LAUSR

Abstract This paper presents a novel numerical framework based on the accurate spectral element method (SEM) for electro-thermo-hydrodynamics (ETHD), in which the coupled electric, flow, and heat fields are solved simultaneously. The electric field potential is estimated by the classic Galerkin variation with the electric field vectors evaluated by the spectral approximation, and the streamline upwind Petrov-Galerkin variation and consistent approximate upwind technique are applied to stabilize the numerical simulation of charge density transport. As for the flow and heat transfer, the improved time-splitting method developed in our previous work is applied to deal with the coupled pressure and velocity in the momentum equations. Three carefully selected cases of analytical solution, pure thermal and pure electric convection, and electro-thermo-convection are performed to validate the algorithm. Then, the electro-thermo-convection in an enclosure with uniform temperature distribution is simulated and the average Nusselt numbers at different electric Rayleigh numbers are presented accurately. Additionally, the sinusoidal temperature boundary conditions are considered that the contours for stream function, temperature, and charge density are analyzed in detail to depict the heat transfer enhancement with ETHD effects.