Loud Whining Noise - 2001 Fiat Punto?

I don't know anything about cars but was hoping someone might be able to help...When I've been driving my car for a while and then stop, say at traffic lights or in a jam this noise occurs that is really loud from the engine. It's like a loud mechanicly sort of whining. I can hear it from the inside of the car and it's even louder outside obviously. People from other cars next to me can also hear it because they always look over. It goes on for about 5-10 seconds then stops. It also stops as soon as I turn the engnie off.

I parked my car in the drive and left the engine running to wait for the sound to happen and it did and then at the end of the whine was a sort of brief chug chug chug noise and then it stopped.

I've taken it to two garages and mentioned it but they said they never heard it but I guess they wouldn't have time to drive it for a while until the engines hot.