During Earth's atmospheric entry of an Apollo-like capsule, what would happen if oxygen hitting heatshield was mixed with fuel injected through heatshield, and ignited?
Edit & addendum : During hypersonic entry, is there a boundary layer, with velocity gradient, from 0 to hypersonic, close to heatshield's skin, where combustion may occur, and what about such a heatshield's shape behaviour? Would it act like a combustion chamber? (illustration below)
Ultimately, would this slow down entry by creating a bigger hypersonic draggy bubble around the capsule, some sort of entry burn, using no oxydizer.