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Dendritic combustion in Hele–Shaw cells is investigated qualitatively using a simplified one-dimensional thermo-diffusive model. Formulas for the velocity, size, and temperature of the flamelets are derived. The temperature and velocity of the flames increase for small radii to allow for their survival regardless of the activation energy. In addition, the results obtained with very large activation energy were compared with experimental results, finding that additional tests are required due to the strong influence of gravity on the velocity and size estimations. Conditions for the existence of this anomalous propagation are investigated, confirming analytically that it can only happen for low Lewis numbers. [ABSTRACT FROM AUTHOR]

In this paper, a theoretical analysis of the condensation of combustion products in narrow gaps between planar plates is performed. The investigation is motivated by the empirical results shown by Veiga-López ["Flame propagation in narrow channels," Ph.D. thesis (Carlos III University of Madrid, 2020)] and the lack of a theoretical description directly applicable to them. In these experiments, he describes how discontinuous condensed water films appeared on the walls of the combustion chamber, forming dry/wet stripes parallel to the flame front at the products region. The formulation developed here is derived from a general approach for condensation, which is simplified considering the conditions of high-temperature combustion products. Notably, the liquid phase disappears from the system of equations, which exclusively contains the gaseous phase. The expressions resulting are analytical, simple, and easy to interpret. They allow us to understand qualitatively the effects of the main physical phenomena of the process, which is described by the interaction between heat exchange, mass transfer, the thermodynamic conditions, and the velocity of the combustion products. The construct is subsequently utilized to perform the numerical parametric studies, to analyze the influence of two main parameters of the problem: gap thickness and flame velocity. Despite the relative simplicity of the model, it predicts similar condensation–vaporization–condensation cycles to those observed at the laboratory. [ABSTRACT FROM AUTHOR]