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I managed to build the circuit and it seems to work except for the red led, it won't turn on when the circuit is charging the battery, any suggestions?
If you need to charge an 18 volt battery, I would recommend a 20 volt zener diode. An 18 volt NiCd Battery should be fully charged at about 21 volts. I am going to try a 20 volt zener and I'll comment with the results. For the resistor I would chose the one rated for the current of your wall wart or power supply. (I would recommend a 24 volt supply)
It wouldn't be worth trying, considering that the Seebeck Effect at each junction would only produce a few milliVolts each, you would have to use hundreds of junctions which would make it very complicated and also very cumbersome to make