The Onset of Double Diffusive Convection in a Couple Stress Fluid Saturated Anisotropic Porous Layer

Abstract

The double diffusive convection in a horizontal couple stress fluid saturated anisotropic porous layer, which is heated and salted from below, is studied analytically. The modified Darcy equation that includes the time derivative term is used to model the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory. The effect of anisotropy parameter, solute Rayleigh number, Lewis number, couple stress parameter, and Vadasz number on the stationary, oscillatory, and finite amplitude convection is shown graphically. It is found that the thermal anisotropy parameter, couple stress parameter, and solute Rayleigh number have stabilizing effect on the stationary, oscillatory, and finite amplitude convection. The mechanical anisotropy parameter has destabilizing effect on stationary, oscillatory, and finite amplitude convection. The Lewis number has stabilizing effect in the case of stationary and finite amplitude modes, with dual effect in the case of oscillatory convection. Vadasz number advances the onset of oscillatory convection. The heat and mass transfer decrease with an increase in the values of couple stress parameter, while both increase with an increase in the value of solute Rayleigh number and mechanical anisotropy parameter. The thermal anisotropy parameter and Lewis number have contrasting effect on the heat mass transfer.

Effect of Internal Heating on Double Diffusive Convection in a Couple Stress Fluid Saturated Anisotropic Porous Medium

“…The expression of thermal Rayleigh number for the onset of stationary convection at the marginally stable steady state, for which the exchange of stabilities are valid correspond to the 0 = The above expression of thermal Rayleigh number is the result of stationary mode for onset of double-diffusive convection in a couple stress saturated anisotropic porous layer given by Malashetty and Premila Kollur [26]. In the case when medium is isotropic i.e.…”

“…Malashetty et al [25] performed linear and weakly nonlinear analyses of double diffusive convection in an isotropic porous medium saturated with couple stress fluid. Malashetty and Kollur [26] studied the onset of double diffusive convection in a couple stress fluid saturated anisotropic porous layer. Shivkumara et al [27] carried out linear and nonlinear stability analysis of double diffusive convection in a couple stress fluid saturated porous layer.…”

Variable Gravity Effects on Thermal Instability of Nanofluid in Anisotropic Porous Medium

“…Nanoparticles are suspended in the nanofluid using either surfactant or surface charge technology, preventing the agglomeration and deposition of these on the porous matrix. Thus the equations of continuity and motion for the nanofluid in an anisotropic porous medium (Chandersekhar 1961;Nield and Kuznetsov, 2009;Nield and Bejan, 2006;Malashetty and Kollur, 2011) …”

Effect of Horizontal Magnetic Field and Horizontal Rotation on Thermosolutal Stability of a Dusty Couple-Stress Fluid through a Porous Medium: a Brinkman Model

“…Greenspan (1969) studied the theory of rotating fluids which has applications in various technological situations which are governed by the action of coriolis force. The double diffusive convective problems of couple-stress fluid through an anisotropic porous medium considering rotational effect have been discussed in the references by Malashetty and Kollur (2011) and . A major part of the universe is filled with charged particles and magnetic field is present in and around the heavenly bodies.…”