Metal Smelting Problems

I need some help with aspects of my economic system related to metals and the manufacture of metal goods.

For example, I want to figure out more accurate values for the amount of coal needed to produce enough heat to melt metals for smelting.

I can find values online for the BTU produced by a given unit of a given type of fuel. And I can find the melting points of various metals and metal alloys.

But how many BTU are needed to reach a given temperature in a forge's hearth, and how long does that temp need to be maintained? People who burn coal to heat their homes have created online calculators to estimate how much coal would be needed to keep a room of a given size heated to a given temperature, but their answers don't agree with each other in the slightest.

Here are the questions I'm struggling with, as many as I can think of:

- how big is the hearth in a forge?
- how many BTU are needed to heat an area of a given volume to a given temperature?
- what is the relationship between the melting point of an ore, pure metal, or alloy, and the temperature needed to smelt it, or forge it? Do you need to reach the melting point, or do you just need to get the metal to a certain level of workability? (Presumably this differs for smelting from ores vs. smithing from already-made ingots.)
- how long does the smelting temperature or temperatures need to be maintained in the hearth? Does this vary between metals?
- how much limestone or other flux is needed when smelting and forging, and with what other variables does that amount vary?

If you can offer help or resources to read, I'd be grateful. I'll be having a poke around the library and in my friend's blacksmithing books when I can, too.

EDIT: I found digital editions of contemporary (17th century) sources through the library's subscriptions. The work I'll be looking at first is A Discovery of Subterraneal Treasure, by one Gabriel Plattes, published in London in 1653. There are others; we'll see what I can dig up. Luckily, 17th-century English is still pretty readable!