The goal of this research is to study flamelets near solid fuel segments embedded in a non-combustible binder material. Flame attachment to surfaces in problems such as spreading flames, fires, and surface-burning propellants is a complicated process. The flame heats the surface, which decomposes into volatiles, which leave the surface as the gaseous fuel that mixes with incoming oxidizer, feeding further combustion. An interesting flame shape called the "flamelet" appears in narrow-channel combustion, microgravity combustion, and combustion over heterogeneous fuels. The model examined here develops a simple description of flamelet attachment and examines the details of the localized near-surface heat transfer and gas phase combustion. In essence, the "flame microstructure" near the surface is described as it interacts with the surface, including the heat flux from the flame, the surface heat flux, their dependence on flame microstructural parameters, and the sensitivity of the flame structure in response to changes in these parameters. Where possible, numerical solutions are compared with analytical formulas and calculations, and extensions are made to describe more general cases.

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