14. Effect of Time-Periodic Boundary Temperature Modulations on the Onset of Convection in a Maxwell Fluid–Nanofluid Saturated Porous Layer

The linear stability of Maxwell fluid–nanofluid flow in a saturated porous layer is examined theoretically when the walls of the porous layers are subjected to time-periodic temperature modulations. A modified Darcy–Maxwell model is used to describe the fluid motion, and the nanofluid model used includes the effects of the Brownian motion. The thermal conductivity and viscosity are considered to be dependent on the nanoparticle volume fraction. A perturbation method based on a small amplitude of an applied temperature field is used to compute the critical value of the Rayleigh number and the wave number. The stability of the system characterized by a critical Rayleigh number is calculated as a function of the relaxation parameter, the concentration Rayleigh number, the porosity parameter, the Lewis number, the heat capacity ratio, the Vadász number, the viscosity parameter, the conductivity variation parameter, and the frequency of modulation. Three types of temperature modulations are considered, and the effects of all three types of modulations are found to destabilize the system as compared to the unmodulated system.