# Background

I am working with a small team on a university project to build a greenhouse heat sink. This will pass warm air at the top of the greenhouse down through a chamber underground filled with a material to absorb and store the warm air. We have two prototype greenhouses; one will act as a control for baseline measurements and the other will have the heat sink.

## Set-up

I have built several temperature sensors and loggers for the final prototype, but some preliminary tests are being made on various materials:

1. Granite chips between 15-25mm, irregular shape
2. Tempered glass fractured into small pieces 7-15mm approx., atleast 2 sides are flat
3. Concrete fragments 30-80mm, irregular shape - test not completed

These were placed in a 5 L box. The box has a small fan and piping at the bottom to blow air into the chamber and release the air through a number of 6 mm holes in the pipe at the base of the box. The top of the box is sealed except for a vent which has the same diameter as the tube with the fan. A PT1000 temperature sensor is also inserted into the centre of each material to capture measurements every second. Here is an image of the test box:

## Procedure

The free air space was calculated on a smaller sample of both materials to give a rough figure of 42% for the granite and 43% for the glass. Two tests were then performed on the granite and then the glass:

1. Both cooled outside for a several hours to about 5.5 °C, then brought into the room and left for 1 hour with the fan on. The temperature was recorded as the material warmed up to room temperature.
2. After the first test the materials were then placed in a freezer and cooled down to -20 °C, the temperature was recorded again.

## Results

As can be seen below, the glass exhibits a lag in both data sets, warming up and cooling down, after which the temperature change becomes more linear. Whereas the granite shows a more linear change in temperature throughout.

Glass Warming (x-axis seconds, y-axis temperature)

Glass Cooling (x-axis seconds, y-axis temperature)

Granite Warming (x-axis seconds, y-axis temperature)

Granite Cooling (x-axis seconds, y-axis temperature)

# Questions

We are discussing the results at the moment and I am interested in expert opinions of the data we collected. The data is interesting and we are interpreting it correctly. Specifically:

• The shape of the glass fragments allows for a more interlocking shape, which could restrict airflow more, but wouldn't this still have a more linear temperature change?
• Could the glass data be due to minor thermal expansion changes in the material?
• The glass has a lower thermal conductivity rating than the granite, is this the reason for the lag?
• Quick thoughts: Thermal mass, thermal conductivity, mean equivalent fragment size and air path may all be relevant. It would seem logical that a high thermal conductivity material will be constrained mainly by surface effects. As conductivity drops the ability to get heat too and from core matters more. Area per volume (square cubed law) matters as does absolute size and even shape. What MAY be useful is tests on a limited number of items of identical dimensions and packing. I imagine this has been very well modelled over many decades. Mar 10 '15 at 14:04
• FWIW - (opinion only): Water is king :-). Multiple smaller sealed containers with black colouration - adjust colour density to play with convective/radiative properties. Air flow around containers. Pepsi 1.5l bottles potentially quite good at larger total volumes. PET plastic is extremely good wrt degradation long term. Mar 10 '15 at 14:07
• Russell thanks, surface area is definitely something we are considering and the larger concrete fragments test will hopefully yield some good data. Checking the total surface area however is not an easy test to make, as we have 3 non uniform materials. We probably won't have time to test smaller uniform batches but agree this would yield better data.
– Ant
Mar 10 '15 at 14:11
• All alternatives for the heat sink will definitely be considered and we are sharing all our findings, so people can play with the idea's, old wine bottles filled with water etc or broken china as not easy to recycle but has good thermal conductivity properties. Our system will have a microcontroller controlling the fan speed, so when more heat is available the system will crank the speed up and slow it down accordingly to release the heat in a more controlled manner.
– Ant
Mar 10 '15 at 14:14
• Great question, my only further suggestion as far as presentation is that you could cut the number of figures in half by plotting the materials together (i.e., one figure each for warming and cooling), since the scales are similar. The less people have to scroll down the page to find your questions, the happier they'll be.
– Air
Mar 10 '15 at 16:14

I would focus on two things - 1) the difference in heat transfer coefficients between the two materials and 2) the difference in heat capacity of the two materials.

1. The heat transfer coefficient is dependent on the physical interface between the air and the solid. Surface area of the materials and the amount of airflow would both factor in. As mentioned above, the smaller the particles, the more surface area, but the more restrictive it will be to airflow. There's a happy balance there that you might have to determine experimentally.

2. The heat capacity of the sink material determines how quickly the material's temperature will respond to a change in ambient temperature. The higher this is, the better the sink will perform. An increase in density and specific heat make for a better heatsink material. This is independent of the size of the rocks or the rate of airflow - bigger heat capacity will always be better.

As for the shape of the curves, I would never expect the rate of temperature change to be linear in this case, because the rate of change will change with difference in temperature. It's an exponential relationship. The granite warming curve looks most like what I'd expect to see for convection cooling/heating in a heat exchanger. The shape of the curve is pretty predictable, and by fitting it to a curve of the form $T = C-A e^{-b x}$ we can predict that the room temperature is about 24ºC. The initial rise in temperature of the glass cooling is especially perplexing.

My hypothesis is that the glass had a plateau instead of the granite because glass is reflective to infrared lighting instead of granite - therefore shielding the mostly radiative heat transfer.

Assumptions: I found a 5L box online with 340mm x 200mm x 125mm dimensions - which, with the insulated bottom, leads to a 0.203 square meter surface area for the box. Based on some calculations, and using the emisstivitys given here, is that during the "heating cycle", over the course of the 1600 seconds of plateau, the glass would have losing heat due to radiation at a rate of 22W - Wolfram tells me that should have been about a 6.53K change, but the box didn't undergo that change.

Considering the experiment was watching for a 15K change total, this is a significant portion of the heat transfer. Therefore the fan really is only doing a small fraction of the thermal work and radiation is picking up a significant portion.

In the infrared spectrum, where most of this heat would be lost, glass and granite seem to behave very differently. Granite seems somewhat transparent in the linked image. This is based on the fact that the edges in the image are blurry - if it were opaque the edges of the piping would be crisp at the hot spots (such as in the linked glass video) - but I'm not an expert in radiation properties of materials. Glass not only blocks the infrared radiation in the video, but according to the video seems to reflect the radiation. It makes sense, that's how greenhouses work.

This would imply that since the sensor is directly in the middle of the box of material the layers of glass continuously reflected back any heat transfer (envision a steak with layers of well done and rare) - stalling out the process. The granite did not have this effect and therefore proceeded to radiate in approximately uniform fashion.

Without further experiments it is hard to come to a definitive conclusion. Further experiments removing radiation effects would prove out the hypothesis.

• this is some useful information and some good practical examples showing granite and glass. We aim to carry out some longer tests on the materials, but built a heat sink in a greenhouse and managed a 1~2C temperature rise over the control greenhouse
– Ant
Jul 9 '15 at 9:39
• That is an encouraging start. Don't forget everything counts when it comes to thermal storage. The 22 watts is tiny, but over 30 minutes it will add up.
– Mark
Jul 9 '15 at 13:30