Effect of anisotropic permeability on double‐diffusive bidisperse porous medium

Abstract

The model of thermosolutal convection in a fluidsaturated bidisperse porous medium of Darcy type is studied in this paper. The permeability is allowed to be horizontally isotropic for both the macro-and microphases. The linear instability and nonlinear stability are analyzed by taking the Soret effect into account. Furthermore, the effect of anisotropy parameter, Soret coefficient, and other physical parameters on the stability of the system are investigated.It is shown that the linear instability boundaries and the energy stability boundaries do not coincide when the layer is heated and salted from below, where a region of potential subcritical instability occurs. The results reveal that the horizontal to vertical permeability ratio plays a crucial role in the stability of the system. It is also observed that for large values of the salt Rayleigh number, the onset of thermal convection is more likely to be via oscillatory convection rather than stationary convection. Furthermore, the onset of stationary convection is significantly influenced by the presence of the Soret coefficient.anisotropic permeability, bidisperse porous medium, doublediffusive convection, linear instability, nonlinear stability

Linear and Non-Linear Stability Analysis for Thermal Convection in A Bidispersive Porous Medium with Thermal Non-Equilibrium Effects

“…Both cases are studied by using golden section search to minimise over 2 a and find the critical values of 2 R for linear instability. Moreover, the critical Rayleigh numbers of nonlinear energy stability E Ra for fixed 2 a and  is determined using equation (18). Then, we employ golden section search to minimise in 2 a and then maximise in  to determine E Ra , where for 2…”

“…This has also been considered further using a variety of geometries and incorporating various other effects, for example, anisotropic parameter and double diffusion cf. Straughan [14][15][16][17], and Saleh and Haddad [18]. The papers by Franchi et al [19] present the effect of local thermal non-equilibrium on a bidispersive porous medium.…”

“…we have stability for the best values of the coupling parameter  . We have to do the minimization in equation ( 8), equation ( 9) and equation (18) numerically by using Matlab routines. For the parameters that are employed in this article, we have to be very careful when minimize 2 R in equation ( 8) and equation ( 9) over 2 a .…”

Effect of local thermal non-equilibrium on the onset of convection in an anisotropic bidispersive porous layer

“…See for example Straughan [16], who investigated the onset of convection for thermal convection in a bidispersive porous medium, when the horizontal permeability are the same in the macopores and the micopores The same author in Straughan [16] performed the linear and nonlinear stability methods when the permeability ratios in the macropores and the micropores are taken to be different. Saleh and Haddad [17] presented an analysis of linear and nonlinear stability to study the anisotropy parameter with soret coefficient effects on the onset of thermal convection in double porosity media. Saleh [18] also considered the Brinkman model to investigate thermosolutal convection in a bidispersive porous medium with anisotropic permeability effect.…”

“…Saleh and Haddad [17] presented an analysis of linear and nonlinear stability to study the anisotropy parameter with soret coefficient effects on the onset of thermal convection in double porosity media. Saleh [18] also considered the Brinkman model to investigate thermosolutal convection in a bidispersive porous medium with anisotropic permeability effect. Recently, Capone et al [19] performed linear and nonlinear stability analysis for the problem of thermal convection in an inisotropic and rotating bidisperse porous medium.…”