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Changes in the Onset of Double-Diffusive Local Thermal Nonequilibrium Porous Convection Due to the Introduction of a Third Component

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Abstract

The two-temperature model of local thermal nonequilibrium is employed to study the onset of convection in a triply diffusive fluid-saturated porous medium. The Darcy equation including the time-derivative term is used to describe the flow in the porous medium. The criteria for the stationary and oscillatory instabilities of the basic flow are obtained in the closed form by performing the linear instability analysis. The topology of neutral stability curves is discussed for finite and infinite values of the Prandtl–Darcy number. The disconnected closed oscillatory neutral curves similar to those witnessed in the non-porous and porous (LTE case) domains are found indicating the requirement of three values of thermal Darcy–Rayleigh number to specify the linear instability criteria. There is degeneracy in the closed oscillatory neutral curve between infinite and finite values of the Prandtl–Darcy number; heart-shaped (quasiperiodic bifurcation) in the former case and closed convex in the latter case. Besides, the sensitivity of governing parameters on the nature of instabilities is emphasized.

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Acknowledgements

The authors wish to thank one of the reviewers profusely for offering constructive comments which helped in improving the paper considerably.

Funding

The author (KRR) gratefully acknowledge the support offered by the “Davangere University”, India, under the Grant No: DU/HRM/2020-21/6045 for this research work.

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Authors and Affiliations

  1. Department of Mathematics, Bangalore University, Bangalore, 560056, India

    I. S. Shivakumara

  2. Department of Mathematics, Davangere University, Davangere, 577002, India

    K. R. Raghunatha

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  1. I. S. Shivakumara
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  2. K. R. Raghunatha
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Correspondence to K. R. Raghunatha.

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Shivakumara, I.S., Raghunatha, K.R. Changes in the Onset of Double-Diffusive Local Thermal Nonequilibrium Porous Convection Due to the Introduction of a Third Component. Transp Porous Med 143, 225–242 (2022). https://doi.org/10.1007/s11242-022-01788-2

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