Abstract
This work is concerned with finding nonlinear stability limits of a thermally stratified horizontal layer governed by the Darcy–Lapwood–Brinkman equations. Time periodic modulation is imposed on either the boundary temperatures or the gravitational field permeating the layer. Unlike the classical theory of porous media, thermodynamic non-equilibrium is assumed within the layer in the form of non-negligible temperature differences. The solid and fluid constituents may undergo their own temperature variations and the heat flow is studied using the two-temperature model. The generalized energy method is employed to determine the relevant limits that suffices the system stability. The non-equilibrium and modulational parameters are found to affect the stability limits that are based on a higher-order Galerkin solution. Moreover, it is established that the stability limits so obtained are unconditional in the Euclidean measure.
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Acknowledgements
One of the authors (MM) thanks DST, India for providing financial assistance in the form of INSPIRE Fellowship when she was at Bharathiar University. This work was supported by UGC, India through DRS Special Assistance Programme in Differential Equations and Fluid Dynamics.
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Saravanan, S., Meenasaranya, M. Unconditional stability of an externally controlled medium with thermodynamic non-equilibrium. Z. Angew. Math. Phys. 73, 206 (2022). https://doi.org/10.1007/s00033-022-01843-4
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DOI: https://doi.org/10.1007/s00033-022-01843-4