I’m not aware of a fan on or for any other clutch… Yes, the clutch fan on the front of your motor…
My friend’s Celica made the same sound when it was low on power steering fluid (had a leak in the system, so it was perpetual). Check that, check the fan, make sure all your belts have around 8-10mm of flex in them, so they’re not too tight, make sure they’re not too loose either.