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We know that combustion of fuels give water and carbon dioxide (during combustion of hydrocarbon) as a byproduct, but why don't these byproducts stop combustion?

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    $\begingroup$ Normal flames are open to atmosphere, so the byproducts, being in gaseous state (due to the flame's temperature), escape off by themselves. An engine, being a closed environment, would need to expel them before the next combustion event occured (the byproducts would not carry away much of the heat generated). That is why an exhaust system is present in automobiles. $\endgroup$ – FreezingFire Sep 27 '16 at 5:52
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You are exactly correct that in a closed system, the buildup of products would inhibit the reaction. As the concentrations of $\ce{CO2}$ and water vapor increase, the concentration of the oxygen will effectively decreases until the reaction slows and eventually stops.

Fortunately we rarely have to worry about this because we rarely try to do such a combustion in a closed system. Rather, as in the case of a car engine for example, there is a system in place to actively vent out the exhaust waste products ($\ce{CO2}$ and water) while pumping in more oxidant (oxygen) and fuel (hydrocarbon gasoline).

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