A home-made solar kettle, its performance and its problems
by Stephen Hewitt | Published
The experimental solar kettle shown in Figure 1 with a reflector aperture of 0.8 square metres can heat water for a single mug of tea or coffee in about ten minutes. Some problems with the design as shown are discussed below.
Figure 2 shows measurements of its heating power. These were recorded by hand using the K-type thermocouple thermometer visible in Figure 1.
The kettle is a parabolic trough, 1m long and 80cm across from rim to rim. The reflector is made with 1mm thick polypropylene sheet 1m x 90cm, covered in metallised plastic. The focal length is 23.7cm.
The water is heated in a 22mm copper water pipe. This pipe is closed at one end and has a right-angle bend at the other for a spout. The pipe is longer than the reflector, and its total horizontal length is about 111cm. The spout, pointing upwards in the photograph, is about 3.5cm long, but needs to be longer. This arrangement holds about 350mL, which is slightly more than a typical mug.
The trough is mounted on a horizontal pivot whose axis of rotation is parallel to the copper pipe. The sun is focussed onto the pipe using the brass screw jack visible in Figure 1 to rotate the trough on its pivot until it points at the sun.
While the water is in the kettle, the spout is in the upright position as shown. To pour water out you use a handle (that is not present in the photograph) to rotate the tube so the spout points downwards. At least that is the idea. There are some practical problems with this.
When water is heated it expands. The kettle is intended to be used with the horizontal water pipe always full. Therefore as the temperature of the water increases it expands and rises up the spout.
This turns out be a useful feature because by starting with the spout empty you can get an idea of water temperature by looking at the level in the spout. The water is its own thermometer.
Further, because the expansion of water is not linear with temperature but increases disproportionately at higher temperatures, it may turn out that the exact (low) starting temperature of the water does not make much difference to its final height in the spout close to boiling. Further work is needed to calculate this effect.
But the spout shown in the photograph is too short. Unless you start with the water already hot and the spout empty, it will reach the top before it gets close to boiling and then continue to dribble out as the temperature increases.
Some estimates of heating power and heat losses
Based on the reasoning below and the slope of the heating curve around 50 °C in Figure 2 the net power after heat losses is estimated to have been at least 215W at around 50°C under the conditions of that day.
The thermocouple K-type probe has turned out to be very convenient for measuring temperature because the probe wire is rigid enough that it can be pushed along the pipe. You can easily feel the increase in resistance and tendency to then buckle when it reaches the far end of the pipe
The temperature measurements made in Figure 2 were with the bare thermocouple immersed in the water and pushed about half way (~ 50cm) down the pipe.
One caveat with these temperature measurements is that the water temperature along the pipe is not uniform and differences of over 10°C have been measured by sliding the probe along the pipe. It seems that the closed end is hotter, but further investigation of this is needed.
A possible artefact of non-uniform temperature is seen in Figure 2, where on the heating curve labelled “13:00 GMT” the highest temperature point (100 °C) seems to be an outlier, above its expected value on a smooth curve. A possible explanation is that the probe was not at the hottest point of the pipe and upon boiling, hotter water or steam has been pushed onto the probe, resulting in a jump in measured temperature.
The following is therefore an attempt to overcome the limitations of a single place of measurement in a volume of water that may have significant temperature differences. It aims to calculate the minimum power per unit length of pipe that must be going into an arbitrarily short length of pipe at the location of the thermometer probe to cause the observed rate of temperature increase. It is based on the assumption that at each moment in time the short length of copper and water remain at an approximately uniform temperature even if there is some temperature variation along the pipe.
If heat is being contributed to this location from elsewhere in the pipe, then the figure still provides a minimum intensity for power somewhere in the pipe.
One measured rate of temperature increase is 0.141°C/s shown in Figure 2 on the curve labelled “13:30 GMT”.
The copper pipe has 22mm outside diameter and a 0.9mm wall thickness. Based on this and the densities in Table 1 calculation shows that the copper pipe has a mass per unit length of 0.533kg/m and contains water of mass per unit length 0.317 kg/m. Multiplying these by their respective specific heat values from Table 1 shows that the power to raise their temperature at a rate of 0.141°C/s is about 215W per unit length of pipe.
|Copper specific heat||384||J/(kg K)|
|Water density (at 50°C)||988||kg/m3|
|Water specific heat||4180||J/(kg K)|
It means that at least in some part of the pipe net power is at least 215W/m and if that were the figure for the whole 1m length of the reflector then the total net power would be 215W.
This is likely an underestimate because it ignores the extra 11% water and 11% copper related to the fact that the copper pipe is actually 11cm longer than the reflector. It also ignores the copper and water in the spout.
The cooling curve in Figure 2 was an attempt to measure heat loss. After the heating curve labelled “12:10 GMT” the same water, with the temperature probe in the same position, everything left untouched, was allowed to cool. The change from heating to cooling was only to adjust the kettle to not point at the sun.
