Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers. Fatima, T., Ijioma, E., Ogawa, T., & Muntean, A. Networks and Heterogeneous Media, 2014. doi abstract bibtex © American Institute of Mathematical Sciences. We study the homogenization of a reaction-diffusion-convection system posed in an ε-periodic δ-thin layer made of a two-component (solid-air) composite material. The microscopic system includes heat ow, diffusion and convection coupled with a nonlinear surface chemical reaction. We treat two distinct asymptotic scenarios: (1) For a fixed width δ > 0 of the thin layer, we homogenize the presence of the microstructures (the classical periodic homogenization limit ε → 0); (2) In the homogenized problem, we pass to δ → 0 (the vanishing limit of the layer's width). In this way, we are preparing the stage for the simultaneous homogenization (ε → 0) and dimension reduction limit (δ → 0) with δ = δ(ε). We recover the reduced macroscopic equations from [25] with precise formulas for the effective transport and reaction coefficients. We complement the analytical results with a few simulations of a case study in smoldering combustion. The chosen multiscale scenario is relevant for a large variety of practical applications ranging from the forecast of the response to fire of refractory concrete, the microstructure design of resistanceto-heat ceramic-based materials for engines, to the smoldering combustion of thin porous samples under microgravity conditions.
@article{
title = {Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers},
type = {article},
year = {2014},
keywords = {Anisotropic singular perturbations,Dimension reduction,Filtration combustion,Homogenization,Thin layers,Two-scale convergence},
volume = {9},
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created = {2019-08-23T19:37:41.826Z},
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abstract = {© American Institute of Mathematical Sciences. We study the homogenization of a reaction-diffusion-convection system posed in an ε-periodic δ-thin layer made of a two-component (solid-air) composite material. The microscopic system includes heat ow, diffusion and convection coupled with a nonlinear surface chemical reaction. We treat two distinct asymptotic scenarios: (1) For a fixed width δ > 0 of the thin layer, we homogenize the presence of the microstructures (the classical periodic homogenization limit ε → 0); (2) In the homogenized problem, we pass to δ → 0 (the vanishing limit of the layer's width). In this way, we are preparing the stage for the simultaneous homogenization (ε → 0) and dimension reduction limit (δ → 0) with δ = δ(ε). We recover the reduced macroscopic equations from [25] with precise formulas for the effective transport and reaction coefficients. We complement the analytical results with a few simulations of a case study in smoldering combustion. The chosen multiscale scenario is relevant for a large variety of practical applications ranging from the forecast of the response to fire of refractory concrete, the microstructure design of resistanceto-heat ceramic-based materials for engines, to the smoldering combustion of thin porous samples under microgravity conditions.},
bibtype = {article},
author = {Fatima, T. and Ijioma, E. and Ogawa, T. and Muntean, A.},
doi = {10.3934/nhm.2014.9.709},
journal = {Networks and Heterogeneous Media},
number = {4}
}
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