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Stability of Flow of a Variable-Viscosity Fluid Saturating a Differentially Heated Vertical Porous Layer

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Abstract

The effect of viscosity varying linearly with temperature and the Prandtl–Darcy number on the stability of buoyancy-driven convection in a vertical porous layer is investigated. The variation in viscosity causes a dramatic change in the base flow and thereby discards the analytical proof of stability even under the limit of an infinite Prandtl–Darcy number. The question about the stability/instability of the basic flow is thus examined by carrying out a numerical solution of the stability eigenvalue problem for infinite and finite values of the Prandtl–Darcy number. It is found that the linear temperature dependence of the viscosity does not activate the instability to small-amplitude disturbances.

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Acknowledgements

We are indebted to three anonymous referees for thoroughly reading the manuscript and for indicating several points which have led to substantial improvements in the work.

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Authors and Affiliations

  1. Department of Mathematics, PES University, Bangalore, 560 085, India

    B. M. Shankar & K. V. Nagamani

  2. Department of Mathematics, Bangalore University, Bangalore, 560 056, India

    I. S. Shivakumara

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  1. B. M. Shankar
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  2. K. V. Nagamani
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  3. I. S. Shivakumara
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Correspondence to B. M. Shankar.

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Shankar, B.M., Nagamani, K.V. & Shivakumara, I.S. Stability of Flow of a Variable-Viscosity Fluid Saturating a Differentially Heated Vertical Porous Layer. Transp Porous Med 150, 1–14 (2023). https://doi.org/10.1007/s11242-023-01975-9

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  • DOI: https://doi.org/10.1007/s11242-023-01975-9

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