Bidispersive thermal convection with relatively large macropores and generalized velocity and temperature boundary conditions

Abstract

In a fluid-saturated bidisperse porous medium at a single temperature, the issue of thermal convection when the Darcy theory is used in the micropores, particularly the effects of slip boundary conditions on the model stability, was examined (whereas the Brinkman theory is used in the macropores). In addition, the effect of general temperature boundary conditions was also addressed. The governing equations of motion are provided, followed by the way in which the related equations of perturbation were derived. In addition, the linear instability and nonlinear stability analyses of the system were introduced, with the numerical approach used to approximate the eigenvalue system resulting from our analysis. The threshold for linear instability was proved to be the same as the one for nonlinear stability, showing that the linear theory accurately captures the mechanism of the onset of thermal convection. The numerical results for stability/instability thresholds were also introduced. The researchers assumed that this was the first time a mixed Darcy–Brinkman model had been used in bidisperse flow with slip boundary conditions.

Stability of Darcy thermosolutal convection in bidispersive porous medium with reaction

“…Presently, we solved the eigenvalue systems () and () using the Chebyshev collocation procedure, further specifics regarding this method can be found in previus studies 53‐59 . For this approach, system () has been changed to second order.…”

Soret effect on stability of Darcy problem in a bidispersive porous medium with an exothermic chemical surface reaction

“…Subsequently, a plethora of studies have been published, addressing various convection issues within bidispersive porous media, such as those in Refs. [3][4][5][6][7][8][9][10][11]. These studies extensively explored the variations in velocity and temperature across macro and micropores.…”

Thermal convection in a linearly viscous fluid overlying a bidisperse porous medium

“…Gentile and Straughan [22], Straughan [51], chapter 13. Analyses of bidispersive thermal convection in isotropic, anisotropic, vertical layer, inclined layer, and with rotation effects are given by Badday and Harfash [1], Capone et al [6], Capone et al [5], Capone and De Luca [3], Capone and Massa [4], Capone et al [7], Chaloob et al [9], Falsaperla et al [18], Gentile and Straughan [20,21], Saravanan and Vigneshwaran [46], Straughan [52,54,53], and the structural stability aspect of the system of equations is considered by Franchi et al [19].…”