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Your body temperature is almost always hotter than the air. Fanning the air allows more energy to be transferred from your body into the air, since more air is coming into contact with your skin.

At least, that’s how I see it.

Since you’re speaking in chemistry terms, I’ll give a chemical explanation..

Your skin feels cooler because when a fan blows on your skin, sweat evaporates off of it. Even if you can’t feel it being wet, there’s always at least a little bit of wetness there. When the moving air particles collide with your skin they do transfer some of that kinetic energy, but it goes both into your skin and into your sweat. As the kinetic energy of your sweat increases, more and more molecules of it gain enough energy to break free from the liquid form and evaporate.

Normally, when you put kinetic energy into something, it will become hotter. If what you’re heating is water, it’ll start to evaporate faster and faster until you reach the boiling point, at which point everything kind of maxes out and it evaporates at maximum rate while not gaining any temperature. When something changes state (such as sweat from liquid to gas), it needs an extra push beyond the normal kinetic energy. In the case of a state change from liquid to gas, this extra energy push is called the “Enthalpy of Vaporization”.

Other than just kinetic energy, substances have a property of “Enthalpy”. I’m not sure how much chemistry you’ve done, so I’ll skip the mathematical definition of enthalpy, and basically just describe it as heat, which is basically a form of energy. Don’t confuse this with kinetic energy though! Enthalpy is more like the inherent energy something has due to its chemical properties (one of these properties is physical state: solid, liquid, gas). A substance in a gaseous state will always have more energy than it would in its liquid state, and this extra energy comes from the Enthalpy of Vaporization. And where does the actual energy for the Enthalpy of Vaporization come from? Yep, your skin. It steals the energy from the heat of your skin, and therefore cools you down.

Sorry for making this so unnecessarily long, but I hope this helps!