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Computational Thermal Sciences: An International Journal

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ISSN Imprimer: 1940-2503

ISSN En ligne: 1940-2554

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THE EFFECT OF CHANGEABLE GRAVITY FIELD ON THE STABILITY OF CONVECTION IN A POROUS LAYER FILLED WITH NANOFLUID: BRINKMAN MODEL

Volume 13, Numéro 6, 2021, pp. 1-17
DOI: 10.1615/ComputThermalScien.2021038043
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RÉSUMÉ

The onset of convective instability in a horizontal nanofluid filled porous layer is investigated for the changeable gravity field. The Buongiorno model for the nanofluid and the Brinkman model for the flow through the porous layer are employed. Three cases of boundaries viz., free−free, rigid−free, and rigid−rigid, are considered in this observation. Also, linear, quadratic, cubic, and exponentially varying gravity fields have been taken to present this problem. The linear stability of the basic state is studied for the normal mode perturbations and, the solution for the corresponding eigenvalue problem is obtained using the bvp4c routine inMATLAB. The critical Rayleigh number and corresponding wavenumber have been calculated and shown graphically for various aspects due to the influence of the governing parameters. It is noted that the basic density Rayleigh number, Lewis number, and modified diffusivity ratio advance the convective motion; whereas the Darcy number and gravity variation parameter postpone the onset of convection. When both boundaries are rigid or free, the modified particle density increment acts as a stabilizing factor; however, when the lower boundary is rigid and the upper boundary is free, it plays the role as a destabilising factor. The flow in a cubic varying gravity field with free-free boundaries is more unstable; whereas the flow in an exponentially varying gravity field with rigid-rigid boundaries is more stable.

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