LINEAR AND NON-LINEAR THERMAL INSTABILITY OF A HORIZONTAL MAXWELL NANOFLUID LAYER WITH THERMAL EQUILIBRIUM

The effect of nanoparticles on the onset of Benard convection in a Maxwell fluid layer of constant viscosity, confined between two parallel boundaries, is investigated. By employing linear stability analysis, we determine the critical Rayleigh number for both stationary and oscillatory convection. The study also examines the impact of various parameters on the Rayleigh number. The results indicate that convection occurs earlier in Maxwell nanofluid compared to Oldroyd nanofluid. To analyse the system under weakly nonlinear conditions, a truncated Fourier series approach is used. As a result, we obtain the thermal Nusselt number and the concentration Nusselt number. Furthermore, we conduct an analysis of the transient behaviour of heat and mass transport, considering both steady and unsteady states.