivity to increase with moisture content and cellulose to take up more water and therefore increase more than fiberglass. The more important thing is that we can now put numbers on these changes. Having a method that can adequately measure the thermal conductivity of moist insulation will allow us to quantify those moisture effects.

So I’ll conclude with these thoughts that it’s now possible to use the line heat source method to measure the thermal conductivity of insulation that wasn’t possible before the things that we worked out now for the TEMPOS. That mathematical inversion is based on a numerical solution to the differential equations that describe heat flow of a heated needle in the insulation. We need an approximate volumetric specific heat for the insulation in order to get an accurate thermal conductivity, but that’s typically not hard to come up with, and we can still get accurate conductivity measurements even if there’s some uncertainty in that measurement. Finally, the ability to use transient methods now makes it possible to measure humidity dependence of thermal conductivity in insulation. Thank you for being with us today.

All right, thank you Gaylon. That’s going to wrap it up for us today. Thank you again everyone for joining us, and we hope you enjoyed this discussion. Please consider answering the short survey that will appear after this webinar is finished to tell us what type of webinars you’d like to see in the future. And for more information on what you’ve seen today, please visit us at metergroup.com. Finally, stay tuned for future METER webinars. Thanks again. Stay safe and have a great day.

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