There has been some discussion here on different TEC products. For the most part, the product number is the number of elements, then the max amps i.e. NNNAA so a 12730 is 127 elements, 30 A max. Different doping of the elements and different geometries will produce slightly different performance.
For Bismuth telluride, the most common materials, each element has a nominal voltage of about .123 at 25C max. So TECs with 127 elements have nominal voltage of about 16V at 25C. The current capacity is determined by the size of each element and the voltage by total number of elements.
Peltier elements have a negative coefficient of resistance, which means the effective series resistance increases with heat. That means more voltage is needed to achieve the same current as the hot side gets hotter, or conversely, that lower current will result from the same voltage. Larger elements have a lower nominal resistance. The effective resistance (R=V/I in a running system) varies with both heat and heat transfer and is typically about twice the nominal resistance with a variance of 20% or more over the range of operation.
The heat transfer is determined by the amps and the temp differential. For a given amperage, the lower the differential, the more heat is transferred. Higher currents move the whole curve, so a larger differential can be sustained, or more heat can be moved for a given differential.
You should never exceed the max current for a TEC. High voltages can also destroy the elements. Because different formulations have different resistance, the voltage needed to sustain current varies somewhat, TEC by TEC, in addition to the hot side temp. 127 element units are designed for a max voltage of around 16V at 25C, which is about 18V at 50C. Some TECs have a design point at 75C or 100C or even 200C instead of 25C or 50C - the elements are the same, but higher temp solder is used to allow the higher operating points.
As my recent tests show, the heat transfer is pretty linear with amps down to some pretty low values, so with a low differential and low voltage you can achieve good efficiency but need a lot of big elements to move the total heat load. The conclusion is that for best efficiency use the biggest elements you can get, as indicated by amp capacity, and run low in the curve. I was looking at an 03140 - 31 elements, 40A max, and 3.5V nominal. They have bigger elements than the 12730, and therefore should move more heat. 4 of them in series would effectively be a 12440. I would expect that to have about 30% better heat capability than a single 12730 at the same voltage.
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