Steady and time-periodic electric field-driven enhancement of heat or mass transfer to a drop: Internal problem

Abstract

Transient heat or mass transfer to a spherical drop of a dielectric fluid suspended in another dielectric fluid in the presence of steady and time periodic electric fields (both uniform and non-uniform) is investigated in this paper. The internal problem or the heat (mass) transfer limit that corresponds to the bulk of the resistance being in the dispersed phase is addressed. Using a finite volume formulation, the energy conservation equation is solved to obtain the transient temperature distribution and the overall Nusselt number for the drop Peclet numbers from 0 to 10,000 and the dimensionless frequency ( ω ∗) from 0 to 50,000 using a fully implicit method. Application of steady and time-periodic fields leads to fluid circulation in the drop which provides an increase in the heat (mass) transfer rate. At first glance one might expect that the time-periodic field, which gives rise to a continuously varying flow field, might provide better mixing and improved heat (mass) transfer enhancement compared to time invariant one which gives rise to a steady flow field. However results show that for low to moderate Peclet numbers, the steady electric field is more effective in heat transfer enhancement compared to non-uniform time periodic field which in turn is more effective than the uniform time-periodic field. This counterintuitive heat (mass) transfer behavior is explained in detail in the paper. On the other hand, at high Peclet numbers, the non-uniform time periodic field provides significant improvement in heat (mass) transfer relative to steady uniform electric field. We show that at high Peclet numbers the maximum heat (mass) transfer enhancement is obtained when the dimensionless electric field frequency is of the order of Peclet number or ω ∗ ∼ O( Pe). By tracking Lagrangian fluid particles, it is revealed that application of non-uniform unsteady electric field results in chaotic advection at high Pe whereas steady and unsteady uniform electric fields do not.