Peltier element theory

Definitions
– Th: Temperature of hot side (K)
– Tc: Temperature of cold side (K)
– ΔT: Th-Tc
– Tavg: (Th+Tc)/2

TEC1-12715
This module is the one I ordered and has a detailed datasheet which includes some plots at Th=27°C (300K) and Th=50°C (323K). No formulas and parameters of the module are provided so these were derived from the plots using the fit option of Wolfram Alpha[1].

The Seebeck effect causes an electromotive force, Uemf when a temperature difference is applied to the sides of the module,
Uemf = SΔT,
Where S is the difference between Seebeck coefficients of the n and p material inside the module. Since the module contains 127 elements, S is equal to 127 times the Seebeck coefficient of a single element.

Formula overview
Uemf = SΔT
I = (U-SΔT)/R
U = IR+SΔT
P = UI = U²/R-(USΔT)/R = I²R+ISΔT
QC = QP-P/2-QL
QH = QP+P/2-QL
QP = TavgSI = TavgS(U-SΔT)/R

References
1. https://www.wolframalpha.com/


Peltier liquid cooler

introduction
Peltier coolers are semiconductor devices which transfer heat from one of its sides to the other. The maximum temperature difference between the hot and cold side is about 65 °C.
I want to combine multiple Peltier elements to create a liquid cooler. My initial plan was to use it for a cloud chamber but I also want to use it for some chemistry experiments like making liquid ammonia and perhaps for cooling my room on a hot summer day. A target cooling temperature of around -30 °C is desired although lower temperatures are even better.

Theory
The peltier elements I will use are TEC1-12715 elements. The last two digits are the maximum current the elements can handle which is 15 Ampere. At a voltage of 12V each element will consume at most 180W. With a total of 6 elements I will need a power supply which can handle 90 Ampere at 12V. This is a concern for later though because for testing purposes I will use a 12V 60Ah car battery.

system overview
The Peltier elements have a surface of 4 by 4 cm. I found some CPU water cooling blocks on ebay which fit perfectly on the Peltier elements. The best part is that these cooling blocks have a flat surface on both sides so two Peltier elements can be attached. To keep the hot side of the elements cooled an AMD stock CPU heatsink is attached to both Peltier elements. The Fan on these heatsinks also needs 12V so it can easily be connected to the Peltier elements. Only when the element is turned on the fan needs to be on.
Instead of using adhesive cooling paste I use normal paste between the Peltier element and the cooler. The element is held in place by a small dot of super glue at each corner. This holds the element firmly in place but swapping an element is still possible if needed.
The two Peltier coolers combined with the water block and the CPU heatsinks will be referred to as a cooling segment.
The coolant will be pumped around by a simple pump with reservoir. All tubes should be insulated for maximum efficiency.

Problems to overcome
One of the problems with Peltier coolers is that they can only reach a limited temperate difference between the hot and cold sides. This means that you can’t always just run the elements at max power. This will heat up the heatsink which in turn causes the cold side to be less cold. A balance should be found between cooling power and heatsink temperature. This will be done by adding temperature sensors to the heatsinks and water blocks and controlling the power of the Peltier elements using these sensor readings.

The datasheet
Luckily the TEC1-12715 elements are well characterized. The datasheet[1] provides a good indication of the performance of this element.

Liquid coolant to use
Liquid coolers usually use water as coolant but because sub zero temperatures are reached water is not an option. In the lab acetone with dry ice is sometimes used as a low freezing point coolant. The melting point of acetone is -94.7 °C which is well below the target temperature. A disadvantage of acetone is that is may be corrosive to the tubing. A better (less corrosive) alternative would be isopropyl alcohol or ethanol which have melting points of -89 and -114 °C respectively.
The higher the heat capacity of a liquid the better. A higher heat capacity means that it takes longer to cool down but when it reaches the object to cool it has more “cooling power”.
Isopropyl alcohol has a heat capacity of 2.11 JmL-1K-1 compared to ethanol with 1.93 JmL-1K-1. Combined the the fact that pure isopropyl alcohol is easier to obtain and that it has a slightly higher boiling point this seems to be the optimal choice as cooling liquid.
The heat capacity of isopropyl is still low compared to the heat capacity of water (4.19 JmL-1K-1). For this reason another alternative was investigated briefly. Adding salts to water lowers its melting point. If calcium chloride is added the melting point can be lowered to -40 °C which is just below the target temperature. A saturated salt solution has some severe disadvantages however. If only a little to much salt is added the salt will form crystals at low temperatures which may break the pump. Another problem is that salt solutions conduct electricity very well and this conductivity may cause severe corrosion to metals (cooling blocks). For these reasons the preferred coolant is still isopropyl alcohol.

References
1. http://www.thermonamic.com/TEC1-12715-English.PDF