2006 Dodge Caravan Whining sound from engine compartment

I just recently have whining sound from the engine compartment of my minivan (2006 Caravan). I had a similar issue before which turned out to be a defective alternator that was replaced. This time though, the whine starts about 2-3 miles from a cold start (I live in Toronto Canada). However, stopping, turning off the engine and turning it on again usually cures the whining.

What I can't fathom though is the whining continues for about 3-5 seconds after the engine is turned off. I am assuming that the whine is caused by a rotating part. But what vehicle part continues to rotate after the engine is turned off?

Any help/comment will be greatly appreciated.

Thanks!