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Sharp Instability Estimates for Bidisperse Convection with Local Thermal Non-equilibrium

Franchi, Franca; Nibbi, Roberta; Straughan, Brian

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Authors

Franca Franchi

Roberta Nibbi

Brian Straughan



Abstract

We analyse a theory for thermal convection in a Darcy porous material where the skeletal structure is one with macropores, but also cracks or fissures, giving rise to a series of micropores. This is thus thermal convection in a bidisperse, or double porosity, porous body. The theory allows for non-equilibrium thermal conditions in that the temperature of the solid skeleton is allowed to be different from that of the fluid in the macro- or micropores. The model does, however, allow for independent velocities and pressures of the fluid in the macro- and micropores. The threshold for linear instability is shown to be the same as that for global nonlinear stability. This is a key result because it shows that one may employ linearized theory to ensure that the key physics of the thermal convection problem has been captured. It is important to realize that this has not been shown for other theories of bidisperse media where the temperatures in the macro- and micropores may be different. An analytical expression is obtained for the critical Rayleigh number and numerical results are presented employing realistic parameters for the physical values which arise. Article Highlights: A two-temperature regime for a bidisperse Darcy porous medium is proposed to study the thermal convection problem. The optimal result of coincidence between the linear instability and nonlinear stability critical thresholds is proven. Numerical analysis enhances that the scaled heat transfer coefficient between the fluid and solid and the porosity-weighted conductivity ratio stabilize the problem significantly.

Citation

Franchi, F., Nibbi, R., & Straughan, B. (2024). Sharp Instability Estimates for Bidisperse Convection with Local Thermal Non-equilibrium. Transport in Porous Media, 151(1), 193-211. https://doi.org/10.1007/s11242-023-02038-9

Journal Article Type Article
Acceptance Date Nov 2, 2023
Online Publication Date Nov 28, 2023
Publication Date 2024-01
Deposit Date Jan 10, 2024
Publicly Available Date Jan 10, 2024
Journal Transport in Porous Media
Print ISSN 0169-3913
Electronic ISSN 1573-1634
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 151
Issue 1
Pages 193-211
DOI https://doi.org/10.1007/s11242-023-02038-9
Keywords Instability, Local thermal non-equilibrium (LTNE), Bidispersive porous media, Global nonlinear stability
Public URL https://durham-repository.worktribe.com/output/2118392

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Copyright Statement
This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.





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