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This question already has an answer here:

How would the shape and size of a flame, e.g. from a simple candle depend on gravity? Suppose all the relevant information is known, including candle dimensions and chemical composition, atmosphere properties (chemical composition, pressure etc.), and anything else.

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marked as duplicate by David Z Nov 7 '18 at 0:03

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For a candle flame, following processes occur. 1. heat transfer (from flame to surrounding and to candle) 2. material transfer (wax vapor diffused outwards and oxygen diffused inwards) 3. heat generation (chemical reaction at stoichiometric mixture location)

with gravity, the above will shift due to free convection flow. This will accelerate heat transfer, material transfer and thus heat generation.

Let's assume everything is the same and only gravity is different a little. Smaller gravity will make less material transfer and less heat transfer. This will shorten the flame or reduce the flame front area. You will end up with short and wider (spherical) flame.

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You'll find the whole analysis in the book of Landau and Lifszyc, Hydrodynamics. This is a complicated theoretical subject which you analyze with a model of flammable gasous mixture in a cylinder tube. First you analyze how flaming surface moves in a tube and then you impose, that the whole gas is moving. Then you make this gas fell out of this tube and you see what shape it might have. There are theorems, that it makes itself smooth, you can add gravity if you want but the real reason it makes itself higher is the buoyancy when your flame is surrounded by the air. I think it's hard but possible to calculate but you must first go through analysis from Landau and Lifszyc.

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After some searches I found this little paper. I will give only a short answer to the question, for details you can read the paper.

So, according to the results obtained for the model in the paper:

  1. the flame length:

    • increases as the gravity level increases from $0g_e$ to $3g_e$
    • decreases from $3g_e$ to $60g_e$
    • and blows off at higher gravity levels
  2. the maximum width of the flame decreases as the gravity level increases.

In the next figure can be observed the evolution of the flame from $0g_e$ to $5g_e$.  Flame shape contours contours at various gravity levels

However, if the top surface of the wick is made inert, the model predicts that the flame blows off at $6g_e$.

$g_e$ - gravity at the level of Earth surface.

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