Instability and bifurcations of electro-thermo-convection in a tilted square cavity filled with dielectric liquid

Abstract

The direction of coupled buoyancy and electric forces has a significant effect on both the fluid flow and heat transfer in an electro-thermo-convection (ETC) system. Here, we theoretically and numerically investigate the instability and bifurcations of ETC inside a tilted square cavity. A linear stability analysis is conducted using a unified linearized-lattice Boltzmann model by solving the coupled linear Navier–Stokes equation, linear Poisson equation, linear Nernst–Planck equation, and the linear energy equation. The numerical simulation is performed by integrating our code with the Palabos library. Results show that the interactions between the stabilizing buoyancy force and electric force lead to a Hopf bifurcation for Rayleigh number Ra =  1 × 105. The steady flow transitions to a traveling-wave flow by a subcritical bifurcation when tilted angles are less than δc ∈ [48°,49°]. For tilted angles above δc, the flow loses its stability through a local oscillation caused by a supercritical bifurcation. Finally, the chaotic behavior is quantitatively analyzed through the calculation of the Lyapunov exponent, which increases linearly with the electric Rayleigh number and is weakly dependent on the tilted angle.