### Abstract

Original language | English |
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Place of Publication | Eindhoven |

Publisher | Technische Universiteit Eindhoven |

Number of pages | 28 |

Publication status | Published - 2014 |

### Publication series

Name | CASA-report |
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Volume | 1402 |

ISSN (Print) | 0926-4507 |

### Fingerprint

### Cite this

*Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers*. (CASA-report; Vol. 1402). Eindhoven: Technische Universiteit Eindhoven.

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*Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers*. CASA-report, vol. 1402, Technische Universiteit Eindhoven, Eindhoven.

**Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers.** / Fatima, T.; Ijioma, E.R.; Ogawa, T.; Muntean, A.

Research output: Book/Report › Report › Academic

TY - BOOK

T1 - Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers

AU - Fatima, T.

AU - Ijioma, E.R.

AU - Ogawa, T.

AU - Muntean, A.

PY - 2014

Y1 - 2014

N2 - We study the homogenization of a reaction-diffusion-convection system posed in an e-periodic d-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 d > 0 of the thin layer, we homogenize the presence of the microstructures (the classical periodic homogenization limit e ¿ 0); (2) In the homogenized problem, we pass to d ¿ 0 (the vanishing limit of the layer's width). In this way, we are preparing the stage for the simultaneous homogenization (e ¿ 0) and dimension reduction limit (d ¿ 0) with d = d(e). We recover the reduced macroscopic equations from [21] 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. Keywords: Homogenization, dimension reduction, thin layers, filtration combustion, two-scale convergence, anisotropic singular perturbations.

AB - We study the homogenization of a reaction-diffusion-convection system posed in an e-periodic d-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 d > 0 of the thin layer, we homogenize the presence of the microstructures (the classical periodic homogenization limit e ¿ 0); (2) In the homogenized problem, we pass to d ¿ 0 (the vanishing limit of the layer's width). In this way, we are preparing the stage for the simultaneous homogenization (e ¿ 0) and dimension reduction limit (d ¿ 0) with d = d(e). We recover the reduced macroscopic equations from [21] 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. Keywords: Homogenization, dimension reduction, thin layers, filtration combustion, two-scale convergence, anisotropic singular perturbations.

M3 - Report

T3 - CASA-report

BT - Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -