When you blow on a fire you bring cold oxygen to it. The fires tends to be starved for oxygen so bringing in more oxygen will make the fire burn faster. However fires also need to maintain its heat so bringing inn cold air will cool it down. So there is a balance of bringing inn enough oxygen to make the fire bigger but not so much that it cools down the fire. For a small fire like a candle you cool it down too much when you blow on it. But for a larger fire you help bring oxygen to it.
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