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

Abstract

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.

Instability and Convection in Rotating Porous Media: A Review

“…For example Capone and Gentile [80] presented sharp stability results in a rotating anisotropic porous layer subject to lack of local thermal equilibrium (LaLotheq, LTNE). Double diffusive convection in a rotating anisotropic porous layer was presented by Galkwad and Kouser [81], Malashetty and Heera [82], and Malashetty and Begum [83]. Double diffusive convection in a rotating porous medium saturated with a coupled stress fluid was considered by Malashetty et al [84], while double diffusive convection in a rotating porous layer saturated by a viscoelastic fluid was investigated by Kumar and Bhadauria [85].…”

Theoretical Study of Cross Diffusion Effects on Convective Instability of Maxwell Fluid in Porous Medium

“…Malashetty and Gaikwad (2001) have studied the effect of cross diffusion terms on double diffusive convection in a porous medium in the presence of horizontal gradients. Malashetty and Begum (2011) have investigated the effect of rotation on the onset of double diffusive convection in a sparsely packed anisotropic porous layer. Recently Gaikawad andKamble (2012a, 20121b, 2014) have investigated theoretically the double diffusive convection in a fluid saturated anisotropic couple stress fluid and porous layer in the presence of Soret and rotational effect.…”

Analytical Solution of Forced Convective Heat Transfer in a Horizontal Anisotropic Porous Media Cylinder: Effect of Variations of Frictional Heating and Heat Generation on the Temperature Profile and Nusselt Number

“…21 in porous layer. 22,23 The mixed convection through a parallel-plate vertical porous channel, which was assumed to be hydrodynamically anisotropic, was studied by Degan and Vasseur. 16 They found that for Da < 10 -5 the viscous effects near the boundaries were negligible, and the permeability ratio and inclination of principal axes of permeability had a strong influence on the thermal convection.…”