Linear and nonlinear stability analysis of double-diffusion convection in an inclined Brinkman porous media with a concentration-based internal heat source

The onset of double-diffusion convection in an inclined porous medium with a concentration-based internal heat source is investigated by performing linear and nonlinear stability analysis. The Brinkman model is employed to model the momentum equation. Effects of different parameters, such as the thermal Rayleigh number (RaT) and solutal Rayleigh number (Ras), the angle of inclination (ϕ), the Lewis number (Le), the Darcy number (Da), and the concentration-based internal heat source (Q), are shown. A normal mode technique has been employed on the disturbance equations to get the generalized eigenvalues problem, which is solved by the Chebyshev-tau method coupled with the QZ algorithm in MATLAB. It was observed that increasing the solutal Rayleigh number stabilizes the system due to the higher concentration at the lower boundary than the upper boundary. It has also been observed that decreasing the Darcy number has a destabilizing effect, which means that decreasing permeability advances the onset of double-diffusion convection. Furthermore, it was observed that an increase in the concentration-based internal heat source destabilizes the system. Our numerical results show that for Ras>0 and ϕ>0°, for all Q values, the subcritical instability only exists for transverse rolls.