An in-depth electro-thermo-hydrodynamic conduction model for weakly conducting dielectric Liquids: Temperature-dependent properties and Rayleigh-Bénard instability

Electrically assisted thermal management of dielectric liquids relies on a precise understanding of how applied electric fields interact with buoyancy-driven convection. This work presents a numerical investigation of electro–thermo–hydrodynamic (ETHD) convection in weakly conducting dielectric liquids subjected to a DC electric field and a destabilizing vertical temperature gradient between parallel-plate electrodes. The flow operates in the conduction regime of electrohydrodynamics (EHD), where free ions arise from reversible dissociation of neutral molecules—a process critically enhanced by the applied field through the Onsager (second Wien) effect. A central novelty of this study is the fully coupled and thermally consistent treatment of temperature-dependent material properties: ionic mobilities are distinguished for cations and anions and allowed to vary with temperature, as are liquid permittivity, viscosity, and density. This departs from the common simplifying assumption of identical, temperature-independent mobilities adopted in most prior conduction-regime studies. Dielectric body forces arising from permittivity gradients are retained alongside Coulomb forces and their influence is systematically assessed. The governing system—incompressible Navier–Stokes equations under the Boussinesq approximation, the heat equation, drift–diffusion–advection ion transport with dissociation–recombination source terms, and Gauss's law—is solved with a second-order finite-volume method. Parametric studies at Ra = 5000, electric Reynolds number Rel = 2, and conduction number C ₀ = 6.5 reveal two distinct dynamical regimes as the temperature-sensitivity parameters L and N are varied, with the purely thermal Rayleigh–Bénard reference (no electric field) yielding a steady-state Nusselt number Nu_RB = 0.5105. When L = N ≤ 1 × 10⁻⁵, the system settles into a stationary thermoconvective state with Nusselt numbers close to Nu_RB (Nu = 0.4809 for L = N = 0 and Nu = 0.4888 for L = N = 1 × 10⁻⁵), indicating that weak temperature sensitivity produces negligible modification of the purely thermal response. When L = N ≥ 1 × 10⁻⁴ with Onsager number O = 200, the system enters a sustained limit-cycle oscillatory (overstable) regime in which the maximum velocity exhibits persistent oscillations that do not decay. The time-averaged Nusselt numbers are Nu = 0.3713 for L = N = 1 × 10⁻⁴ and Nu = 0.4231 for L = N = 2 × 10⁻⁴, both below Nu_RB, demonstrating that the oscillatory ETHD forcing reduces the net heat flux relative to purely thermal convection (−27% and −17% respectively). These results demonstrate that the interplay between field-enhanced dissociation, temperature-dependent permittivity, and mobility asymmetry governs both the stability threshold and the heat-transfer efficiency of ETHD conduction, and that a thermally consistent formulation is indispensable for quantitative prediction. The findings provide actionable design guidelines: operating with fluids of weak temperature sensitivity ( L , N ≪ 1 × 10⁻⁴) produces stationary convection close to the purely thermal RB response, while strong temperature sensitivity ( L , N ≳ 1 × 10⁻⁴) combined with high O triggers sustained oscillatory convection with a reduced time-averaged heat flux (−27% to −17% relative to Nu_RB depending on the sensitivity level).