In this paper we propose a set of guidelines to select a solver for the solution of nonlinear programming problems. With this in mind, we present a comparison of the convergence performances of commonly used solvers for both unconstrained and constrained nonlinear programming problems. The comparison involves accuracy, convergence rate, and convergence speed. Because of its popularity among research teams in academia and industry, MATLAB is used as common implementation platform for the solvers. Our study includes solvers which are either freely available, or require a license, or are fully described in literature. In addition, we differentiate solvers if they allow the selection of different optimal search methods. As result, we examine the performances of 23 algorithms to solve 60 benchmark problems. To enrich our analysis, we will describe how, and to what extent, convergence speed and accuracy can be improved by changing the inner settings of each solver.
Over the last several decades, cooling technologies have been developed to address the growing thermal challenges associated with high-powered electronics. However, within the next several years, the heat generated by these devices is predicted to exceed 1 kW/cm2, and traditional methods, such as air cooling, are limited in their capacities to dissipate such high heat fluxes. In contrast, two-phase cooling methods, such as microdroplet evaporation, are very promising due to the large latent heat of vaporization associated with the phase change process. Previous studies have shown non-axisymmetric droplets exhibit different evaporation characteristics than spherical droplets. For a droplet pinned atop a micropillar, the solid-liquid and liquid-vapor interfacial area, the volume, and thickness of the droplet are the major factors that govern the evaporation heat transport process. In this work, we develop a shape optimization tool using the particle swarm optimization algorithm to maximize evaporation from a droplet confined atop a micropillar. The tool is used to optimize the shape of a nonaxisymmetric droplet. Compared to droplets atop circular and regular equilateral triangular micropillar structures, we find that droplets confined on pseudo-triangular micropillar structures have 23.7% and 5.7% higher heat transfer coefficients, respectively. The results of this work will advance the design of microstructures that support droplets with maximum heat transfer performance.
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