I have a 2002 Subaru Outback with manual transmission. After driving the car for 30 minutes, a very loud whirring/humming noise starts (no noise or very very little the first 30 minutes). It get's louder with higher speeds, but is still very annoying at low speeds after the 30 min mark. When stopped, there is no noise at all. 

I took the car to a mechanic and he thought it might be a wheel bearing, but he checked them all and said they were fine. 

Based on reading past posts, I thought it might be one of the differentials. Based on what I read, I checked if my wheels clunk when making slow, tight turns and there is clunking after driving for at least 30 min but turns smoothly when the car is first started. 

Is there a way to check how the front and rear differentials are doing? If the fluid levels are ok, are the diffs ok? 

Thanks

and there is clunking after driving for at least 30 min but turns smoothly when the car is first started.

is this car new to you?

are all 4 tires exactly the same? same brand/model/size and near each other in wear? They need to be.

 

if tires are the same, and, if you are saying your car DOES exhibit this; that is, turns smoothly in tight circles when stone cold, but, jerk-y/bucks/'holding back' in tight circles on dry pavement when warmed-up, that can often mean the center diff is bad.

Wheel bearings increase the tone at the same rate you speed up, 2x as fast and 2x the pitch.

Differentials pitch up by 4x the speed change, also diffs usually only make noise when on the gas and get quiet coasting.

I've owned the car three years. It makes noise while coasting as well. I'll have to check the amount of noise change with speed. 

I just changed the front and rear differential gear oil, but no change. If it's the diff the damage had been done, but not sure how to be positive about that .