Noob - Help Power for a DC Fan question

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SliderF18
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Hey guys. I am trying to put a fan into a helmet. I have a 3.7VDC, 650mAh lithium ion rechargable battery. I have sourced and found a great battery! The afore mentioned battery is the constant. Now I am having problems finding a DC Fan that will work with my battery. So far I have found only 5V DC Fans. I feel as though I am not getting enough power to run the fan! When I hook the 3.7V battery up to the fan, it only last about 4 hours on one charge. When I hook 3 1.5V AAA batteries up to the same fan, it runs much stronger and longer! What do you suggest I do in order to complete my project? I do not think a 3V DC fan exists. Thanks in ADVANCE!
 
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I thought about that, but the Lit-Ion is SUPER THIN and Small! In order to do 3 AAA's I would have to get a battery holder, and then somehow mount it to the helmet. I would prefer not to do that. That is why I thought I would ask the experts
 
Digikey shows one 3.3V fan and one 3V fan. Use the "Voltage" property in the right-hand column of this selection guide to pick one or the other or both, and then click on "Apply Filters":

http://search.digikey.com/scripts/DkSearch/dksus.dll?Cat=917586;keywords=fan

You will always get better battery life from primary cells like alkalines, versus rechargeable batteries of the same size. The choice to use rechargeable comes down to economics and convenience (is it easier to recharge rather than replace repeatedly).