If the assumption is made that the rate of heat loss at a given water temperature is approximately the same during heating and cooling then the slopes marked in Figure 2 show that heat losses at around 90°C are a significant fraction of the received power. In fact the measured rate of heat loss is over half the measured net rate of heating after losses.
Making this assumption means that adding the measured rate of temperature loss to the measured rate of net temperature gain should give an estimate of the hypothetical rate of temperature increase that would have occurred without the heat loss. This assumption could be tested by summing these at multiple temperature points along both curves to test whether the sum is constant, but this has not been done here.
Using the the gradients marked in Figure 2 near 90 °C on the heating and corresponding cooling curve then gives:
0.102 + 0.054 = 0.156 °C/s.
This therefore represents an estimate of the hypothetical rate of temperature increase that would have occurred without the heat loss.
Using this figure instead of the 0.141°C/s in the calculation above would mean an input power of about 238W (ignoring the difference in density of water at 90 °C).
The area of reflector facing the sun when correctly aligned is 80cm x 1m or 0.8 square metres.
If solar radiation was 1kW/m2 the reflector should receive 800W. So the estimate of 238W of input power onto the copper pipe would mean an optical efficiency of 29.7%. The actual value of solar radiation was not measured and 1kW may be an over estimate. The 238W may be also be an underestimate for the reasons stated above but together they provide no evidence that the kettle is transferring most of the incoming radiation onto the surface of the pipe. Some reasons to suspect that it is not are shown in Figures 3 and 4. This remains an area for further investigation.
Outstanding problems and possible solutions
Ejecting boiling water
The kettle ejects most of the water when it boils. This is potentially hazardous. In its current form the kettle is not suitable for taking water all the way to boiling point. One possible solution is to add bend(s) to the spout so that the opening can point downwards into a waiting mug or container that it automatically fills when it boils.
Another possibility is to mitigate the hazard by providing something to catch the boiling water and intend that the kettle should be used to heat water but not to boiling point. A recommendation on the side of a packet of speciality coffee (Union) bought in England in 2022 is “Water just off the boil (92°).” And the website of the UK Tea and Infusions Association says “The water temperature for black tea should be 90 to 98°C and for green tea around 80°C”
Pouring water in and out
It has usually proven difficult or impossible to get water in or out simply by rotating the pipe to raise or lower the spout. Usually the pipe must be tilted too. This is especially needed to reliably ensure that the pipe is initially full with no trapped air. In the current design this can be done only by tilting the whole kettle including the supporting stand.
A possible solution is to mount the supports for the copper pipe on hinges with an adjustable stop. The stop would ensure that when they are allowed to rest under gravity the pipe is aligned correctly on the focal line, but each end of the pipe can be independently raised to tilt the pipe in the necessary direction for pouring.
Dribbling scalding water
As explained above, the kettle starts to dribble scalding water at temperatures below boiling point. The solution is to extend the spout.
Non uniform temperature along the pipe.
The variation in temperature along the pipe has not been investigated in detail. In particular it seems apparent that the water in the spout, which is beyond the end of the reflector, is unlikely to reach the temperatures of the water in the horizontal pipe in the focus (at least without steam being pushed through it). This might be of particular concern for anyone who wanted to use the kettle to ensure water was sterile.
It seems quite possible that even if the kettle is allowed to boil in its current form, that water that has not yet reached boiling point will be pushed out by steam from further down the pipe.
As shown in Figure 4 the focal line of the kettle is not perfectly straight and as shown in Figure 3 it spills at least some light in some conditions. Further work involves assessing the optical efficiency, or how much of the sun's radiation might be missing the water pipe.
A possible solution that might also mitigate some other problems is to use a larger diameter copper pipe.
A minor construction error was to forget that a curve parallel to a parabola is not a parabola. The parabola shape is provided at each end of the trough by 6mm marine plywood cut into a concave curve (which can be seen in Figure 4). However the reflector has a thickness of 1mm plus the thickness of the metallised plastic. The front of the reflector is therefore about 1mm away and parallel to the shape cut into the plywood. For the front of the reflector to be an accurate parabola, the plywood curve should have been something else. That something else could either have been computed at each point or perhaps derived analytically. The error with a thicker reflector might become more significant.
Polypropylene thermal expansivity
Polypropylene has a coefficient of thermal expansion of 70 - 92 x 10-6/°C according to engineeringtoolbox.com in October 2022 (while at least one other website states a higher maximum value). The 92 x 10-6/°C value would mean that the 1m reflector could change its length by 1.8mm in a 20 °C change in temperature. This could represent a problem if it shrinks and tries to pull itself into a tighter curve than the parabola or if it expands and buckles. In this kettle four original locating holes drilled one near the end of each rim later seemed to be misaligned. Whether this was caused by thermal expansion or other reasons is not sure.
A solution might be to use a different reflector material. In October 2022 one supplier (metals4u.co.uk) was offering a polished stainless steel mirror of 1m2 for £46.13 + VAT.