When we wave a fan, we push away the layer of hot air close to our face and replace it with a layer of cooler air. Once this new layer of air heats up, it is replaced by another layer of air that has not yet warmed up… This is why we always feel comfortable.
In fact, after the layer of air directly touching our face heats up, it becomes an invisible air barrier, “warming up” our face, which means it delays the continuous loss of heat in that area. If this layer of air is not in motion, it is only slowly pushed upwards by the colder (and denser) air around it.
However, when we use a fan to disperse “the barrier”, our face is continuously exposed to new layers of air that have not yet warmed up, transferring heat to those layers. As a result, our body cools down and feels pleasantly refreshed.
This also means that in a room with many people, fanning helps us feel cooler by removing the cold air surrounding others and pushing the hot air towards them.