Journal
TRANSPORT IN POROUS MEDIA
Volume 141, Issue 3, Pages 737-769Publisher
SPRINGER
DOI: 10.1007/s11242-022-01746-y
Keywords
Upscaling; Heat transport; Thin porous media
Categories
Funding
- Projekt DEAL
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [327154368 -SFB 1313]
- DFG [EXC2075 -390740016]
- Stuttgart Center for Simulation Science (SimTech)
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The heat transport through thin porous media is affected by the local pore geometry and the boundary conditions. By solving cell problems, the impact of local grain shape on the effective heat conductivity is demonstrated.
Heat transport through a porous medium depends on the local pore geometry and on the heat conductivities of the solid and the saturating fluid. Through upscaling using formal homogenization, the local pore geometry can be accounted for to derive effective heat conductivities to be used at the Darcy scale. We here consider thin porous media, where not only the local pore geometry plays a role for determining the effective heat conductivity, but also the boundary conditions applied at the top and the bottom of the porous medium. Assuming scale separation and using two-scale asymptotic expansions, we derive cell problems determining the effective heat conductivity, which incorporates also the effect of the boundary conditions. Through solving the cell problems, we show how the local grain shape, and in particular its surface area at the top and bottom boundary, affects the effective heat conductivity through the thin porous medium.
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