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

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.1. Introduction. Double diffusive or thermosolutal comes from the coupled temperature and salinity diffusion in a fluid. In a binary fluid, the competing gradient are Dufour (thermo-diffusion) and Soret (diffusion-thermo) effects. Nield and Kuznetsov [15] studied both effects in a nanofluid where stationary and oscillatory 2010 Mathematics Subject Classification. Primary: 76R10, 80A20; Secondary: 76A02.

Effects of LTNE on Two-Component Convective Instability in a Composite System with Thermal Gradient and Heat Source

“…Internal heat, using a local thermal non-equilibrium model, was analyzed analytically by Altawallbeh et al [2,3] in a Maxwell fluid-porous layer with and without a magnetic field. Abidin et al [4] conducted a study to examine the effects of viscosity in a binary fluid layer. In a two-component system, the closed form of the solution to Marangoni convection with a magnetic field and salinity gradients was studied by Komala and Sumithra [5].…”