An Explanation to the Nusselt–Rayleigh Discrepancy in Naturally Convected Porous Media

We model hydrothermal convection using a partial differential equation formed by Darcy velocity and temperature—the velocity formulation. Using the Elder problem as a benchmark, we found that the velocity formulation is a valid model of hydrothermal convection. By performing simulations with Rayleig...

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Bibliographic Details
Published in:Transport in porous media 2021-03, Vol.137 (1), p.195-214
Main Authors: Huang, Po-Wei, Wellmann, Florian
Format: Article
Language:English
Subjects:
Civil Engineering
Classical and Continuum Physics
Convection modes
Earth and Environmental Science
Earth Sciences
Geotechnical Engineering & Applied Earth Sciences
Hydrogeology
Hydrology/Water Resources
Industrial Chemistry/Chemical Engineering
Partial differential equations
Porous media
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Summary:We model hydrothermal convection using a partial differential equation formed by Darcy velocity and temperature—the velocity formulation. Using the Elder problem as a benchmark, we found that the velocity formulation is a valid model of hydrothermal convection. By performing simulations with Rayleigh numbers in the non-oscillatory regime, we show that multiple quasi-steady-state solutions can be one of the reasons that caused the Nusselt–Rayleigh discrepancy found in previous experiments. The results reveal more understandings about the nature of uncertainty of convection modes in porous media.
ISSN:0169-3913
1573-1634
DOI:10.1007/s11242-021-01556-8