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Ah now this IS an area of expertise of mine, there is so much I could tell you but I'll try to simplify it and make it brief. If you want to know more about something specifically, ask a specific question. :-)
First some assumptions about what you are asking:
\(\huge\cdot\) You're working with type A or B fires only
\(\huge\cdot\) You're working with open air, not a compartment fire
\(\huge\cdot\) You're working with a diffusion flame, not premixed
Some notes about fire that most people don't know
\(\huge\cdot\) Fire is a rapid exothermic chemical reaction producing light & heat in varying intesities
\(\huge\cdot\) Fire is refers to the whole system of the reaction, flame refers to the reaction surface, particularly the visible part
\(\huge\cdot\) Fire is hollow, and forms a fluid-like surface of reaction that deforms with turbulence. The reaction occurs on flame sheets
\(\huge\cdot\) Fire is typically limited by the amount of oxidizer (typically oxygen) that can diffuse in. Explosives on the other hand have oxygen already ready in the fuel's molecule itself, so they can react insanely faster.
\(\huge\cdot\) Fire rises due to buoyancy, which is an effect of changes in density interacting with gravity
Classic diffusion flame example (candle)
DISCLAIMER: In the real world these steps don't occur distinctly, they are kind of gradually blended in from one to the next. Clearly definable, but blended at their edges.
1. Luminous flame sheet surface, where primarily carbon dust (i.e.: soot) is responsible for the bright "orange" glow you see. The final products are made here, namely steam, carbon dioxide, carbon monoxide, and soot.
2. Infrared flame sheet, where the majority of the exothermic chemical reaction occurs, formaldehyde, hydrogen peroxide, free radical hydrogen (i.e.: just the protons), free radical electrons, and hydroxide (OH\(^-\)) are the intermediary stage reactants & products found here.
3. Pyrolysis zone, where more complex hydrocarbons of the fuel are quickly being broken down into methane gas and hydrogen (H\(_2\)) gas.
4. Premixed flame base, thanks to the fuel below getting pyrolyzed by the intense radiant heat coming from the reaction above it shining down, the fuel is vaporized an a little of it forms a premixed flame of oxygen and hydrogen. The reaction is much more efficient and reacts a lot of hydrogen gas and carbon monoxide with additional oxygen gas, making a nice blue to ultraviolet frequency flame that is barely visible to the human eye.
What a coincidence! I recently saw a very animation that explains what a flame is. You might find it helpful: http://vimeo.com/40271657