So, it is theoretically possible to stay up as long as you like without any on-board fuel. That theory was recently proven by an amateur experimenter. You just need to install a BUNCH of thermal generators on the ground along your line of flight! The first half of the video is making the plane - jump to 1:15 if you want to see the results right away.

http://www.youtube.com/watch?v=t2sozrof3HY

Why not just use all the thermal generators that are already here, and not use any fuel on the ground or in the airplane?