Comparison of the effect of suction-injection-combination on Rayleigh–Bénard convection in the case of asymmetric boundaries with those of symmetric ones

Abstract

The effect of suction-injection-combination (SIC) on the linear and weakly nonlinear stability of Rayleigh–Bénard convection is considered in the paper for the cases of symmetric and asymmetric boundary conditions. Using the Maclaurin series with an appropriate number of terms, expression for eigenfunctions is obtained. The linear theory corroborates the results obtained using the chosen eigenfunctions in the limiting case of the no-SIC effect by matching accurately with the exact values concerning the critical Rayleigh number (Rac) and the wave number (αc). It is found that the effect of SIC is to stabilize the system in the case of symmetric boundaries irrespective of SIC being pro-gravity or anti-gravity. However, the effect of SIC is to stabilize/destabilize the system depending on SIC being pro-gravity or anti-gravity in the case of the asymmetric boundaries. We also noted a similar effect in the case of αc wherein a maximum error of order 10−4 was observed. The main novelty of the present work is studying the influence of SIC on the nonlinear dynamics of the considered problem. It is shown that the effect of SIC is to hasten the onset of chaos. Using various indicators (the largest Lyapunov exponent, the time series solution, the amplitude spectrum, and the phase-space plots), the dynamical behavior of the system is analyzed and the influence of SIC on the dynamics is recorded. The change due to the boundary effect and the SIC on the size of convection rolls and the trapping region where the dynamical system evolves within a bound is highlighted in the paper.