Thermo electrics work by creating a temperature differential of about 20 degrees Fahrenheit or so. For a wort chiller application, the system would start with 212 on the cooling side and be rejecting that heat to a room full of air at 72 F. In theory this could take the wort down to 52 or so, but before that, the thermo unit is likely to be coping with 212 F or a little less than that on one side and something higher than 230 on the other side (the electrical energy going into the thermal unit to create the temp differential has to be rejected by the external heat sink along with the thermal energy from the wort.) The rate at which this heat can be rejected to the surrounding air will be slow enough that the hot side of the cooling element will likely get cooked before the job is done.
In mini fridge applications of thermo electric units, a warm bottle of beer takes forever to cool from room temp to 55 or less because of this slow rate of heat rejection. I've also had a thermo electric cooler burn up in my garage during a hot summer because the element couldn't reject heat as fast as it was getting into the cooler from the hot surroundings.
Air doesn't have a high enough heat capacity for something like this to work any faster than a conventional chiller. The heat has to be absorbed by something. Water has a much higher heat capacity, generally comes out of a tap at lower than room temp and is able to sop up more thermal energy, at a much faster rate. Hence liquid cooled cpu's and tap water powered wort chillers.
Also the total quantity of thermal energy and the rate at which CPUs generate it is low enough and slow enough for a thermo unit with a large heat sink to reject it to a 72 F room at the same rate. There is a lot of energy in 2 to 5 gallons of boiling water and it takes many times that volume of 72 F air to absorb it. Much more than a CPU fan can move in an hour or two. Even cooling wort from 170 F is a trick and the closer to target, the smaller the temperature difference with the surrounding atmosphere and the slower the rate of cooling.
A thermo unit may be usefull for chilling the inbound water for a conventional chiller, to increase the temp diff once the wort begins to approach target. It may also be possible to use some sort of tap water chiller on the hot side of the thermo unit. The thermo unit would, in this capacity, function as a way to use electrical energy to accelerate the rejection of Wort heat to flowing tap water. This would also help a great deal when the Wort begins to approach target temp and the cooling slows down. There's alot to try but be ready to burn up a few power supplies and a few thermo electric units on accidents and unknowns. But fear not, I am a pessimist who tends to say nay at even the greatest of ideas. Besides, the beer gods will likely smile upon any sacrifices you make in their name.
Just remember how many BTUs you had to put into the Wort to make it boil or even just to get 170 F. While much of that energy is lost to inefficiency and never makes it into the beer, you're still gonna have to get many of those BTUs out of the wort somehow if you want to re-achieve room temp or something lower.
Suggested google reading; thermodynamics, specific heat, heat transfer, british thermal units, converting joules to BTUs to watts, and back. And try looking at BTU ratings on air conditioners and HVAC units. Its all about conservation of energy. You put energy in when you brew, and take it back out when you chill.
