Well clearly you burn more energy waving anything around then by not doing so. But the point of a hand fan isn’t to decrease energy use but to increase relative comfort. A nice slight breeze is usually enough to make us *feel* slightly cooler even though we’re using energy to do it. Exercise bikes back in the day operated on this principle, by having the thing you move also be a fan that sends air at you. So, by pedaling you also create a breeze to help you keep cooler.
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