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Onset of LTNE anisotropic porous convection: effect of asymmetric temperature boundary conditions

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Abstract

The onset of buoyancy-driven convection in a fluid-saturated anisotropic porous layer is studied by employing a local thermal non-equilibrium (LTNE) model. The porous layer is assumed to be bounded by impermeable boundaries with isoflux and isothermal conditions prescribed at the lower and upper boundaries, respectively. The anisotropy in permeability as well as fluid and solid thermal conductivities is considered. The linear instability analysis has been performed, and the eigenvalue problem is constituted using the procedure of normal mode analysis. The threshold values of the Darcy–Rayleigh number and the wave number for the onset of convection are extracted numerically using the shooting method. Increase in the mechanical anisotropy parameter and decrease in the thermal anisotropy parameters, scaled inter-phase heat transfer coefficient and the ratio of porosity-modified conductivities encourage a destabilizing influence on the onset of convection. For lower isoflux and upper isothermal boundaries case, small temperature differences are found to be sufficient to trigger the convective instability when compared to both boundaries isothermal.

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Authors and Affiliations

  1. Department of Mathematics, School of Applied Sciences, REVA University, Bengaluru, 560064, India

    Suma Shyabal & B. N. Hanumagowda

  2. Department of Mathematics, Dr. G. Shankar Government Women’s First Grade College and Post Graduate Study Centre, Ajjarakadu, Udupi, 576101, India

    M. Ravisha

  3. Department of Mathematics, Government First Grade College and Centre for PG Studies, Thenkanidiyur, 576106, India

    A. L. Mamatha

  4. Department of Mathematics, Bangalore University, Bengaluru, 560 056, India

    I. S. Shivakumara

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  1. Suma Shyabal
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  2. M. Ravisha
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  4. A. L. Mamatha
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  5. I. S. Shivakumara
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Correspondence to M. Ravisha.

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Shyabal, S., Ravisha, M., Hanumagowda, B.N. et al. Onset of LTNE anisotropic porous convection: effect of asymmetric temperature boundary conditions. Eur. Phys. J. Plus 138, 106 (2023). https://doi.org/10.1140/epjp/s13360-023-03717-8

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