Effect of maximum density on double diffusion convective instability in vertical Brinkman porous layer

This study investigates the effect of the maximum density property on the instability of double-diffusive convection in the vertical Brinkman porous layer. Different from the classical Boussinesq approximation, the density relation is modified to a quadratic polynomial. Then, the Navier-Stokes equations are transformed into Orr-Sommerfeld eigenvalue problem by linear stability analysis and then solved numerically by Chebyshev collocation method. The effects of the various dimensionless parameters on the instability of linear density temperature relation (LDTR) and quadratic density temperature relation (QDTR) systems are determined, respectively, by analyzing the growth rate and neutral stability curves. The results show that PrD suppresses instability, while Le and Da enhance it. Moreover, a critical PrD exists between the two density systems. Below this value, the LDTR system is more prone to instability, while beyond it, the QDTR system becomes more susceptible to instability. Furthermore, LDTR system can exhibit two distinct instability modes, whereas QDTR system only supports traveling wave modes, with instabilities mainly occurring in the low wave number region.