I've determined the amount of energy this generates compared to what it uses. I may have the honour of having the project this year with the most inefficient method harvesting of energy!

I measured the amount of current being supplied to the battery to determine the effective mAh generated or saved. I did this measurement for the device with and without the cooling fan. The circuitry drew about 6mA on average, while the fan drew nearly 60mA on average. As you can see below, the amount of energy harvested is no where near what is used.

There are a lot of things that are interesting to note here. The current supplied when the energy harvesting chip was starting up was very constant around 3.0uA to 3.3uA. Then once everything received enough power (I assume) it rapidly began increasing (rapid in terms of uA anyways). 

With the fan, the current generated rose very fast and leveled off around 40uA. Just after the cup was removed however, the energy generated fell off quickly. Once again it plateaued around 3uA before going to 0. These results show that even though the copper stays hot a while after use, it is not hot enough to charge the battery. A big part of this is that without the fan, the temperature differential of the TEG falls as the heat continues to flow.

Without the fan, the energy generated peaked much lower and gradually fell, far before the cup was removed. The reason for this as mentioned above was the fact that the heat sink could not exchange the heat fast enough without the fan, causing the temperature differential to fall.

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The Math

The energy generated with the fan running was certainly better, but it came at a cost. The fan itself took over 1000 times as much energy to run that was generated at the peak. This means that the battery life would not be extended a meaningful amount when the fan was running.

I determined the equivalent mAh generated by calculating the average mA generated across the measurements, and multiplying that by the length of time. This may not be the exact or best way to determine the actual mAh added back to the battery, but was the best I could do.

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With Fan

Battery capacity = 3000mAh

mAh drawn over 600s = 10mAh

Amount of device uses without generated energy = 300

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Average current supplied over 600s = 15.9uA

mAh generated over 600s = 0.002262mAh

Amount of device uses with generated energy = 300.068

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This has barely extended the life of the battery, extending it by about 0.023% (yes the decimal is in the right place).

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Without Fan

Battery capacity = 3000mAh

mAh drawn over 975s = 1.625mAh

Amount of device uses without generated energy = 1846.15

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Average current supplied over 975s = 9.25uA

mAh generated over 975s = 0.002505mAh

Amount of device uses with generated energy = 1849.00

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This has extended the life of the battery, extending it almost 3 full uses! The battery life is extended by about 0.15%. Without the fan, the device is able to generate enough electricity for one full use after 577 uses. That is a LOT of tea/coffee.

The results are very poor, but they are results!