No abstract

The model of double-diffusive convection in a porous medium layer was analyzed using the Brinkman model and concentration based on an internal heat source. Linear instability analysis of the model was performed. Particularly, we analyzed the effect of slip boundary conditions on the instability of the system. We analyzed when the instability started and computed the critical Rayleigh number as a function of the slip coefficient. K E Y W O R D S Brinkman model, double-diffusive, slip boundary conditions, linear instability, Rayleigh number, slip boundary conditions

A model for double-diffusive convection in anisotropic and inhomogeneous porous media has been analysed. In particular, the effect of variable permeability and thermal diffusivity has been studied using the Brinkman model. Moreover, we analyse the effect of slip boundary conditions on the stability of the model. Due to numerous applications in micro-electro-mechanical-systems (MEMS) and other microfluidic devices, such a study is essential to have. Both linear instability analysis and nonlinear stability analysis are employed. We accurately analyse when stability and instability will commence and determine the critical Rayleigh number as a function of the slip coefficient.

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.

This paper is concerned with the question of the beginning of convective motion in a fluid saturated porous layer, containing a salt in solution, heated below and salted above and below. This model has a single temperature and employs the Darcy theory in the micropores, the Brinkman theory, however, being utilized in the macropores. The effect of slip boundary conditions on the stability of the model is also studied. General boundary conditions regarding temperature and salt are also taken into account. It will be shown that the linear instability threshold is the same as that of nonlinear stability if the layer is salted from above, indicating that the linear theory entirely captures the physics of the onset of thermal convection. In the case of salting from below, the behavior of the transition from stationary to oscillatory convection is investigated in detail, as the boundary conditions change from prescribed temperature and salt concentration toward those of prescribed heat flux and salt flux. The nonlinear stability threshold does not coincide with that of linear instability; thus, regions of possible subcritical instability are still present. We believe that the problem presented in this paper has not been addressed before and that its study will have great scientific value and impact.