Why is airflow into a fan so much less than airflow out the front?

A fan cannot create air, and in theory, all the air comming out of a fan should have gone into the fan from the back, so why is it that it is cooler when you hold your hand infront of a fan rather than in the back?

Shouldn’t the same volume of air be moving out the front of the fan as the back (It can’t create air, so this must be true right?)? And therefore the cooling effect from behind equal the cooling effect out the front?

Or is it because the fan focuses air out the front, and doesn’t gather it from a focused point?

You got it in one!

But, given that the blades are flat through cross-section, how does the fan focus aird forward, but draw it from a wider area to the back? Surely, the rear aspect of the blades should be a precise opposite of the front?

The fan creates a low pressure area at the rear into which air flows from all directions, including from in front to the fan. That is why a ducted fan is more efficient that non-ducted. The shield just at the outer tips of the blades prevents air from in front flowing backwards over the blade tip to the low pressure behind.

The strong stream in front comes from the blades giving the air a high initial velocity straight away from the fan.

Air at the back of the fan diffuses into the area of reduced pressure. Air that goes through the fan gains momentum, and is forced out the front. The fan blade supplies momentum to the air as it goes through.
Now if you mount the fan inside a pipe…

Aaaah. Lightbulb moment. Thanks, both of you.