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I've noticed this in match-sticks, and mango wood. After the flames die out, the brand glows red for a while. The glow is brightest right before it dies out.

My guess is that immediately before the glow dies out, any air channels in the wood are fully dried by the heat to the extent that the 'reverse wind' sweeps in to oxygenate the burning portion. This wind is so strong that the burn cannot advance and therefore glows brightest right where it is before burning itself out. This is just my guess. Why does it glow brightest before it dies out?

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While the match is burning, fresh unheated air is continuously drawn past the end. This limits the temperature of the burning end. Once the match is blown out, the amount of airflow will be greatly reduced. Although the amount of heat generated will also be reduced, the fact that less heat gets carried away will allow the end to get hotter than it could otherwise. – supercat Oct 16 '14 at 17:10

I'm not entirely sure about my answer so don't shoot me if I'm wrong...

My suggestion would be that if the fire dies and shrinks into the woodstructure, it almost completely consumes the remaining air in the air channels. As we all know, air carries tiny water droplets which normally would cool the fire, so if the fire is now in a state where there is less oxygen (and thus less water droplets), it will gain heat. This heat will energize electrons which will emit a brighter light. (hotter electrons emit more light)

I hope this makes sense, if not, correct me because I would really like to know if I'm right or not.

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It could also be because as it is burning not all of the energy is in the visible range but as it cools down more and more of it is till it just drops off.

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