I thought it was the fan clutch too but the car overheats on highway too. Did you replace with a used engine, re manufactured or rebuild the old one to be specific? Check the fan clutch which is silver looking thing with small fins attached behind the radiator fan and is driven by the water pump. The small electric fans are for the AC
The fan Clutch can fail in many ways.
1. Any fluid leakage means it's toast.
2. They can seize solid. That's the "sounds like an airplane".
3. They can fail to engage. Engine overheats.
4. With the clutch firmly bolted to the waterpump, any fore/aft play in the fan blades means the bearings are shot. This often happens before the bearings lock up, as in #2 above.