Look up some YouTube videos of candles or lighters used in zero-gravity. It’s a sphere.

The candle shape on earth is caused by the weight of the air.

The third reference from the article provides some pointers (see also references there).

https://arxiv.org/pdf/1803.10400

But its not trivial at all, its a complex fluid dynamics problem. I stumbled upon all the "coupled candle oscillators" literature when I was looking for a shortcut to a semi-physical candle model. But there is no easy way out...

Faraday did a whole series of lectures about a single candle, essentially covering a surprising amount of physics and chemistry. Super simple and fascinating: https://www.gutenberg.org/ebooks/14474

seems like a very complicated simulation problem. i'd be surprised if you could derive from first principles.

you need to model the atmosphere as environment, heat flow, wicking action, chemical reactions, fluid dynamics under gravity. Then model human perception to turn the spectral radiance into a perceived shape.