Onset of convection in the Rayleigh-Bénard flow with temperature dependent viscosity: An asymptotic approach

Abstract Soret driven ferrothermoconvective instability in multi-component fluids has a wide range of applications in heat and mass transfer. This paper deals with the theoretical investigation of the effect of temperature dependent viscosity on a Soret driven ferrothermohaline convection heated from below and salted from above subjected to a transverse uniform magnetic field in the presence of a porous medium. The Brinkman model is used in the study. It is found that the stationary mode of instability is preferred. For a horizontal fluid layer contained between two free boundaries an exact solution is examined using the normal mode technique for a linear stability analysis. The effect of salinity has been included in magnetization and density of the fluid. The critical thermal magnetic Rayleigh number for the onset of instability is obtained numerically for sufficiently large values of the buoyancy magnetization parameter M1 using the method of numerical Galerkin technique. It is found that magnetization and permeability of the porous medium destabilize the system. The effect of temperature dependent viscosity stabilizes the system on the onset of convection.

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The onset of convection in fluids with strongly temperature-dependent viscosity cooled from above with implications for planetary lithospheres

Earth and Planetary Science Letters ◽

10.1016/j.epsl.2004.05.013 ◽

2004 ◽

Vol 224 (3-4) ◽

pp. 371-386 ◽

Cited By ~ 33

Author(s):

Sarah E. Zaranek ◽

E.M. Parmentier

Keyword(s):

Temperature Dependent ◽

Temperature Dependent Viscosity ◽

Onset Of Convection ◽

Dependent Viscosity

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Rayleigh-Bénard Convection of Non-Newtonian Power-Law Fluids with Temperature-Dependent Viscosity

ISRN Thermodynamics ◽

10.5402/2012/614712 ◽

2012 ◽

Vol 2012 ◽

pp. 1-10 ◽

Cited By ~ 10

Author(s):

Mourad Kaddiri ◽

Mohamed Naïmi ◽

Abdelghani Raji ◽

Mohammed Hasnaoui

Keyword(s):

Heat Transfer ◽

Power Law ◽

Temperature Dependent ◽

Temperature Dependent Viscosity ◽

Bénard Convection ◽

Benard Convection ◽

Power Law Fluids ◽

Dependent Viscosity ◽

Rayleigh Benard Convection ◽

Rayleigh Benard

Two-dimensional steady-state Rayleigh-Bénard convection of thermodependent power-law fluids confined in a square cavity, heated from the bottom and cooled on the top with uniform heat fluxes, has been conducted numerically using a finite difference technique. The effects of the governing parameters, which are the Pearson number (0≤m≤10), the flow behaviour index (0.6≤n≤1.4), and the Rayleigh number (0<Ra≤105), on the flow onset, flow structure, and heat transfer have been examined. The heatlines concept has been used to explain the heat transfer deterioration due to temperature-dependent viscosity effect that m expresses.

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Rayleigh-Benard-Marangoni Ferro Convection with Concentration and Temperature Dependent Viscosity

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.b1087.0782s619 ◽

2019 ◽

Vol 8 (2S6) ◽

pp. 458-461

Keyword(s):

Perturbation Technique ◽

Temperature Perturbation ◽

Temperature Dependent ◽

Regular Perturbation ◽

Rigid Boundary ◽

Temperature Dependent Viscosity ◽

Fluid Parameter ◽

Dependent Viscosity ◽

Surface Tension Forces ◽

Rayleigh Benard

The inception of Rayleigh-Benard-Marangoni (RBM) Ferro convection with concentration and temperature dependent viscosity is investigated theoretically and the resultant is further enhanced numerically using Galerkin method. We observed that the effect of Rayleigh number together with internal heating suppressed the onset of RBM Ferro convection. The nonlinear nature of magnetic fluid parameter has no impact on the onset of Ferro convection. The latent values found numerically by Galerkin weighted Residual technique and regular perturbation technique are found to be alike, indicating the fact that the obtained solutions are near exact in nature. The result of the BC’s for lower and upper free rigid boundary at temperature dependent surface tension forces are found to be immaculately insulate to temperature perturbation.

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