Stability and Dynamics of Two-Layer Nanofluid Convection System

This paper explores thermal convection in a system consisting of two infinite horizontal nanofluid layers with finite depths layered one above the other. A horizontal non-porous nanofluid layer is assumed to lie over the porous nanofluid layer and heated from below. Conservation equations along with the upper, lower and interface boundary conditions are formulated and linearised. Obtained linearised equations are subjected to perturbations and the system is analysed w.r.t. each perturbation. The Chebyshev Tau method is used to find the eigenvalues, and the approach of normal modes is used to analyse the linearised perturbed equations. The impact of various parameters depth ratio, Darcy number, thermal conductivity ratio and volume fraction of nanoparticles has been analyzed on the thermal instability of two-layer convection. The criteria for the convection in both layers are discussed and presented through graphs. It is observed that the marginal stability curve shows the bimodal nature of convection in a double nanofluid layer system. For the case when both layers have the same kind of nanoparticles, convection shifted to the upper layer with the increase in the depth ratio for various parameters except for Darcy number in which convection shifted to the upper layer with the decrease in the depth ratio whereas dissimilar behaviour is found for Darcy number when both layers contain different kind of nanoparticles (copper and aluminium nanoparticles). Also, a very small increase in the depth ratio shifts the convection to the upper layer in the case of different nanoparticles in both layers.