A Finite-Volume Method for Electro-Thermoconvective Phenomena in a Plane Layer of Dielectric Liquid

This article presents a numerical algorithm for electro-thermoconvective phenomena in a dielectric liquid confined between two parallel plates. The liquid is under the simultaneous actions of a direct current electric field and a thermal gradient. Free charge carriers are considered to be introduced by unipolar injection. The fully coupled equations including a reduced set of Maxwell's equations, the Navier–Stokes equations, and the energy equation, together with the equations of state, are solved with a finite-volume method. A total variation-diminishing scheme is especially used to solve the convection-dominated charge density equation. The method is validated with four test cases that possess some analytical solutions. As an application example, we evaluate the heat transfer enhancement resulting from injection-induced electroconvection in a bounded cavity filled with silicone oil.