Instability of thermal convection in a porous layer saturated with a nanofluid using general boundary conditions

Purpose This paper aims to study the onset of convection in a horizontal porous layer saturated with a nanofluid. The Brinkman formulation is used to describe the porous matrix, while the nanofluid model takes thermophoresis and Brownian motion into consideration. This study also investigates how slip conditions and general thermal boundary conditions affect the stability properties of the system. Design/methodology/approach The linear instability theory is theoretically adopted, and the eigenvalue system associated with the theory is found. The numerical method based on the Chebyshev collocation technique is used to analyze linear instability thresholds by solving the eigenvalue system. Findings The numerical results clearly identify the regions of instability, as well as the zones where either oscillatory or stationary convection dominates at the onset of convection. They further reveal the stabilizing roles of the Brinkman parameter, the medium’s volume and the heat capacity ratio, while highlighting the destabilizing effects of nanoparticle concentration, slip, the Lewis number and Biot-type parameters. In addition, the findings show that the modified diffusivity ratio and the modified nanoparticle density increment have a negligible influence. Originality/value This study extends previous research by considering general temperature conditions and incorporating all relevant factors in the analysis. While earlier studies often relied on simplified mathematical models to reduce computational complexity, this work provides a more comprehensive investigation of the problem, offering detailed insights into its stability characteristics.