The purpose of the furnace is to contain the heat generated by the burner or other heat source so that the material inside the furnace reaches the desired temperature. A side effect is reduction of fuel used and safety and comfort of the operator. A relatively cool outside surface of a furnace makes it easier and safer to work nearby. And the less heat lost, the less fuel required.

For metal founding, the material whose temperature we are raising is the metal we are trying to melt and the crucible containing it. The fuel can be gaseous (propane, LPG, acetylene, ...) liquid (oil, kerosene (paraffin), or solid (wood, charcoal, coal or other) or maybe electrical (by using an arc, induction or resistive heating elements.) We'll concentrate on non-electrical furnaces here. In the case of a cupola, there is no crucible, as such, but the well must be maintained hot enough to keep the melt liquid. The entire host section serves as a "crucible" and the iron (or other metal) melts down into the catch basin (is that the right term?) to be tapped.

Furnaces can constructed with two layers of "refractory" materials, the "face" or "hot face" and insulation. The primary functions of the hot face material are to withstand the direct heating and chemical attacks of the combustion and the mechanical attacks of the operator putting tongs, crucibles?, metal bits and what-not in the furnace. A good high-temperature refractory will stand up to all these abuses for a good length of time and will be relatively easy to patch when the inevitable wear out occurs.

Since most of the tough and hard hot face materials have relatively poor insulating properties, they can be surrounded by one or more layers of insulation. Nearest the hot face, the insulation must withstand the greatest temperatures. Nearer the outer walls, the temperature is lower. In large furnaces, several different layers of insulation may be applied, since higher-temperature insulations cost more and are less effective than lower-temperature insulations.

For hobby-size furnaces, one layer of a hard high-temperature material is often used for the entire furnace body. Some people wrap a layer of Kaowool or other ceramic- or mineral-fiber insulation around the outside of that for better insulation. Such fibrous materials should be surrounded by a shell to contain loose fibers.

The crucible must fit inside the furnace with sufficient space around it for the combustion gases to surround the crucible and heat it evenly (and for the lifting tongs to grab it without damaging the furnace wall.) Ideally, the output from the burner should swirl around the crucible several times before exiting through the exhaust vent (usually at the top of the furnace.) The inside of the furnace will glow and heat the crucible through radiation from the walls as well as through the convection from the hot gases.

Some random notes:

The smaller a furnace is, the quicker it will reach operating temperature, but the smaller it's throughput will be.

You just can't put a 4 inch crucible inside a 4 inch bore furnace.

It will take longer to heat a furnace constructed entirely of high temperature hot-face capable refractory than one consisting of a thinner layer of hot-face material and a layer of insulation.

The bottom of the furnace should have a "plinth block" or refractory pedestal for the crucible to sit on.

The bottom of the furnace should have a drain hole in it for the inevitable metal leak to find an escape route.

It is also important to use the furnace atop an insulating and containing surface, such as a bed of sand, so when the inevitable metal leak finds its way out the drain hole, it doesn't set the house, lawn, garage or kitchen table alight. That would be bad bongos indeed.

The interior of a furnace will never get hotter than the temperature of the heat source, so don't plan to melt platinum with an air-propane flame. No matter how much insulation you have, the temperature won't rise high enough.