whole house fan for a flat roof??

My wife and I just bought a 2000 square foot two-story brownstone. We would like to consider putting in a whole house fan, in order to minimize our use of our central AC. It’s a typical flat roof situation, so we have no attic. The roof is about 2 feet, or less, from our second floor ceiling. Is there a strong whole house fan that can vent directly to a flat roof, not through an attic? Is this a good idea for us?

Thanks in advance for any thoughts on this!!

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