Try the easy stuff first!
With the engine cold, open the hood and have someone else look and listen for the noise. Make sure the other person is not wearing any jewelry or anything that can snag (sleeves, hair, scarf, etc). Have that person try to localize the noise. If the noise disappears shut off the engine and repeat it. When an engine becomes warm then things expand.
If it is coming from the fan then carefully look for anything rubbing or loose. Loose fan shroud, fan hitting shroud, wire hitting fan, screw is loose, broken part rubbing, damaged fan blade, dead mouse tail rubbing fan blade, etc. Do the easy stuff first before checking the more serious stuff.
Same thing for the engine cover. Have someone press down on the engine cover while you start the car or while its on. Screws become loose, things break, etc.
Localize the noise, where exactly is it coming from.