The blast furnace is a T5 Tech that comes in at the end of the tech tree, unlocking this tech provides access to multiple modular structures such as the air intake base and hot air stove base. Both are required for the a blast furnace to function (It is recommend that you also research "Slag Reprocessing" which is the following tech after the blast furnace research, this will be explained further later).

For a fully functional blast furnace you need to supply it with a set number of inputs which can be viewed at the terminal once a "Mode" has been set as shown below!

As shown in the screenshot this blast furnace consumes 324,000L/min of hot air while a hot air stove can only supply 108,000L/min to fully supply a maxed blast furnace so you would need 3 hot air stoves to supply this blast furnace with enough air to maintain its temperature. For those 3 hot air stoves you would also need to supply them with 324,000L/min of regular air which is provided through an air intake and each air intake can provide 162,000L/min of air each therefor you need only 2 to supply all 3 hot air stoves previously mentioned.
In summary for 1 Blast Furnace (all modules selected) you need

• 3 Hot Air Stoves
  
• 2 Air Intakes

Additionally the hot air stoves have something called adjacency bonus which lets them consume 25% less power for each hot air stove that is making full contact with another so the most efficient layout for the hot air stoves is generally just going to be a row. The way you lay your blast furnace setup out is completely up to you but the graphic below is generally a fairly compact design that can be tiled by just flipping it upside down.

The preferred method for fluid/gas transfer with modular structures is through "Pipelines" these are much larger than the regular pipes you might have been using up until now but the air intake, hot air stove and blast furnace all feature large pipe connections to allow input or output using them.
It is important while connecting your hot air input that you set the filter behind the pipe connector to hot air else it will not accept the gas into the furnace

The blast furnace outputs molten versions of each metal which must then be processed in a casting machine in order to get rods in the case of Technum and plates in the case of Xenoferrite however be aware that you will need a total of 96 Casting machines in order to fully process the constant output of a blast furnace and this is also where the slag reprocessing research comes in that was mentioned in the first section.

Slag reprocessing allows you to turn the blast furnace slag into cement which you can then reuse elsewhere in your factory or it can be incinerated. The quantity of cement produced by a single blast furnace is not a large amount therefor I would personally suggest just voiding the cement slag in a flare stack rather than trying to re purpose it for use elsewhere in your save.

As mentioned before the blast furnace outputs molten metal which is processed into plates or rods, this is the T3 recipe and is therefor the most efficient method for turning your raw ore into usable resources. The ratios for each tier are as follows;

• T1 - 1 Ore Rubble: 1 Plate/Rod
  
• T2 - 1 Ore Rubble: 1.5 Plate/Rod
  
• T3 - 1 Ore Rubble: 3 Plate/Rod

Each blast furnace requires 3 material inputs in order to begin smelting, mineral rock, coke ignium and ore (the type of ore depends on what material you selected on the terminal). In the case of a blast furnace using all possible module slots you will need to feed it 1280/min Ore (Specifically this must be ore not rubble. This can be made in a crusher) 640/min coke ignium; this can be made in an advanced smelter from ignium ore which must be made in a crusher from ignium ore rubble. 640/min coke ignium only comes out to 256/min of ignium ore rubble so the numbers aren't as bad as it may first appear. Finally you will need 256/min of mineral rock which should be very plentiful and once supplied with all of these things your blast furnace will output 11520L/min of molten metal which needs to be processed into plates or rods in 96 casting machines which comes out to 3,840 items/min of output from just a single blast furnace!

All resources mentioned above must be fed into this hopper located at the top of the blast furnace. I recommend using freight elevators to get them up here.

This section will include a list of some common mistakes made while setting up a blast furnace. Go through this list and check each of them and if you still can't find your problem I would suggest asking in the Foundry official Discord here: discord.gg/foundry-game

• Check that you have set the hot air filter in the back of the large pipe connection between the blast furnace and hot air stoves, this can be accessed by using the walk way of the blast furnace.
  
• Make sure your air intakes and hot air stoves are connected to your high voltage grid and turned on!