The Effect of Rotation on the Onset of Double Diffusive Convection in a Horizontal Anisotropic Porous Layer

Double diffusive convection in a rotating anisotropic porous layer, saturated by a viscoelastic fluid, heated from below and cooled from above has been studied making linear and non-linear stability analyses. The fluid and solid phases are considered to be in equilibrium. In momentum equation, we have employed the Darcy equation which includes both time derivative and Coriolis terms. The linear theory based on normal mode method is considered to find the criteria for the onset of stationary and oscillatory convection. A weak non-linear analysis based on minimal representation of truncated Fourier series analysis containing only two terms has been used to find the Nusselt number and Sherwood number as functions of time. We have solved the finite amplitude equations using a numerical scheme. The results obtained, during the above analyses, have been presented graphically and the effects of various parameters on heat and mass transfer have been discussed. Finally, we have drawn the steady and unsteady streamlines, isotherms, and isohalines for various parameters.

Section: Stationary Statementioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Non-Linear Two Dimensional Double Diffusive Convection in a Rotating Porous Layer Saturated by a Viscoelastic Fluid

Kumar

Bhadauria

2010

“…Malashetty and Swamy (2007) have examined the combined effect of rotation and anisotropy on the onset of convection in a horizontal porous layer using linear and a weak nonlinear theory. Recently many authors have studied the effect of anisotropy on the onset of convection in a porous layer (Govender 2007;Malashetty and Heera 2008;Malashetty et al 2009b;Gaikwad et al 2009a,b;Malashetty and Swamy 2010).…”

Section: Introductionmentioning

confidence: 99%

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

Malashetty

Kollur

2010

Self Cite

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.

“…Recently many authors have studied the effect of anisotropy and/or rotation on the onset of convection in a horizontal porous layer (see e.g., Govender 2006Govender , 2007Govender and Vadasz 2007;Malashetty and Swamy 2007). More recently Malashetty and Heera (2008) studied the effect of rotation on the onset of double diffusive convection in a horizontal anisotropic porous layer using a linear and nonlinear theory. The linear and nonlinear double diffusive convection in a rotating sparsely packed porous layer using a thermal non-equilibrium model was investigated by Malashetty et al (2009).…”

Section: L Mmentioning

confidence: 99%

The Effect of Rotation on the Onset of Double Diffusive Convection in a Sparsely Packed Anisotropic Porous Layer

Malashetty

Begum

2011

Self Cite

The effect of rotation on the onset of double diffusive convection in a sparsely packed anisotropic porous layer, which is heated and salted from below, is investigated analytically using the linear and nonlinear theories. The Brinkman model that includes the Coriolis term is employed for the momentum equation. The critical Rayleigh number, wavenumber for stationary and oscillatory modes and a dispersion relation are obtained analytically using linear theory. The effect of anisotropy parameters, Taylor number, Darcy number, solute Rayleigh number, Lewis number, Darcy-Prandtl number, and normalized porosity on the stationary, oscillatory and finite amplitude convection is shown graphically. It is found that contrary to its usual influence on the onset of convection in the absence of rotation, the mechanical anisotropy parameter show contrasting effect on the onset criterion at moderate and high rotation rates. The nonlinear theory based on the truncated representation of Fourier series method is used to find the heat and mass transfers. The effect of various parameters on heat and mass transfer is shown graphically. Some of the convection systems previously reported in the literature is shown to be special cases of the system presented in this study.