The size of a battery determines how long it lasts to drive a load (your fan).
Go to the website of a battery manufacturer like Energizer and click on Technical Info to see the datasheet for every battery they sell:
1) A little 9V alkaline battery can supply 0.24A for only half an hour when its voltage will be less than 7V. In 1.5 hours its voltage will be less than 6V.
2) Eight little AAA alkaline cells in series make 12V. They can supply 0.24A for 1 hour when the voltage will be 9.6V and for 2.5 hours when the voltage will be 8V.
3) Eight AA alkaline cells in series make 12V. They can supply 0.24A for 3.5 hours when the voltage will be 9.6V and for 7 hours when the voltage will be 8V.
You can look up how long C and D cells will last yourself.
I would use rechargeable Ni-MH cells.
And no one mentioned a switch mode power supply or microcontroller to get the apsolute maximum life out of the the batteries?
Are you guys loosing your touch?
forumlicker came close =) I'd use a 9pack of NiMH rechargeable, 2000ma AA's will last you close to 10 hours. Cheap RC car batteries (labeled 12V) and a charger might work better do, they use C and sometimes D cell Nicads.