Onset of Benard-Marangoni instabilities in a double diffusive binary fluid layer with temperature-dependent viscosity

Nurul Hafizah Zainal Abidin; Nor Fadzillah Mohd Mokhtar; Zanariah Abdul Majid

doi:10.3934/naco.2019040

Article Contents

2019, Volume 9, Issue 4: 413-421. Doi: 10.3934/naco.2019040

This issue Previous Article Conformal deformations of a specific class of lorentzian manifolds with non-irreducible holonomy representation Next Article Stability analysis of stagnation point flow in nanofluid over stretching/shrinking sheet with slip effect using buongiorno's model

Onset of Benard-Marangoni instabilities in a double diffusive binary fluid layer with temperature-dependent viscosity

1.
Laboratory of Computational Sciences and Mathematical Physics, Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2.
Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Perak Branch, Tapah Campus, 35400 Tapah Road, Perak, Malaysia
3.
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

^* Corresponding author: norfadzillah.mokhtar@gmail.com
^* Corresponding author: norfadzillah.mokhtar@gmail.com

The reviewing process of the paper is handled by Gafurjan Ibragimov, Siti Hasana Sapar and Siti Nur Iqmal Ibrahim

Received: January 2018

Revised: July 2018

Published: November 2019

he present research was partially supported by MOHE for FRGS Vote no 5524808.

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Abstract

The effect of temperature-dependent viscosity in a horizontal double diffusive binary fluid layer is investigated. When the layer is heated from below, the convection of Benard-Marangoni will start to exists. Linear stability analysis is performed and the eigenvalues from few cases of boundary conditions were obtained. Galerkin method were used to solve the numerical calculation and marginal stability curve is obtained. Results shows that an increase of temperature-dependent viscosity will destabilized the system. The impact of double diffusive coefficients are also revealed. It is found that the effect of Soret parameter exhibits destabilizing reaction on the system while an opposite response is noted with an increase of Dufour parameter.

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Mathematics Subject Classification: Primary: 76R10, 80A20; Secondary: 76A02.

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Figure 1. Effect of $ B $ to Rayleigh number

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Figure 2. Effect of $ Sr $ to Rayleigh number

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Figure 3. Effect of $ Df $ to Rayleigh number

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Figure 4. Effect of $ B $, $ Sr $ and $ Df $ to Marangoni number

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Figure 5. Effect of $ B $ on $ Ra_c $ for various values of $ Le $

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Figure 6. Effect of $ B $ on $ Ra_c $ for various values of $ Rs $

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