Thermal instability analysis of convection in a horizontal nanofluid layer with free-free boundary condition

Convective flows are commonly observed in geophysical systems and hold both fundamental and practical significance in engineering and technological applications. The initiation of convective flow whether stationary or oscillatory is known to cause defects such as striations, dendrites and bubbles in manufactured products. This study investigates the influence of viscous elasticity and an applied magnetic field on convective instabilities in a deep horizontal layer of viscoelastic nanofluid with free-free boundary conditions. A linear stability analysis was employed to identify the onset of both stationary and oscillatory instabilities. A closed-form expression for the critical Rayleigh number was derived using the Galerkin-typed weighted residuals method. The impact of the scaled stress relaxation parameter, scaled strain retardation parameter and Chandrasekhar number on system stability was analyzed. The results indicate that the magnetic field effectively delays the onset of both stationary and oscillatory convective instabilities in viscoelastic nanofluids.