two fan noises 92 e32

I am experiencing two fan noises (Just purchased car).
One; if I turn the key on (but dont' start the engine) I hear a fan like noise
from the engine. I also hear this noise more loudly when I turn the car off (after running the engine).
Both fan-like noises are definately coming from the engine area (not interior).
The louder of the two is when I turn teh car off - it's like it's sighing "Ohhh you're done.."
Are these noises normal?
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