Heat/mass transfer from a drop translating in steady and time-periodic electric fields: External problem

Enhancement of heat or mass transport from a spherical drop of a dielectric fluid translating 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 external problem or the limit of the majority of the transport resistance being in the continuous phase is considered. Using a finite volume formulation, the transient energy (species) conservation equation is solved for Peclet numbers (Pe) varying from 10 to 1000 and dimensionless electric field frequency (ω∗) from 10 to 50,000 using a fully implicit method. To map the infinite domain in the radial direction, an exponential transformation is employed that provides a fine grid spacing near the drop surface where sharp variations are expected and a coarser grid in the far field where low gradients prevail. The transient temperature distribution and the local and the average Nusselt numbers are obtained and the heat/mass transfer enhancement due to the application of electric field is determined. The effect of electric field is expressed in terms of L, the ratio of the maximum electric-field-induced surface velocity to the translation-induced surface velocity. For the steady and time-periodic electric fields, the heat transfer enhancement increases monotonically with Pe and with L. Also, the heat transport rate is higher when the continuous phase is more viscous compared to the dispersed phase. The steady uniform electric field gives the highest average Nusselt number for heat transfer from the drop surface to the continuous phase, followed by the non-uniform time periodic electric field and then the time periodic uniform electric field. The enhancement relative to pure translation exhibits a non-monotonic dependence on electric field frequency but the highest value is obtained at ω∗ = 0. Earlier studies have shown that there is significant enhancement in the heat/mass transfer in the drop interior with a time periodic electric field compared to a steady uniform electric field when the majority of the transport resistance is in the drop. The results presented here show that an opposite behavior is obtained in the drop exterior, i.e. a steady electric field provides higher heat/mass transfer enhancement compared to a time periodic electric field, when the bulk of the transport resistance is in the continuous phase. Therefore whether the steady or the time periodic electric field provides the most enhancement of heat/mass transfer for a conjugate problem will depend on the relative transport resistance in the two phases.