Over any liquid, its saturated vapors are present. When the surface is blown off, the steam above the water is simply blown off by the fan and the steam becomes unsaturated. And it turns out that the molecules from the water go into the environment trying to compensate for the fact that the vapor above the surface is unsaturated. At the same time, flying away water molecules take energy. As a result of this, the total energy of the system decreases, which leads to a decrease in temperature.
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