The temperature you run your fire at will determine how fast wet wood will dry and start to smoke. The amount of water in the wood will determine how hot the actual "burning front" can get. If you run a cool fire the water will evaporate and cool the burn more effectively. The smoke "window" will probably not be as long... Run it too hot and the wood will surface dry faster and start smoking sooner. The wood will burn slightly cooler, but the extra heat will reduce the cooling effect and allow a hotter burning front, therefore less smoke per unit of wood. Get the temperature right and the wood will burn at a relatively uniform rate, produce lots of smoke, and last longer.
Dry wood will burn faster and hotter, produce less smoke, and require more tending.
The total heat equation inside the smoker is surprisingly complex and the nature of burning wood, which is a very erratic fuel source, in small controlled burns makes it difficult to make errorless blanket statements. Water (steam) venting from your smoker carries a tremendous amount of heat with it. But things like atmospheric pressure, ambient temperature, relative humidity, and many other variables each bring their own correction factor for calculating burn rates.
Wet wood produces more smoke than dry under typical smoker conditions. Wet wood burns longer under typical smoker conditions. Wet wood will add heat to the smoker for a longer period of time and at a more consistent rate under typical smoker conditions. Those are facts brought to use by Physics. You may find exceptions, but those are symptoms of a marginal smoker set-up.
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