Effect of Imposed Wall Temperature Oscillations on the Stability of Natural Convection in a Square Enclosure

Abstract

The present numerical study is directed toward buoyancy-driven laminar flows in a two-dimensional square enclosure with differential heating at the vertical walls. The top and bottom walls are insulated. A time-dependent temperature varying sinusoidal perturbation is imposed on the hot vertical wall. The cold vertical wall is maintained at a constant temperature. The fluid is air with a Prandtl number of 0.72. Computations were carried out at one imposed frequency, which is of the same order as the first natural frequency of the system. It was found that the perturbations destabilized the flow in that higher amplitudes lead to lower critical Rayleigh numbers for the flow transitions. Computations spanned four regimes: periodic, quasi-periodic with two frequencies, quasi-periodic with three-frequencies, and chaotic.