As you all know, transformer contains windings which carry electric current and electric current in the transformer winding produce heat. This heat is taken up by oil in transformer tank in case of oil filled transformers
Now consider different cases:
1) All transformers are fitted with radiator through heat of the oil or simply we can say oil is cooled by atmospheric air. This type of cooling is called ONAN(Oil Natural Air Natural).
2) To make transformer more efficient and to reject the heat from the oil, as the transformer capacity increases , fans are fitted below tranformer radiator. This type of cooling is called ONAF(Oil Natural Air Forced).
3) Further to provide more efficient cooling, large transformers are fitted with pumps which pump the oil between radiator and transformer tank. This type of cooling is called OFAF(Oil Forced Air Forced).
AN cooling class
In dry type transformer, there is no oil so entire heat is rejected in air. So fans are provided in transformer to cool the windings . This type of cooling is called AN (Air Natural).