Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers
2014 (English)In: Networks and Heterogeneous Media, ISSN 1556-1801, E-ISSN 1556-181X, Vol. 9, no 4, 709-737 p.Article in journal (Refereed) Published
We study the homogenization of a reaction-diffusion-convection system posed in an epsilon-periodic delta-thin layer made of a two-component (solid-air) composite material. The microscopic system includes heat flow, diffusion and convection coupled with a nonlinear surface chemical reaction. We treat two distinct asymptotic scenarios: (1) For a fixed width delta > 0 of the thin layer, we homogenize the presence of the microstructures (the classical periodic homogenization limit epsilon --> 0); (2) In the homogenized problem, we pass to delta --> 0 (the vanishing limit of the layer's width). In this way, we are preparing the stage for the simultaneous homogenization (epsilon --> 0) and dimension reduction limit (delta --> 0) with delta = delta (epsilon). We recover the reduced macroscopic equations from  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 resistance-to-heat ceramic-based materials for engines, to the smoldering combustion of thin porous samples under microgravity conditions.
Place, publisher, year, edition, pages
Springfield: American Institute of Mathematical Sciences, 2014. Vol. 9, no 4, 709-737 p.
Homogenization, dimension reduction, thin layers, filtration combustion, two-scale convergence, anisotropic singular perturbations
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kau:diva-39784DOI: 10.3934/nhm.2014.9.709ISI: 000346795500009ScopusID: 2-s2.0-84915779556OAI: oai:DiVA.org:kau-39784DiVA: diva2:901169