Electro-thermo-convective flow of a dielectric liquid due to nonautonomous injection of charge by an elliptical electrode

Electro-thermo-hydrodynamic (ETHD) flow induced by the simultaneous Coulomb and buoyancy forces in a dielectric medium is studied using the lattice Boltzmann method. Nonautonomous charge injection from a high temperature inner elliptical electrode to two cold parallel-plate electrodes is considered. Systematical simulations are conducted for ETHD problems with different injection models and non-dimensional parameters, including electric Rayleigh number T, Rayleigh number Ra and the ellipticity e of the elliptical electrode. It is found that the charge transport process, flow instability and heat transfer enhancement are significant affected by nonautonomous injection, especially in the Coulomb force dominant flow regime and the large ellipticity cases. Quantitatively, for dielectric liquid M = 10, e = 2 and Pr = 10 under strong injection C = 10, when compared to the autonomous charge injection assumption, nonautonomous injection shown an average of 16.4% increases in the mean Nusselt number within the range of driving parameters explored (10³ ≤ Ra ≤ 10⁷, 300 ≤ T ≤ 1800).