Numerical investigation of heat transfer to a non-spherical drop suspended in an electric field: internal problem

摘要

Heat transfer to a drop of a dielectric fluid suspended in another dielectric fluid in the presence of an electric field is numerically investigated. The internal heat transfer problem is considered where the bulk of the resistance to the heat transfer is assumed to be in the dispersed phase. We have analyzed the effect of drop deformation on the heat transport to the drop. The deformed drop shape is assumed to be a spheroid and is prescribed in terms of the ratio of drop major and minor diameter. Both prolate and oblate shapes are considered with a range of diameter ratio b/a from 2.0 to 0.5. The electrical field and the induced stresses are obtained analytically. The resulting flow field is determined by numerically solving the Navier-Stokes equations in the continuous and the dispersed phase. An alternating-direction-implicit (ADI) method is used to obtain the transient temperature field for drop Peclet number from 5 to 1500. Heat transfer results for a nearly spherical drop (b/a chemical bounds 0.99 and b/a chemical bounds 1.01) show excellent agreement with the results available in published literature. Results indicate that the drop shape significantly affects the flow field and the heat transport to the drop. At very low and very high Peclet numbers, the steady state Nusselt number is higher for a deformed drop than that for a sphere. However, at intermediate Peclet number, the Nusselt number for a sphere may be higher than that for a deformed drop. For both prolate and oblate drops, the steady state Nusselt number increases with increasing Peclet number, and at high Peclet number, becomes increasingly independent of the Peclet number. The maximum steady state Nusselt numbers for an oblate drop are higher than that for a prolate drop.