Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers

摘要: We study the homogenization of a reaction-diffusion-convection system posed in an $\varepsilon$-periodic $\delta$-thin layer made two-component (solid-air) composite material. The microscopic includes heat flow, diffusion and convection coupled with nonlinear surface chemical reaction. treat two distinct asymptotic scenarios: (1) For fixed width $\delta>0$ thin layer, we homogenize presence microstructures (the classical periodic limit $\varepsilon\to 0$); (2) In homogenized problem, pass to $\delta\to 0$ vanishing layer's width). this way, are preparing stage for simultaneous ($\varepsilon\to 0$) dimension reduction ($\delta\to $\delta=\delta(\epsilon)$. We recover reduced macroscopic equations from [25] precise formulas effective transport reaction coefficients. We complement analytical results few simulations case smoldering combustion. chosen multiscale scenario is relevant large variety practical applications ranging forecast response fire refractory concrete, microstructure design resistance-to-heat ceramic-based materials engines, combustion porous samples under microgravity conditions.