Check out Project Pluto on Wikipedia [1], and the Direct Air Cycle part of the Aircraft Nuclear Propulsion page [2]. From the Pluto page,
"The principle behind the nuclear ramjet was relatively simple: motion of the vehicle pushed air in through the front of the vehicle (ram effect), a nuclear reactor heated the air, and then the hot air expanded at high speed out through a nozzle at the back, providing thrust."
1 - https://en.m.wikipedia.org/wiki/Project_Pluto
2 - https://en.m.wikipedia.org/wiki/Aircraft_Nuclear_Propulsion#...
while we're at it, have a fun tangential short story by Charlie Stross about rockets, missiles, volatile oxidizers, and more, with only a touch of plausible-sounding scifi nonsense: