Fluid Saturated Anisotropic Porous Layer Research Articles

An analytical study of linear and nonlinear double diffusive convection in a fluid saturated anisotropic porous layer with Soret effect

The double diffusive convection in a horizontal anisotropic porous layer saturated with a Boussinesq fluid, which is heated and salted from below in the presence of Soret coefficient is studied analytically using both linear and nonlinear stability analyses. The normal mode technique is used in the linear stability analysis while a weak nonlinear analysis based on a minimal representation of double Fourier series method is used in the nonlinear analysis. The generalized Darcy model including the time derivative term is employed for 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 parameters, solute Rayleigh number, Soret parameter and Lewis number on the stationary, oscillatory, finite amplitude convection and heat and mass transfer are shown graphically.

The Onset of Convection in an Anisotropic Porous Layer Using a Thermal Non-Equilibrium Model

The stability of a horizontal fluid saturated anisotropic porous layer heated from below and cooled from above is examined analytically when the solid and fluid phases are not in local thermal equilibrium. Darcy model with anisotropic permeability is employed to describe the flow and a two-field model is used for energy equation each representing the solid and fluid phases separately. The linear stability theory is implemented to compute the critical Rayleigh number and the corresponding wavenumber for the onset of convective motion. The effect of thermal non-equilibrium and anisotropy in both mechanical and thermal properties of the porous medium on the onset of convection is discussed. Besides, asymptotic analysis for both very small and large values of the interphase heat transfer coefficient is also presented. An excellent agreement is found between the exact and asymptotic solutions. Some known results, which correspond to thermal equilibrium and isotropic porous medium, are recovered in limiting cases.

Effect of a Variable Gravity Field on Convection in an Anisotropic Porous Medium With Internal Heat Source and Inclined Temperature Gradient

The convective instability of a horizontal fluid-saturated anisotropic porous layer, with internal heat source and inclined temperature gradient, subject to a gravity field varying with distance in the layer, is investigated. A linear stability analysis is performed and the resulting eigenvalue problem solved using a Galerkin technique. In the absence of an inclined temperature gradient, an increase in the variable gravity parameter above −1 destabilizes the system. In its presence interesting developments occur. An increase in the heat generation destabilizes the system when the variable gravity parameter is nonnegative. When it is negative the opposite effect is seen.