The beer cooler
Beer cooling at it’s finest
Cooling a beverage is a dream project for Peltier enthusiasts that enjoy a beer, and this set up finally surpassed my goal of taking a can of beer at room temperature and chilling in less time than it takes to drink a beer (in moderation, of course).
The set up itself isn’t optimized yet and looks a bit ungainly, but it managed to cool a can of 350mL of water from around 16°C to 4°C in about 20 min, with peak cooling rates of around 1°C/min. And it did this with just 23W.
Not only did it cool effectively, but it also revealed some weird behaviour of water around 4°C, which was entirely new information to me. While the effect is known to science, it’s not something could be called well known.
Beyond that, it’s an excellent set up to explore some of the numbers and misconceptions about “efficiency”, Peltier devices and heat pumps in general.
The temperature plot of the beer cooler experiment: the liquid starts at 16°C, has peak cooling at around 1°C/min, does some weird stuff at 4°C and some supercooling weird stuff as well
Efficiency shenanigans
Websites often refer to Peltiers as having only 5% efficiency
Peltier devices are often quoted as having an efficiency of only 5%, which is one of those internet falsehoods that persists like the supposed “fact” that we only use 10% of our brains. For Peltiers, it’s likely that the “5%" number arose from applications like this, where the final objective is to cool a can of water. This kind of objective makes efficiency calculations easy to do, but the results can be misleading.
Water requires about 4.2J (Joules) of energy per 1mL and 1°C change (or 1K, to be scientifically correct). So, in the above graph, cooling 350mL water from 16°C to 4°C requires 350mL x 12K x 4.2 = 17,600J of energy to be pumped out of the can. Since the Peltier set up required 23W for 20 minutes, this equates to 23 x 20 x 60 = 27,600J. This means the “efficiency” was about 63%, or a COP of 0.63.
Is this good? Well, in this kind of application, efficiency is a misleading metric.
As any good beer drinker knows, it normally takes a very long time to chill a beer, at least 2 hours. A modern compressor based fridge uses about 40W on average, adding up to 288kJ over 2 hours. Using the same metric, this makes a fridge about 6% efficient. Of course, this is nonsense, but you can see how the “efficiency” calculated in this way can yield some terrible results. It’s likely that this kind of calculation is how Peltiers gained a reputation as being about “5% efficient”.
In this particular application, it’s not the efficiency that is important. 23W for 20min is about 0.007kWh, or about 0.15¢ ($0.0015) worth of electricity. It’s expected that with some optimization and better insulation, it might only require 10W to do the same thing. But whether it’s 10W or 23W, it’s pretty small. The real game changer here is the speed of cooling.
The true problem
Cooling a beer quickly requires good thermal contact
The reason that normal fridges and Peltier coolers are so slow is nothing to do with the heat pump. It’s just basic physics. Water is actually a pretty bad conductor of heat, at 0.61W/m/K and air is even worse at 0.026 W/m/K. This compares to copper which clocks in at 400W/m/K. While convection can help both for air and water, natural convection is pretty slow.
Having a beverage can standing on the shelf of a cooler picking up cold from the surrounding air is expected to have a thermal resistance in the order of 5 K/W (Kelvin per Watt). The can has a heat capacity of around 1500J/K (Joules per Kelvin), so this results in a time constant of around 2 hours. It doesn’t matter how good your heat pump is, the only way to speed this up is by either starting colder (e.g. putting the beer in the freezer) or by reducing the thermal resistance, e.g. putting the beer on a bag of green peas, or both (beer on a bag of green peas in the freezer).
For cooling well below ambient, the system also needs to provide energy to offset the leakage of “cold” back into the environment (absorbing heat from the environment). This depends on the quality of the insulation, but more importantly the surface area. One reason why this experiment outperformed a traditional fridge (even without optimization) is that surface area of the parts that are cold is relatively small, meaning the leakage is only in the order of a few watts. A fridge large enough to hold food and drinks for a household is likely to leak about 100W. Using a heat pump at say COP 2.5, allows us to arrive at the 40W that a typical modern fridge uses. Again, it’s important to note that this has little to with cooling of the can itself. The can itself consumes about 1W of actual electrical energy to cool from 16°C to 4°C in 2 hours, assuming a COP of 2.5. It’s not zero, but relatively small compared to the energy required to overcome leakage via the insulation.
