IN my experience a bad fan clutch sounds more like a sort of grinding noise than a whirring. I associate whirring with the power steering pump (check fluid) as the most likely cause...beyond that you'll just have to sniff around. Does yours have a serp belt or v-belts? If you can't pin it down and you have individual v-belts you could pull them one at a time and see if the sound changes.

Steve Carlson - 95 Trooper LS expo rig
Serenity now!