Heat transfer enhancement due to internal circulation within a rising fluid drop

Motion of drops and bubbles plays a critical role in the efficiency of industrial operations such as extraction. As the drop moves in the continuous phase, the tangential shear stress induced by the continuous fluid at the drop interface results in internal circulation, which may enhance transport of components and energy between the dispersed phase (drop) phase and the continuous phase. In the present study, computational fluid dynamics (CFD) simulations have been used to study this aspect in detail. Coupled calculations for the two phases have been carried out for fluid flow over a spherical, non-deformable drop of a given diameter. The predicted internal circulation is validated by comparing with analytical results for very low Reynolds numbers and experimental data at higher Re. The calculation framework is then used to study the convective-diffusive heat transfer to the drop for various combinations of Re and Pr. The heat transfer within the drop is found to comprise of three regimes, two diffusion controlled heat transfer regimes (initial and final) connected by an intermediate convection controlled heat transfer regime. The heat transfer enhancement by convection has been deduced and is found to depend both on Re and Pr. A dimensionless correlation has been developed to predict the convective heat transfer enhancement.