The effect of a single droplet on heat transfer through a square enclosure heated by side-walls

Abstract

Extending our previous investigations on the motion of a single droplet in confined natural convection flows, the present work describes the influence of droplet motion on heat transfer, considering a binary liquid confined in a square enclosure heated by the side-walls. Our model assumes an incompressible flow of two Newtonian fluids with the same dynamic viscosity, density, and thermal expansion coefficient. Additionally, we assume both fluids to have distinct thermal conductivity and heat capacity coefficients. Considering a Rayleigh number of $Ra=10^4$ and a Prandtl number of $Pr=7.0$, we investigated the influence of the droplet position, $x_d$, on the instantaneous Nusselt number, $Nu$, for two possible motion patterns: the droplet orbiting within a periodic flow or trapped at the enclosure’s center. Our results indicate that the relative heat capacity of the fluids significantly influences Nusselt when compared with the relative thermal conductivity. We also observed that when trapped at the central region, the droplet causes $Nu$ to decrease by 5%, assuming an almost constant value regardless of both relative thermal properties. However, when orbiting in periodic motion, the droplet caused $Nu$ to oscillate periodically, reaching its maximum value $N{u}_{\text{max}}$ as it moves toward the vicinity of the hot wall. While increasing the relative thermal properties resulted in an enhancement of $N{u}_{\text{max}}$, the average Nusselt number, $\overline{Nu}$, displayed modest variation, while $N{u}_{\text{min}}$ remained the same for all cases. Furthermore, our investigations showed that $N{u}_{\text{max}}$ increased by up to 24.4%, equivalent to doubling the Rayleigh number of the mono-phase flow. Therefore, our results highlight significant heat transfer enhancement potential, paving the way for further investigation in future work.