A whining noise is caused by a faulty power steering pump. When the pump has air in the system or has trouble creating pressure, it produces a loud whining noise.
As a pump is continually used, the seals inside the unit become worn. When these seals fail, they form leaks that drain out the power steering fluid. When the fluid is almost complete drained from the system, the steering wheel will have dry spots when turning, and the pump will begin to whine. Without repairing the leaks, the pump will eventually fail.
There are commercial products available that contain additives to help slow power steering leaks, but the best option is to replace the unit and hoses themselves to ensure a leak-free pressurized system.