Higher net power from a solar kettle heating water in glass rather than copper
by Stephen Hewitt | Published
The solar kettle shown in Figure 1 has sometimes produced over 400W/m2 of calculated net heating per unit area of reflector aperture at water temperatures of up to 50 °C when heating dyed water directly through the walls of a glass bottle. This is more than its highest power recorded so far with a copper pipe. With the double-walled insulating glass bottle (shown nearer the camera) it has produced a net heating power of over 270W/m2 all the way up to 100 °C.
The kettle was described in a previous article, which also presented figures for the rate of temperature increase it achieved in the water and the copper of its pipe. The rates of heating with the copper pipe have been measured in dozens of heating trials under various conditions since then, some of them published in subsequent articles.
Figure 2 shows the two different glass bottles that were tested. One was a cylindrical 500mL olive oil bottle with a metal screw cap. The other was a double-walled insulating borosilicate glass bottle of about 470mL sold as a “tea flask” or “Teeflasche” for hot drinks.
Figure 5 shows some raw temperature measurements as the water is heated in these bottles under various conditions. The details of these measurements are explained below.
Net heating power density
Figure 7 shows a derived parameter intended to allow comparisons of efficiency amongst all the cases, including the different glass bottles and the copper pipe, using different areas of reflector and holding different amounts of water. This is defined here as net heating power density, which is the power per unit area of reflector aperture involved. The reflector aperture is the area of reflector facing the sun in a plane perpendicular to a line between the sun and the kettle.
For example, the double-walled bottle has a length of 21cm of glass that absorbs light from the reflector. The width of the reflector aperture from rim to rim is 81cm. The wooden strip supporting the bottles blocks sunlight and this strip is 4.5cm wide, meaning that 4.5cm in width of this aperture is lost. So the aperture area heating the double walled bottle is (0.81 - 0.045)x0.21 m2
The net means the heat retained in the water and possibly other materials of the kettle and not lost to the environment during heating.
The glass bottles
The olive oil bottle was from a British supermarket, cylindrical, made of clear glass and of nominal volume 500mL. Its outside diameter was around 6cm for about 21.5cm of its length, and it then had a much narrower neck of length approximately 6.5cm, making the total length about 28cm.
In most of the heating tests this neck was covered with aluminium foil to prevent it receiving any sunlight from the reflector. (The motivation was to eliminate uncertainty of how much heat the neck would absorb, especially when it was not full, see below). The bottle label was removed on the side facing the reflector but left (as potential insulation) on the side facing away from the reflector and towards the wooden strip supporting it.
The mass of glass in the olive oil bottle, measured by weighing, was 403g.
The double-walled glass bottle was of outside diameter approximately 6.8cm, and the glass weighed 510g. The inner walls appeared thinner than the outer walls (and of course the dimensions were slightly less) so it must be that less than half this mass, quite possibly significantly less, could be in contact with the water. For these reasons the calculations on heat gain below will neglect the thermal capacity of this bottle.
For the bottle standing on a surface such as a table top with its (opaque) lid on, the length of glass from the bottom of the lid down to the surface is 22.5cm. But the bottom of the liquid inside the inner container (that can absorb sunlight) is about 1.5cm above that surface, meaning there is a length of about 21cm of liquid which can receive sunlight.
The total mass of glass in the double-walled bottle, measured by weighing, was 510g.
Measurements of heating power with bottles
For heating with these bottles, the kettle was modified. The copper pipe was removed and a wooden strip held the glass bottle with its central axis on the focal line of the parabolic trough. The surface of this wood facing the bottle was covered with reflective self-adhesive metallised plastic film, the same used for the reflector, with the intent of reducing radiant heat loss from the glass.
Measurements with a glass bottle have been made in two different ways. The first way, for the olive oil bottle only, was with a ~1mm hole drilled through its metal cap. This allowed insertion of the KT-thermocouple wire and continuous measurement of water temperature during heating. The kettle was tilted (Figure 4) to avoid water dripping out through the hole.
