So let's say I have a super cooling "battery" basically a brick that cools anything that touches one end of it to ~0k. Now, using handwavium I can thermally isolate it so that it doesn't just cool everything infinitely. What I want to know is:
given this "cooling battery" what is the best way to create lift using WW2 era technology?
There can be some flex there, since my civilization is supposed to be slightly more advanced than others of the time, but nuclear solutions are a no go, since that would have too much impact on the outcome of the war. Some ideas I've had are
Temperature Gradient Turbine
Put our super cooling battery on one side of a tube, and a heat source on the other, the difference in temperature will cause the air to move around the tube. Place a turbine inside the tube, and you have thrust.
Use our super cooling batter to produce a brick of frozen Hydrogen, put this in a tube and take away the battery, the Hydrogen will begin to rapidly expand, if a hole is left in the bottom of this tube, we have thrust.
Super Cooled Environment
If we cool the air around our pilot, or only on the top of a pair of wings, will that have a noticeable effect on flight? Note: This idea is a long shot, I'm just trying to think outside the box, or tube as the case may be
Ideally I'd like something as rooted in hard science as possible, with certain amounts of handwavium applied where necessary (eg. creating containment fields for our super cooled air, preventing humidity from forming huge blocks of ice)