Nonlinear Stability and Linear Instability of Double-Diffusive Convection in a Rotating with LTNE Effects and Symmetric Properties: Brinkmann-Forchheimer Model

The major finding of this paper is studying the stability of a double diffusive convection using the so-called local thermal non-equilibrium (LTNE) effects. A new combined model that we call it a Brinkmann-Forchheimer model was considered in this inquiry. Using both linear and non-linear stability analysis, a double diffusive convection is used in a saturated rotating porous layer when fluid and solid phases are not in the state of local thermal non-equilibrium. In addition, we discussed several related topics such as the effect of solute Rayleigh number, symmetric properties, Brinkman coefficient, Taylor number, inter-phase heat transfer coefficient on the stability of the system, and porosity modified conductivity ratio. Moreover, two cases were investigated in non-linear theory, the case of the Forchheimer coefficient $\mathcal{F}=0$ and the case of the Taylor-Darcy number $\tau =0$. For the validation of this work, some numerical experiments were made in the non-linear energy stability and the linear instability theories.