For the double-walled bottle and later with the olive oil bottle, the lid was on and the bottle sealed. Obviously heating a sealed bottle is potentially dangerous because the resulting increased pressure in the bottle might cause it to crack or explode. This could happen because the bottle is heated too long without opening it to release the pressure or because there was not enough initial air space in the bottle for the expansion of the water with temperature or for other reasons. There is no published pressure rating for either of these bottles and their ability to withstand internal pressure is unknown. In particular the internal walls of the double-walled bottle look rather thin. Another potential hazard is that if the water inside is heated to a temperature above 100°C, then when the bottle is opened the water will start to boil and might splash out of the bottle.
Care was taken to ensure there was enough space in the bottle for the water to expand. During heating, the remaining amount of air space in the bottle was monitored, and this can be seen through the glass, as in Figure 1.
Care was also taken not to allow large a temperature increase without opening the bottle to release the pressure. Prior experience with the unsealed olive oil bottle was useful in estimating the temperature rise that was likely in a given time period.
Periodically the sealed bottle was taken off the kettle, and in the case of the olive oil bottle placed quickly into an insulating bag (seen in Figure 2). Then in either case the water was mixed by turning the bottle upside down and back five times, taking about a second each time. (The intent here was to ensure a uniform water temperature. This procedure however, transferred a lot of heat into the glass and may have been a methodological mistake) The bottle was then opened and the temperature measured as soon as possible by dipping the bare KT-thermocouple probe into it.
Then the bottle was either quickly returned to the kettle to continue heating or delayed and allowed to cool somewhat. In the case of a delay, there was a second shaking and temperature reading just before putting it back to resume heating.
Figure 5 shows plots of measured water temperature against time under various conditions.
Derivation of relative heating powers
Figure 7 shows the net heating power density as defined in the section above, calculated from the raw temperature measurements. There are various uncertainties and assumptions in calculating this, discussed next. In particular the mass of water in the olive oil bottle in many cases has some uncertainty. In general it was approximately up to the shoulder of the bottle, where the narrower neck starts, and this level has subsequently been weighed as 483g of water.
The copper pipe extends the full 1m length of the reflector and therefore the aperture involved is full width and length of the reflector, 0.81m2.
Temperature measurements during heating with the copper pipe on 2 October 2022 were presented in the first article on this solar kettle. Temperature measurements during heating with the copper pipe on 1 December 2022 were presented in a subsequent article. These measurements are used here to derive power density figures for comparison in Figure 7.
As discussed in the first article the temperature of the water along the pipe does not increase at a completely uniform rate and this presents a problem for determining the power from the temperature measurement at a single point. For the purposes of this article, the assumption has been made that all the water and all the copper in the kettle was heated at the same rate as the water in the centre where the temperature was measured. These values in Figure 7 for the copper pipe are therefore likely to be over-estimates.
This entire mass of copper, including the spout and the full length of the pipe, measured by weighing, was 601g. In general the water in the copper pipe during heating tests has not been weighed, but standardised by filling the kettle so that the water level is just at the bottom of the spout - ie the 111cm length of the horizontal part of the pipe is full of water, with water at ambient temperature. This amount of water has been measured by weighing to be approximately 355g.
Olive oil bottle
As noted above the mass of glass in the olive oil bottle is 403g. Taking the specific heat of glass as 840kJ/(kg K) means a heat capacity in the glass of 339kJ/K. The amount of water heated is typically over 460g. Taking the specific heat of water as 4180J/(kg K) means a heat capacity of the water of 1922J/K which means that the glass would typically (but depending on the mass of water) represent 339/1922 or ~18% of the total heat capacity if all the glass were heated to the same temperature as the water.
