You don't hear anything abnormal while it's running?? I have heard alternators sound much louder than they should when the bearings get bad, but you need to be more specific about what you hear and what side of the vehicle it's coming from.. How long does this noise last? How many miles on it? Sound like a bearing maybe? Can you have someone turn it on and off while you try to pinpoint where it's coming from? Could be a bearing from one of the components that the serpentine belt is turning or if it sounds like it's more on the driver side it could be something in the transmission. Need to be more specific about where the noise is coming from, what it sounds like and how long it lasts before we can even guess what it could be. Does it happen every time you shut it off? Does it happen if the engine is cold or only when hot?

 

Could be the bearings on one of the electric cooling fans cashing in its chips. I just had a cooling fan crater, it sounded more like someone strangling a gerbil, immediately after the engine was shut off.
Replaced the fan assembly with a used one from a Donor Pac, the sound went away and all is good.

 

That's a very good possibility. You should be able to tell by moving the fans. They should spin freely (with engine off of course). If any back and forth movement then probably a good idea to replace them. Did you try to pinpoint the noise while looking under the hood? Have someone turn it on and off for you?