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Advection-enhanced heat and mass transport from a single droplet neutrally suspended in a simple shear flow has been studied using high-fidelity numerical simulation. The capillary number ranges from 0.01 to 0.5, which encompasses the entire range of small deformation, large deformation, and breakup of the droplets. The Reynolds number is from 0.01 to 1, including regions of both weak and strong advection. The temperature and mass concentration are modeled as the concentration of a passive scalar released at the droplet surface. Two Schmidt numbers, 10 and 100, are considered, for which flow advection plays a role in the transport of passive scalar. For unbroken droplets, the interaction between the carrier fluid and the suspended droplet leads to several different flows around the droplet. The fluid motions together with scalar diffusion constitute a coupled transport mechanism for passive scalar. The dependence of scalar release rate on Reynolds and Peclet numbers can be roughly described by the correlation for a rigid sphere. For broken droplets, the basic flow features around the droplet during the process of elongation and breakup are similar to those of an unbroken droplet. The variation of the scalar release rate can be decomposed into several stages, corresponding to the process of droplet elongation and breakup. The variation of the scalar release rate exhibits a high correlation with the capillary, Reynolds, and Peclet numbers. This suggests that it is feasible to develop an empirical model that incorporates the effects of the number and size distributions of child droplets after breakup. 

Smart microgrids (SMGs) may face energy rationing due to unavailability of energy resources. Demand response (DR) in SMGs is useful not only in emergencies, since load cuts might be planned with a reduction in consumption but also in normal operation. SMG energy resources include storage systems, dispatchable units, and resources with uncertainty, such as residential demand, renewable generation, electric vehicle traffic, and electricity markets. An aggregator can optimize the scheduling of these resources, however, load demand can completely curtail until being neglected to increase the profits. The DR function (DRF) is developed as a constraint of minimum size to supply the demand and contributes solving of the 0-1 knapsack problem (KP), which involves a combinatorial optimization. The 0-1 KP stores limited energy capacity and is successful in disconnecting loads. Both constraints, the 0-1 KP and DRF, are compared in the ranking index, load reduction percentage, and execution time. Both functions turn out to be very similar according to the performance of these indicators, unlike the ranking index, in which the DRF has better performance. The DRF reduces to 25% the minimum demand to avoid non-optimal situations, such as non-supplying the demand and has potential benefits, such as the elimination of finite combinations and easy implementation.