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Topology optimization of the heat transfer quality in two-dimensional heat conduction problem at enclosure as one of the typical thermo-physical problems has always been quite important. In this paper a level set-based topological optimization procedure of two-dimensional heat conduction problem include point and speared thermal on computational domain load using finite elements method is developed. In level-set method, all structural boundaries are parameterized by a level of dynamic implicit scalar function of higher order. Changes of this function can easily model the detachment and attachment of dynamic boundaries in topology procedures. The same shape functions of finite elements analysis are employed to approximate the unknown temperatures and geometry modeling of the design domain. The objective function is to minimize thermal power capacity and sensitivity analysis on some heat conduction problems is investigated to deal with the topology optimization using level-set method with the finite elements scheme. Finally, topology optimization results of 3 heat conduction problems under both include point and spread thermal load cases are presented to demonstrate the validity of the proposed method. The proposed method lead to a significant reduction of the computational cost and time and it can be applied to a wide range of topology optimization problems arising from the heat transfer.

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In this research, the deformation of a non-Newtonian leaky-dielectric droplet suspended in another non-Newtonian fluid under a uniform electric field is simulated. The aim of this research is the studying the effect of the electric field on the hydrodynamic of non-Newtonian droplets and also the comparison between the behavior of Newtonian and non-Newtonian droplets in the presence of an electric field. The power law model is used to describe non-Newtonian fluid behavior. The level set method is employed to determine the location of the interface. Also, the ghost fluid method is used to apply discontinuities at the interface. By applying an electric field, a non-Newtonian droplet deforms similarly to a Newtonian one. This deformation may occur either in the direction of the electric field or perpendicular to it. By increasing the electric Capillary number (ratio of electric force to surface tension force) the deformation of the non-Newtonian droplet with different power law constants increases. In this research, the behavior of different non-Newtonian droplets with different power constants was compared and it was observed that by an increase in the power law constant the drop deformation increases. According to the results, the deformation of a shear-thinning droplet under an electric field is less than the deformation of a Newtonian droplet and the deformation of a Newtonian droplet is less than the deformation of a shear thickening droplet.