So far, we've been heating the 'inside' surface of the metal walls by
radiation (BLUE) and convection (RED) from the fire. What happens now?First, CONDUCTION transfers heat THROUGH the metal (GRAY) (molecule to molecule), in an effort to equalize the temperature of the whole metal thickness.
Then, on the OTHER side, heat is carried away in the fluid there (air) by our old friends, CONVECTION (GREEN) and RADIATION (not shown).
This is moderately effective, and is generally referred to as natural convection.