Rayleigh-Benard convection subject to time dependent wall temperature in a fluid-saturated porous layer

Abstract

The stability of a Boussinesq fluid-saturated horizontal porous layer, heated from below, is examined for the case of a time-dependent wall temperature. Forchheimer flow model with effective viscosity larger than the viscosity of the fluid is considered to give a more general theoretical result. A method based on small amplitude of the modulation proposed by Venezian (1969, J. Fluid Mech., 30, 243-254) is used to compute the critical values of the Rayleigh number and wave number. The shift in the critical Rayleigh number is calculated as a function of frequency of modulation, Prandtl number, porous parameter, and viscosity ratio. It is shown that the system is most stable when the boundary temperature is modulated out of phase. It is also found that the low-frequency thermal modulation can have a significant effect on the stability of the system. The effect of the viscosity ratio and Prandtl number on the stability of the system is also brought out.The stability of a Boussinesq fluid-saturated horizontal porous layer, heated from below, is examined for the case of a time-dependent wall temperature. Forchheimer flow model with effective viscosity larger than the viscosity of the fluid is considered to give a more general theoretical result. A method based on small amplitude of the modulation proposed by Venezian is used to compute the critical values of the Rayleigh number and wave number. The shift in the critical Rayleigh number is calculated as a function of frequency of modulation, Prandtl number, porous parameter, and viscosity ratio. It is shown that the system is most stable when the boundary temperature is modulated out of phase. It is also found that the low-frequency thermal modulation can have a significant effect on the stability of the system. The effect of the viscosity ratio and Prandtl number on the stability of the system is also brought out.