A system includes a combustor. The combustor has a combustor wall with a combustor dome at an upstream end of the combustor wall, and an outlet at a downstream end of the combustor wall opposite the upstream end. The combustor wall includes an inner wall portion and an outer wall portion defining an interior of the combustor therebetween. Each of the inner wall portion and outer wall portion extends from the combustor dome to the downstream end of the combustor wall. The combustor wall includes an air cooling passage embedded inside at least one of the inner wall portion and the outer wall portion. The air cooling passage extends from the upstream end of the combustor wall to the downstream end of the combustor wall.