Title:

How a Candle Burns: Understanding Combustion Dynamics Using Free Boundary Problems and Phase Change

This project investigates the usability of a simplified theoretical mathematical model intended to mimic qualitative features of combustion. The goal of this model is to create a self-contained, consistent mathematical description of a dynamical system which undergoes both phase change and material consumption. The resulting model will be analyzed to characterize steady-state solutions (where material profiles and consumption rates are assumed to be constant in time), and the stability of those steady states will be investigated. The purpose of this research is pedagogical in nature, to arrive at a model which can mimic some features of a candle and give students an introduction to free-boundary value problems, and multi-phase physical models. The simplified model in this poster explores the case where solid and liquid phases have equivalent thermal properties, allowing for exploration of the heat equation in a moving frame of reference. Following the conference, this simplified model will be modified to fully incorporate the phase-change boundary.

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