Instability of double-diffusive convection in a nanofluid layer with vertical throughflow and slip boundary conditions

Abstract In this study, the onset of double-diffusive convection in a nanofluid layer is analyzed when a uniform vertical throughflow is applied, with the velocity of the fluid at the confining boundaries described by slip conditions. The model also considers buoyancy forces caused by temperature and concentration differences in the nanofluid. These effects produce a coupled system of linear eigenvalue equations that describe perturbations around the basic throughflow state. The Adomian decomposition method is applied to derive semi-analytical expressions for the steady-state temperature field and nanoparticle concentration field. These base-state solutions are subsequently validated by comparison with a direct Chebyshev–collocation computation. The associated stability problem is then treated numerically using the Chebyshev collocation technique. Neutral stability curves and the corresponding critical thresholds are determined to assess how the system responds to variations in key parameters, including the nanofluid Lewis number, nanoparticle Rayleigh number, solutal Rayleigh number, throughflow velocity, Brownian motion parameter, thermophoresis parameter, and slip coefficient. The results indicate that stationary instability dominates over the parameter range considered, and the role of each parameter on the critical conditions is discussed. In particular, the sign of the nanoparticle Rayleigh number plays a key role in determining how nanoparticle-induced buoyancy affects the onset of instability, as well as how throughflow and slip conditions influence the critical thresholds. Overall, the study presents a detailed analysis of the onset of double-diffusive convection in a nanofluid model of higher complexity than those based on simplified slip and no-slip formulations.