Linear and nonlinear thermosolutal instabilities in an inclined porous layer

Abstract

We investigate the double-diffusive instability in an inclined porous layer with a concentrationbased internal heat source by conducting linear instability and nonlinear energy analyses. The effects of different dimensionless parameters, such as the thermal (Ra T ) and solutal (Ra S ) Rayleigh numbers, the angle of inclination (φ), the Lewis number (Le) and the concentration-based internal heat source (Q) are examined. A comparison between the linear and nonlinear thresholds for the longitudinal and transverse rolls provides the region of subcritical instability. We found that the system becomes more unstable when the thermal diffusivity is greater than the solute and the internal heat source strength increases. It is observed that the system is stabilized by increasing the angle of inclination. While the longitudinal roll remains stationary without the region of subcritical instability, as the angle of inclination increases, the transverse roll switches from stationary-oscillatory-stationary mode. Our numerical results show that for Ra S < 0, for all Q values, the subcritical instability only exists for transverse rolls. For Ra S ≥ 0, however, the subcritical instability appears only for Q = 0 and Q ≥ 0, respectively, for longitudinal and transverse rolls.

Stability of transient natural convection in impulsively heated inclined fluid layer

“…is uniformly bounded over the space H of all admissible solutions {u, v, w, θ, p} of the system (15)- (18). To prove this, we use equations ( 10)-( 11) to get,…”

“…Using the Lyapunov method, the critical value of Rayleigh number is calculated and compared with that of the linear instability analysis. Kumar et al [18] recently discussed the linear instability and the non-linear stability of a heated inclined porous layer with a concentration based internal heat source.…”

Thermosolutal Convection of Natural and Anti-Natural Solutions Through an Angled Cavity Under Cross Gradients in Temperature and Concentration

“…Their primary discovery was that the from drag effect, which serves as a stabilizing impact, considerably affects Hopf bifurcation and subcritical convection. Linear instability and nonlinear stability were used by Kumar et al, [15] to analyze the double-diffusive instability in an inclined porous layer with and without an internal heat source dependent on concentration. The Papanastasiou model for explaining the rheological behavior, Saxena et al, [16], and the lattice Boltzmann method were used to simulate a 2D DDNC.…”

Energy stability of thermally modulated inclined fluid layer

“…The energy method (Joseph 1976, Straughan 1992) is important to study as it provides a stability boundary and a sufficient condition for the stability of the basic flow with respect to perturbations of arbitrary finite magnitude. The energy method is used by various researchers to find the stability limits of dynamical problems (Homsy 1974, Joseph 1976, Straughan 1992, Luo et al 2010, Singh et al 2013, Kumar et al 2020a, 2020b. Kumar et al (2020b) studied the stability of thermal convection in an inclined porous layer by using linear instability and energy analysis.…”