When in the furnace user interface, it is only possible to place items in the "items to be smelted" area. You cannot "click" on the fuel area to either put in or remove fuel such as coal, wood, etc. You can also not take out any smelted items from the "smelted" area of the furnace (e.g. smooth stone, gold ingots, iron ingots, etc.) Additionally, you cannot remove placed items from the "items to be smelted" area. Basically, when you place an item in a furnace to be smelted, it is stuck there, unless fuel is already in the furnace. In that case, the item smelts, but is stuck in the "finished smelting" area.