Numerical simulation of an electro-thermal convection system with Joule heating

Electro-thermal hydrodynamics involves the coupling of electric field, temperature field and fluid motion, where the interaction between the electric field and fluid flow, along with Joule heating effect, plays a key role in the system evolution. In this study, a dimensionless multiphysics mathematical model for the electro-thermal hydrodynamics is formulated and solved using a first-order linear fully discrete numerical scheme. In practical applications, temperature gradient in the electro-thermal convection system is typically induced by either boundary temperature difference or internal Joule heating; this work focuses primarily on the latter scenario. Numerical experiments are conducted to test the stability, convergence and conservation of total charge in the proposed numerical scheme. Furthermore, by simulating the cavity driven flow, the influence of the electric field-related parameters on the electro-thermal hydrodynamics behavior is investigated. The results indicate that the intensity of electrohydrodynamic disturbances increases with the magnitude of the applied electric field. Finally, the numerical results are compared with existing studies on open cavity cooling system, testing the effectiveness of the model in simulating actual electro-thermal convection conditions.