After removing the boiled water from a hot kettle, which is wet, the water evaporates rapidly if air is blown over it. What is the science behind this phenomenon?
This is basically the same thing that happens with convective heat transfer. The main mechanism for water escaping from the surface is diffusion. Removing moist air and replacing it with drier air increases the concentration gradient of water in the air near the surface and, by Fick's first law, increases the diffusive flux (basically, @Martin's mechanism). In the case of convective heat transfer, removing hot air and replacing it with cooler air increases the temperature gradient in the air near the surface, and, by Fourier's law of heat conduction, increases the heat flux.
We know that moving air has a lower pressure than static air. So, when you blow over a hot wet surface, you create an area of lower pressure than usual(static air). This creates an ease for the water, or any liquid on the surface, to readily convert to gaseous form. But keep in mind, this blowing action not only lowers the pressure, but also cools the hot surface, so if incase the hot surface has a means to keep hot, this process will eventually stop the liquid from evaporation all together.
Also, the use of pressure cookers work in the same way, but vise versa. By creating a high pressure environment and not allowing the water to easily convert into a gas, a higher over all temperature is attained, more than the water's boiling point. this allows the food to cook quicker.