So right now I've been tasked to come up with a world for a story that centers around what we could probably describe as post-civil war era. Coal is a resource needed for fueling machines and modes of industry, but it can only be mined with the use of slaves. The only way to get slaves however is through warfare as the offspring of slaves are conscripted into the army without ever knowing their parents, which brings up the heat and central plot of the story. Does this economy make sense and can it hold?
This would be unsustainable, as you'd have slaves at every critical point of your economy. With your coal mining slaves being deprived of their children, they would have literally nothing to lose by triggering massive explosions in the mines (Coal dust is EXTREMELY explosive). Which would cripple your economy, devastate your ability to make war, and end your source of conscription.
Morale in your army would be low as well, as they would have no family that they knew about back home. Nobody to defend. This would also tax loyalty.
This could work out only if there were a way to move up out of slavery and if the soldiers DID know their parents. (Fight to free mom and dad!).
As it is, I don't see this working for long.