Two distinct parts to break apart here.
First is evaporative cooling. This makes sense. People are moist and evaporating water cools the object down more than just the air alone.
Second part is that air is insulative. By “blowing away” the small cold or hot air layer around us we become colder faster.
Now for fans and non human objects.
Fans speed up the air to move more hot or cold air faster to remove the hot or cold air surrounding the object faster. For instance cars have radiator fans to aid in air cooling in addition to air just moving through the radiator by driving.
Evaporative cooling also effects objects, however the effect is generally more noticable with people because we are so moist compared to everything around us.
Take a towel outside on a cold day and leave it out there for a couple hours. It will eventually become the same temperature as the environment. It will become the same temperature faster with wind, because the heat will transfer away faster.
Take a towel that is wet. It is actually possible for the wet towel to be colder(temporary) than the environment due to the additional heat lost due to evaporation. The towel will of course freeze or all the moisture will evaporated away and then the towel will become the same temperature as the environment.
Want to get a rough idea of wind chill? Moisten the tip of the thermometer. This helps simulate skin moisture and approximate temperature actually felt on the skin.
Wind chill is not unique to people, however is is a good approximation of actual temperature felt by the skin.
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