https://doi.org/10.1140/epjp/s13360-026-07349-6
Regular Article
Boundary and LTNE effects on the onset of porous convection
1
Department of Physics, Government College for Women (Autonomous), 571401, Mandya, India
2
Department of Mathematics, Government First Grade College, 577004, Davanagere, India
3
Department of Mathematics, Maharani’s Science College for Women (Autonomous), 570005, Mysore, India
4
Department of Mathematics, Bangalore University, 560056, Bengaluru, India
a
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Received:
14
December
2025
Accepted:
19
January
2026
Published online:
6
February
2026
Abstract
The onset of Darcy–Bénard convection in a fluid-saturated porous layer is studied within the framework of local thermal nonequilibrium (LTNE), with emphasis on the influence of various hydrodynamic boundary conditions. The layer is heated from below by a prescribed constant heat flux and cooled from above under fixed-temperature conditions. Four combinations of velocity boundary conditions are considered at the upper and lower boundaries: impermeable–impermeable, porous–porous, impermeable–porous and porous–impermeable. LTNE effects are modelled using a two-temperature formulation in which the fluid and solid phases possess distinct temperature fields coupled through a finite interphase heat transfer coefficient. Linear stability of the quiescent basic state is analysed using normal-mode decomposition, yielding an eigenvalue problem that is solved numerically by a shooting method. The critical conditions for the onset of convection are determined in terms of the Darcy–Rayleigh number and the corresponding critical wave number. The critical Darcy–Rayleigh number is found to be maximal for impermeable/impermeable boundaries and minimal for porous/porous boundaries, with mixed boundary configurations exhibiting intermediate stability characteristics. Several limiting cases are discussed, and previously reported results are recovered.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
