Numerical analysis on the heat/mass transfer to a deformed droplet under a steady electric field

•Transport mechanism at different Pe is analyzed.•Heat transfer rate decreases with deformation rate at moderate Pe.•Oblate droplet has the best heat transfer performance when convection dominates.•Direction of flow circulation has little impact on the heat/mass transfer. Transient heat/mass transfer to a deformed droplet suspended in the ambient fluid in the presence of a steady electric field is investigated. By considering an internal problem, a numerical model is established to incorporate the flow field and heat transfer in a two-dimensional axisymmetric framework with the phase field method to track the deformed interface. The model is validated, and an excellent agreement is achieved. For a spherical droplet, as Peclet number (Pe) increases from 10 to 1000, the number of the region with closed contours of temperature increases from 1 to 4 (with 2 for Pe=100), which may explain the increase of Nu at this range of Pe. When Pe further increases to infinite, the transport is limited by the rate of cross-streamline conduction. At low Pe, the transport process is dominated by the conduction, and the heat transfer rate is always enhanced for a deformed droplet with smaller conduction length scale and greater surface area. However, at moderate Pe, the heat transfer rate is suppressed by the deformation rate (D). The analysis on the transport mechanism suggests that the conduction and convection play the comparable roles in affecting the transport process, and the deformation will weaken both the conduction near the surface and the convection in the droplet interior. The oblate droplet is less suppressed by the deformation rate compared with the prolate droplet. When Pe is large (e.g., Pe=1000), the heat transfer rate of oblate droplet will increase with the D. However, for prolate droplets, the overall transfer rate presents a non-monotonous trend with D. The transient behaviors of the heat transfer at high Pe and the length scale of the cross-streamline conduction for different deformed droplets are discussed. Furthermore, it is inferred that the oblate droplet has the advantage in driving more fluid into the droplet interior when the convection dominates.