scholarly journals Stability Convection in a Couple Stress Fluid Saturated in an Anisotropic Porous Medium with Internal Heating Effect

2020 ◽  
Vol 76 (2) ◽  
pp. 75-84
Author(s):  
Nadia Diana Mohd Rusdi ◽  
Nor Fadzillah Mohd Mokhtar ◽  
Norazak Senu ◽  
Siti Suzilliana Putri Mohamed Isa
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Couple Stress ◽  
Anisotropy Parameter ◽  
Mechanical Anisotropy ◽  
Mode Analysis ◽  
Couple Stress Fluid ◽  
Heating Effect ◽  
Internal Heating ◽  
Anisotropic Porous Medium

Internal heating effect with stability convection in a couple stress fluid saturated in an anisotropic porous medium has been studied numerically using linear stability analysis. The presence of internal heating on couple stress fluid in an anisotropic porous medium heated from below has been verified. The momentum equation and Boussinesq approximation is used for the density variation in the porous medium. By using Chebyshev Tau method numerically, the eigenvalue problems of the perturbed state were obtained from a normal mode analysis. The effect of the Rayleigh number, internal heat source and anisotropy parameter has been shown graphically. The critical Rayleigh number also has been obtained and plotted on the system. From the result, it is found that the mechanical anisotropy parameter and internal heating effect destabilized the system while couple stress fluid and thermal anisotropy parameter help in stabilizing the system.

Double-Diffusive Magneto Convection in a Compressible Couple-Stress Fluid Through Porous Medium

2011 ◽  
Vol 66 (5) ◽  
pp. 304-310 ◽  
Author(s):  
Pardeep Kumar ◽  
Hari Mohan
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Couple Stress ◽  
Mode Analysis ◽  
Couple Stress Fluid ◽  
Onset Of Convection ◽  
Linearized Stability ◽  
Medium Permeability ◽  
Solute Gradient ◽  
Double Diffusive

The double-diffusive convection in a compressible couple-stress fluid layer heated and soluted from below through porous medium is considered in the presence of a uniform vertical magnetic field. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the compressibility, stable solute gradient, magnetic field, and couple-stress postpone the onset of convection whereas medium permeability hastens the onset of convection. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The stable solute gradient and magnetic field introduce oscillatory modes in the system, which were non-existent in their absence. A condition for the system to be stable is obtained by using the Rayleigh-Ritz inequality. The sufficient conditions for the non-existence of overstability are also obtained.

scholarly journals The onset of thermal convection in couple-stress fluid in hydromagnetics saturating a porous medium

2014 ◽  
Vol 62 (2) ◽  
pp. 357-362
Author(s):  
Gian C. Rana
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Convection ◽  
Couple Stress ◽  
Normal Mode Analysis ◽  
Linear Stability Theory ◽  
Mode Analysis ◽  
Couple Stress Fluid ◽  
Stress Parameter ◽  
Medium Permeability

Abstract In this paper, the effect of magnetic field on thermal convection in couple-stress fluid saturating a porous medium is considered. By applying linear stability theory and the normal mode analysis method, a mathematical theorem is derived which states that the viscoelastic thermal convection at marginal state, cannot manifest as stationary convection if the thermal Rayleigh number R, the medium permeability parameter Pι the couple-stress parameter F and the Chandrasekher number Q, satisfy the inequality the result clearly establishes the stabilizing character of couple-stress parameter and magnetic field whereas destabilizing character of medium permeability.

scholarly journals Thermal Instability in a Layer of Couple Stress Nanofluid Saturated Porous Medium

2017 ◽  
Vol 47 (1) ◽  
pp. 69-84 ◽  
Author(s):  
Ramesh Chand ◽  
G. C. Rana ◽  
Dhananjay Yadav
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Couple Stress ◽  
Thermal Instability ◽  
Volume Fraction ◽  
Saturated Porous Medium ◽  
Normal Mode Analysis ◽  
Lewis Number ◽  
Mode Analysis ◽  
Brownian Diffusion

Abstract Thermal instability in a horizontal layer of Couple-stress nanofluid in a porous medium is investigated. Darcy model is used for porous medium. The model used for nanofluid incorporates the effect of Brownian diffusion and thermophoresis. The flux of volume fraction of nanoparticle is taken to be zero on the isothermal boundaries. Normal mode analysis and perturbation method is employed to solve the eigenvalue problem with the Rayleigh number as eigenvalue. Oscillatory convection cannot occur for the problem. The effects of Couple-stress parameter, Lewis number, modified diffusivity ratio, concentration Rayleigh number and porosity on stationary convection are shown both analytically and graphically.

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