The enhancement of convective heat transfer by an electric field is but one aspect of the complex thermoelectric phenomena which arise from the interaction of fluid dynamic and electric fields. Our current knowledge of this area is limited to a very few experimental studies. There has been no formal analysis of the basic coupling modes of the Navier–Stokes and Maxwell equations which are developed in the absence of any appreciable magnetic fields. Convective flows in enclosures are particularly sensitive because the limited fluid volumes, recirculation, and generally low velocities allow the relatively weak electric body force to exert a significant influence. In this work, the modes by which the Navier–Stokes equations are coupled to Maxwell’s equations of electrodynamics are reviewed. The conditions governing the most significant coupling modes (Coulombic forces, Joule heating, permittivity gradients) are then derived within the context of a first-order theory of electrohydrodynamics. Situations in which these couplings may have a profound effect on the convective heat transfer rate are postulated. The result is an organized framework for controlling the heat transfer rate in enclosures.

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