Freezable Ice Pack for Fans

In theory this is a really good idea- it’s a freezable gel pack that goes on top of any standard fan. Let that fan blow ice cold air instead of just air. Sounds good. In execution, the Cool Breeze Fan Pack has one major issue- the ice pack blocks the fan! I’m (clearly) not an engineer but I think that the ice pack needs to be on the backside of fan. Not sure if that would help the air flow. The reviews seem to agree- maybe it just needs to be on a larger fan so more air can circulate? I don’t know.