I ordered a Competition Solar 47701 Solar 20 Watt with Charge Controller to run a 6in 10 watt fan. Will a 12v 18ah deep cycle battery be sufficient? This is for camping!!!!
Depends on the amount of Sunlight your AO gets, and the loss of Energy, in charging the Battery, due to Charging Inefficiency....
There are some unanswered questions embedded. That said, that battery will surely drive the fan. Whether or not that panel will keep the battery charged is going to depend on how many trees are overhanging your campsite, and how many days of rain you expect in camp as well as how many hours a day you need to be fanned.
You are drawing less (but not much less) than 1 amp. Given that, and the depending on the duty cycle (on/off time) of the fan, and assuming 50% efficiency of the panel and a fully charged battery in ideal temperature ranges, you should get 8 to 10 hours of run time. Now whether that panel will fully recharge your battery, or maintain a charge while the fan is in operation is another question and will depend upon what @ghrit stated above. Just my uneducated SWAG...
If this is just for a camping fan , I , ME (Sloth) would not pack in a heavy 18Ah gel cell to have breeze , I'd use LI-Ion cells 18650 as the smallest to larger ones . Also the Panel of 20W would be of high voltage type , Do A series parallel charge / load . . That math works ! Sloth