Here the approximation has been made to ignore the heat transferred to the glass in the case of the continuous temperature measurement with a hole in the lid, which might mean all these power values are underestimates. The maximum amount of the underestimation from this assumption, if the entire glass were in fact at the same temperature as the water, would therefore be around 18%.
In the case of the sealed bottle, where the bottle was shaken every time before taking a temperature measurement, the assumption is made that the glass and water were at equal temperatures at the point of measurement, so the heat capacity of the glass has been included in the calculation. The total heat gain has been taken to be the sum of the heat absorbed by the glass and by the water since the last measurement.
However this may result in an underestimation of the heating for every measurement period after the first. The underestimation might be also be significant, by the following argument, which can be summarised as: the shaking causes extra heat loss which is not accounted for.
This argument rests on the assumption that the extra heat in the glass caused by shaking is rapidly lost to the environment and by the next measurement the glass has no more heat in it than it would have done if the bottle had not been shaken.
During undisturbed heating, the outside of the olive oil bottle loses heat There will be temperature gradient across the glass wall from somewhere closer to ambient on the outside to somewhere closer to the bulk of the water on the inside. The average temperature across the entire mass of glass at any instant will be somewhere between these two. It doesn't matter exactly what these temperatures are, the point is that the average temperature of the glass is somewhere between ambient and the temperature of the water. It is not related to the temperature of the last measurement.
When the bottle is put into the bag and shaken, lets assume that the temperature of the whole of the water and the glass becomes uniform, with heat moving out of the water into the glass. This means that when the bottle is shaken, the amount of heat that goes into the glass from the water is not a fixed fraction of the increase in temperature since the last measurement, but depends on the difference of the water and the ambient temperature. For example if the glass is (say) on average at a temperature halfway between the water and ambient, then when the ambient is 10°C and the water is 90°C, the average of the glass will be 50°C. When the bottle is shaken, heat will leave the water and move to the glass and afterwards they will be at the same temperature, which will be somewhere close to 90°C. But this means that the heat that has gone from the water into the glass is enough to raise half the glass by nearly 40°C. If the previous temperature measurement was not long ago, say at 80°C, we will only give the kettle credit, so to speak, for raising water and glass by 10°C, whereas in fact it has just raised half the glass by over 40°C. This might mean that the glass can create bigger underestimations than the 18% of the heat capacity that it represents.
No attempt to correct for this has been made in Figure 7, which means the calculated values for each sealed olive oil bottle for its heating periods after the first might be significantly too low.
In Figure 7, no adjustment in temperature range has been made for the effect of shaking the bottle. The water just before shaking was presumably at a slightly higher temperature than measured just after shaking so the net power really applies to a temperature range stretching slightly higher than the one shown. No attempt is made here to calculate this.
It can be argued that for comparisons between cases in Figure 7 temperature would be better expressed as temperature above ambient on the x axis, rather than an absolute value. However the differences in ambient temperature are not very great.
For the double-walled bottle, the glass is simply ignored, so the derived power figures assume that all the heat has gone into the water. They are therefore likely to slightly underestimate the power.
The outside of the olive oil bottle remains relatively cool to touch compared with the measured temperature of the water inside. I could take it off the kettle with bare hands even when the water temperature was high, but then shaking it made it too hot to hold almost immediately. In later experiments I took the bottle off the kettle with bare hands and quickly dropped it into the sleeve shown in Fig 2. The intention was to slow heat loss before the temperature had been measured, but it also avoided the need for gloves. (Whether handling the bottle like this is wise or completely safe is outside the scope of this article.)
This effect might be an unexpected benefit of a batch method of heating as in this kettle. Evidently moving the water overcomes a thermal barrier between the bulk of the water and the glass walls and causes much greater heat transfer. In a continuous circulation system, like a commercial power generation plant, water would be in constant motion during solar heating, whereas in this kettle it is still.
