# Thermal Conductivity

Why do we need to measure thermal conductivity?

Thermal conductivity is the measurement of how thermally conductive a sample is. The value is known as a thermal conductivity constant, also known as the k-value. This constant is obtained through the Fourier’s Law of Heat Conduction:

Where P= power (W)

k= thermal conductivity constant (W/mK)

A= cross sectional area of the sample (m^2)

dT= temperature different across the sample

dx= thickness/depth of the sample (m^2)

The higher the thermal conductivity constant, the more thermally conductive the sample is. Thermal conductivity is used in our Solar Cooking research in order to determine the best composite that will be thermally but not electrically conductive. The experiment to determine the thermal conductivity is shown below:

The heat sink is made up of an aluminum box filled to the brim with a pre-made block of ice. The heat source is also an aluminum box filled with boiling water, as to keep the temperature at a constant 100 degrees C. The idea is that the heat from the bottom box will flow through the sample and into the heat sink, melting the ice. As the ice melts, it flows through a tube into a beaker where it is collected and measured after all the ice as melted. The data points that need to be collected while conducting the experiment are as follows:

mass of the ice

amount of time it takes for all the ice to melt

temperature gradient (temperature difference between the top and bottom of the sample)

cross-sectional area of the sample and the thickness

This design was inspired by two papers, which can be found here and here.

The first iteration of this design was filled with problems. We used an aluminum sample to determine whether the thermal conductivity constants the experiment gave us were valid, as the k-value of aluminum is known (180-230 W/mK). The first design gave us a value of 2 as the thermal conductivity: off by a factor of about 100.

We found flaws in our experimental design, mainly with the thermal contact between the sample and the two aluminum boxes. The main problem was that the thermocouple wires were interfering with the sample’s ability to make really good thermal contact with the underside of the heat sink and the heat source. To solve this problem, we machined a groove on the lid of the heat source aluminum box and on the underside of the heat sink;:

Machined groove on the heat sink and heat source

This allowed for the thermocouple to be slid into the groove and not disrupt the contact made by the aluminum sample.

This second iteration brought the thermal conductivity of aluminum to 175 W/mK. The thermal conductivities of what we have found so far are shown in a table below:

 Sample Name Thermal Conductivity (W/mK) Aluminum (calibration sample) 175 JBWeld + MgO (1:1 ratio) 0.8-1 MgO powder 10- 11.54 MgO: Cement (10:1 ratio) 8-10

Side notes: although the thermal conductivity of MgO is traditionally around 30-60 W/mK, this depends on the mechanical pressure placed on the sample. The thermal conductivity of MgO powder should theoretically increase as it is packed together more closely as it will increase thermal contact that way. Refer to this study in the Journal of Applied Physics that proved just that.

We noticed that even though the thermal conductivity of MgO is higher than that of MgO+Cement, it must be incredibly packed for it to reach higher thermal conductivities. In industry, there are special machines that compress MgO into the coils of stoves, and it is machinery that will most likely not be available in our target countries (East Africa). The thermal conductivity of MgO increased by 1 when the addition of a weight was added. The weight weighed 1 kg. In addition, we will most likely use a 5:1 ratio with the MgO+Cement because upon testing, we realized that the 5:1 expands as it dries and leaves less air bubbles as it dries.

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