Taken from the Thaumcraft-Wiki:
The Arcane Bellows does not have a function of it's own - it's main use is to grant bonuses to Crucibles and Arcane Furnaces, or to increase the vis pressure within certain blocks.
When placed adjacent to a Crucible the bellows boosts the rate at which it can smelt items and also slightly improves the efficiency of the crucible, allowing it to produce more Vis and less Taint for each item smelted.
When placed adjacent to an Arcane Furnace it boosts the speed at which the Furnace smelts ores. and also increases its chance to produce multipe smelting results.
Bellows can be connected to Tanks or Pumps. Each bellows increases the suction in these blocks by 10 TCB. Bellows can be connected directly to conduits as well to increase the suction in that section, but multiple bellows will not increase the suction in a single conduit beyond 10 TCB.
This block only can be conected horizontally. This limits the number of bellows to 4.
Placing an Arcane Furnace below a crucible increases the percentage of vis produced by 10%. Each Arcane Bellows attached to the furnace increases the vis percentage by an additional 2.5%. Attaching an Arcane Bellows directly to a crucible has no effect.