Heat/Mass Transfer to a Drop Translating in a Perpendicular Electric Field

Abstract

Enhancement of heat or mass transport in a spherical drop of a dielectric fluid translating in another dielectric fluid in the presence of uniform electric field is investigated. The internal problem or the limit of the majority of the transport resistance being in the dispersed phase is considered. The transient energy conservation equation is solved using a fully implicit finite volume method. In the literature, there is a plenty of studies that had been carried out when the electric field acts in the same plane of translation. In this paper, considering creeping flow regime, numerical computations have been conducted when the electric field acts perpendicular to the plane at which translation acts. As such the flow is no longer a two dimensional flow as a third component velocity comes to picture. At the first glance, thoughts of transport enhancement come to mind on the presence of a third velocity component that might promote mixing and consequently enhance transport effectiveness. Results are expressed in terms of the Nusselt number. Nusselt numbers are plotted in terms of Peclet number, Fourier number and the parameter L which is defined as the ratio of the maximum electric-field-induced surface velocity to translation-induced surface velocity. The code was validated by comparing, results for Peclet numbers of 500 and 1000 to corresponding cases available in literature. Results showed good agreement with previous results. A 3-D grid of 20×40×60 has been considered to cover the computational domain. A grid independence study has been carried out by doubling the whole grid. Results show acceptable results compromising accuracy and code running time. The effect of electric field is expressed in terms of parameter L. For low Peclet numbers (Pe ≤ 250), the application of electric field perpendicular to the plane at which translation acts leads to enhancement of heat/mass transport compared to that in pure translation. Such enhancement is about the same when the electric field and translation act in the same plane. On the other hand, for moderate Peclet numbers (Pe= 250∼1000), the transport enhancement is significant when compared to the enhancement obtained by an electric field acts in the same plane of action of translation as well as pure translation. These results can be understood by comparing time scales for diffusion and convection. When Peclet number is low the convection time scale is very large and hence mixing is not that effective in promoting heat / mass transfer. Whereas for moderate Peclet number, when the convection time scale gets smaller, heat/mass transfer is considerably enhanced compared to low Peclet numbers.