6533b854fe1ef96bd12adf59

RESEARCH PRODUCT

A Non-normal-Mode Marginal State of Convection in a Porous Rectangle

Peder A. TyvandJonas Kristiansen NolandL. Storesletten

subject

PhysicsConvectionConvective heat transferGeneral Chemical Engineering0208 environmental biotechnologyBoundary (topology)02 engineering and technologyMechanics010502 geochemistry & geophysicsVDP::Matematikk og Naturvitenskap: 400::Matematikk: 41001 natural sciencesCatalysisFinite element method020801 environmental engineeringHeat fluxNormal modeThermalRectangle0105 earth and related environmental sciences

description

Author's accepted manuscript (postprint). This is a post-peer-review, pre-copyedit version of an article published in Transport in Porous Media. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11242-019-01263-5. The fourth-order Darcy–Bénard eigenvalue problem for onset of thermal convection in a 2D rectangular porous box is investigated. The conventional type of solution has normal-mode dependency in at least one of the two spatial directions. The present eigenfunctions are of non-normal-mode type in both the horizontal and the vertical direction. A numerical solution is found by the finite element method, since no analytical method is known for this non-degenerate fourth-order eigenvalue problem. All four boundaries of the rectangle are impermeable. The thermal conditions are handpicked to be incompatible with normal modes: The lower boundary and the right-hand wall are heat conductors. The upper boundary has given heat flux. The left-hand wall is thermally insulating. The computed eigenfunctions have novel types of complicated cell structures, with intricate internal cell walls.

yearjournalcountryeditionlanguage
2019-03-14Transport in Porous Media
https://doi.org/10.1007/s11242-019-01263-5