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

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 incorporates the effects of buoyancy forces arising from temperature and concentration variations in the nanofluid, leading to a coupled system of linear eigenvalue equations governing perturbations about the throughflow basic state. The steady-state temperature and nanoparticle concentration are obtained using the Adomian decomposition method, while the stability problem is solved numerically via the Chebyshev collocation method. Neutral stability curves and critical values are computed to examine the influence of parameters such as the nanofluid Lewis number, nanoparticle and solutal Rayleigh numbers, throughflow velocity, Brownian motion parameter, thermophoretic 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.