Although it is presumably not borosilicate and presumably not intended to be exposed to heat, the (same) olive oil bottle has survived repeated heatings on the solar kettle without yet cracking or shattering. On different occasions water in it has reached the following temperatures: 82°C, 79°C, 71°C, 69°C, 86°C, 90°C, 94°C, 94°C, 94°C, 81°C, 72°C, 80°C, 72°C, 60°C, 79°C.
Another possible stress on the glass may be an increase in internal pressure, as discussed above. The sealed bottle has yet not been taken all the way from ambient to temperatures like those above without opening it part way at least once. With both bottles, I usually noticed an audible hiss on opening the lid after heating. Obviously heating a bottle too long or developing enough pressure to shatter the bottle could be very hazardous. But how long would be “too long” is a question for further work.
An increase in pressure with temperature is expected for at least four reasons.
The increase in volume of the water with temperature will decrease the the remaining available space for gas in the bottle, compressing the air that was sealed into the bottle. There is no upper limit on the compression factor, since it depends only the relative size of the space remaining when the water was cold to the space remaining when it is hot. If not enough space were left for even the water to expand, there seems no doubt that the water would break the bottle.
The usual increase in pressure with temperature for a gas in a fixed volume.
The increase in water vapour pressure with temperature, which of course will reach 1 atmosphere at 100 °C. This partial pressure of water vapour will be an independent addition to the increase in air pressure from other causes.
Dissolved gasses such as carbon dioxide and oxygen become less soluble at higher temperatures.
Standard bottle glass is selective in the sense that it is transparent to visible light and near-infrared (IR) - the parts of the spectrum containing almost all the sun's energy - but opaque to longer wavelengths of infrared emitted by the hot water in these bottles.
From the shape of the power curves related to temperature, it looks as though compared to the copper pipe the single wall bottle has higher net heating power at low temperatures but lower net heating at higher temperatures. The double-walled bottle has higher heating power at all temperatures.
A higher net heating power at low temperatures where heat losses are small suggests higher power input from the sun rather than less heat loss.
Possible explanations for a higher input power are:
- Perhaps the larger diameter bottle catches sunlight that misses the copper pipe
- Perhaps the glass and dyed water combination has higher absorptance than the copper surface.
Therefore there are reasons to investigate whether either of these things can be improved with the copper pipe. It was already apparent from its brightness in full sunlight that the copper pipe does not absorb all the solar energy.
Given the larger surface area and larger mass of water in the bottles per unit length of reflector, it is not surprising that the ratio of heat loss to input power for the bottle is higher than the copper pipe.
No significant attempt was made to insulate the unused half of the bottles in these experiments, just a piece of reflective foil on the wood facing the bottle. Insulating the unused half could be investigated.
The trough is under-powered for the amount of water per unit length that the bottle contains in the sense that it has taken over 30 minutes to heat water from 30°C to 100°C in the double-walled bottle and this is probably too long to wait for a cup of tea. (Of course the trough has enough length to heat four of these bottles at the same time, which might be good for a tea party.)
A parabolic dish or conical reflector that heats the bottle from all sides might be more efficient than a parabolic trough, because the half of the bottle circumference that is facing away from the trough is leaking heat and receiving nothing in return.
Possible applications of heating glass bottles
A glass bottle could be used for cooking food. For example the double-walled bottle used here has an opening the full width of the bottle which would allow pieces of food to go easily in and out. Food in water (for example a stew) could be heated on a solar cooker and then the bottle containing the hot food could be transferred into a further insulating container for heat-retention cooking. But if a sealed bottle is going to be used then the safety aspects need to be addressed.
Obviously it is not inherently necessary that a bottle is sealed in order for it to be used in solar cooking but the idea of cooking in a sealed bottle, if it can be done safely, also leads to the idea of sterilising food to preserve it for long term storage in that same bottle. The bottle could be sealed cold and the food heated by solar radiation through the walls.
Depending on the natural colour in the water from the food itself, it might be necessary to introduce an additional food dye to absorb the sunlight.