Onset of Rayleigh-Benard Convection with Periodic Boundary Temperatures Using Weakly Nonlinear Theory

Abstract

This paper investigates the Rayleigh Benard instability of a viscous, Newtonian, Boussinesq fluid with time-periodic boundary temperature modulation using the framework of weakly nonlinear theory. Critical Rayleigh number is computed for asymptotic stability criterion using the energy method accompanied by variational algorithm. Subcritical instability is found to occur under two conditions: when modulation is in anti-phase and when modulation is imposed only on the lower boundary. Supercritical stability is witnessed during in-phase modulation. In all the three cases of the relative phase of two boundary temperatures, the effect of modulation is found to be weaker for infinitesimal disturbances. The findings of the present study could be referred in several applications where appropriate temperature modulation is of prime concern.