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Ekeoma Ijioma
| Speaker: |
Ekeoma Ijioma
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| Date: |
Tuesday July 27, 2010
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| Title: |
Homogenization
technique applied to a smoldering combustion model (Master's
thesis presentation)
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Abstract
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We study a semi-linear
reaction-diffusion (RD) system modeling reverse smoldering combustion
of a thin cellulose material (e.g. paper) under the influence of
oxidizing wind.
The basic geometry of our material consists of a collection of many
small thin solid cylinders periodically distributed in space that we
call microstructures. The main working assumption is that the
microstructure depends on two independent parameters: δ - the height of
the cylinder (oriented in Oz direction) and ϵ - the width of a
square cell that is copied periodically to cover the x-y plane. After a
volume averaging of the RD system along the z coordinate, we obtain the
so-called micro problem.
The main objective is to use periodic homogenization methods to study
the asymptotic behavior of the solutions to the micro problem as the
parameter ϵ goes to zero. This method gives an upscaled RD system (that
we refer to as macro problem) together with explicit formulae for the
effective coefficients.
We use COMSOL Multiphysics to solve numerically the micro problem for
decreasing values of ϵ and compare the obtained results with the
solution of the macro problem
ϵ = 0). We see that our model captures the expected behavior of
concentrations and temperature profiles as observed in smoldering
combustion experiments.
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