The Peltier design / experimental set up
Two coupling cells outside the can
For this application, the core part of the Peltier system can be called a “coupling cell”. On the hot side, the Peltier has a aluminium cooling block with pumped water, that efficiently takes the heat away to a larger water tank (e.g. 15L). On the cold side are custom made copper blocks with a flat 40x40mm face for coupling with the Peltier, and a 68mm curved face for coupling with the can. The first version used a single TEC 12708 Peltier and copper block and could be run off a 5V 2A USB supply (10W), and was pretty effective, requiring about 30min to cool a store bought beer (at around 14°C) to 4°C.
The second version used two slightly more powerful TEC 12710, but more importantly used two coupling cells. The idea was to increase the contact surface area which should effectively halve the cooling time, all other factors being equal, and having one on each side allows the set up to firmly clamp on to the beer can. The TEC was operated at 4A constant current, a value which is known to be fairly light for a 10A TEC, with each Peltier having about 12W of waste heat.
At this current, each TEC 12710 has maximum cooling ability of 25W, giving a total 50W of cooling for the system. The actual cooling will be significantly lower due to the thermal resistance of the system (water tank —> Peltier —> copper block —> can —> water) and also the increasing temperature difference as the water cools down.
Three precision temperature sensors (medical grade thermistors, 24 bit ADC datalogger, 0.001°C resolution) were placed inside the can, located approximately 2cm apart on a vertical stick aligned along the centre of the can. Three sensors were used as it was expected to see some spatial variation along the vertical axis as well as evidence of convection.
The results of the experiment
When the Peltier power is applied (time = 6min), the copper blocks quickly cool to well below ambient, and after several minutes goes below freezing. This is known from previous experiments and is evident from the frozen condensation on the exposed parts of the blocks.
Inside the can, there is an initial phase where large temperature differences exist, which encourage circulation and convection, which in turn ensures good thermal coupling. During this phase the cooling rate reaches around 1°C per minute, which suggests an 24W (350mL water, 4.19J/K/mL), so about half of the maximum cooling power, and operating at a COPc of about 1.0 (100%). This , which is to be expected for this set up.
As expected, there is a noticeable temperature difference between the three sensors, with the lower sensor having the lowest temperature, due to changes in the density of water as it cools, causing natural convection. In simple terms, the colder water will settle to the bottom.
After about 18min (24min on the graph time), when the water reaches around 4°C, something weird happens: the temperatures of the three sensors invert, with the highest sensor reading the lowest temperature. Variously theories were proposed for this, ranging from defective sensors, abrupt changes in heat flow due to water freezing near where the copper blocks contact the can, stuff ups with the hot side water circulation. In the end though it turned out to be just science: at around 4°C, the density of water does actually begin to reverse and decrease, so that colder water stays on top.
Ice as is well know, floats on water, a property that is related to the hexagonal lattice structure that ice uses as a solid. As water approaches the point of freezing, the molecules begin to arrange into this structure, leaving voids that decrease the density and make it lighter. This then leads to the effect of the water freezing from top down, rather than bottom up as might be expected. The effect is well known in science but probably rare to see it in practice, as few experimentalists would bother to have sensors vertically orientated like this.
After the temperature profile inverts, the upper sensor continues it’s downward trend and even falls well below zero, reaching around -5°C before suddenly it snaps to zero (see around 47min point on the above graph). This effect is more widely known: water can often be supercooled, and then snap freezes.
Once the freezing occurs, the set up appears to stabilise, however this can also be misleading: while in the water phase it requires 4.2J/°C/mL, freezing requires 334J/mL. Assuming that by this stage, the Peltier system is only delivering 10W of cooling (due to the large temperature difference), this means it requires 33s for every mL of water that gets frozen, and would take over 3hrs to freeze the can completely. Which gives me a new idea …