Rayleigh–Benard convection subject to time dependent wall temperature in a porous medium layer saturated by a nanofluid

Abstract

The stability of a porous medium saturated with a nanofluid with thermal conductivity and viscosity dependent on the nanoparticle volume fraction is examined in the case of a time-dependent wall temperature. The regular perturbation method based on the small amplitude of modulation is employed to compute the critical Rayleigh number and the corresponding wave number. The stability of the system characterized by a correction Rayleigh number is calculated as a function of the concentration Rayleigh number, porosity, Lewis number, heat capacity ratio, Vadasz number, viscosity variation parameter, conductivity variation parameter and frequency of modulation. It is found that the low frequency symmetric thermal modulation is destabilizing while moderate and high frequency symmetric modulation is always stabilizing. The nanofluid is found to have more stabilizing effect when compared to regular fluid. The asymmetric modulation and lower wall temperature modulation is stabilizing for all frequencies.