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In this study, the effects of magnetic field on the flow field, heat transfer and entropy generation of Cu-water nanofluid mixed convection in a trapezoidal enclosure have been investigated, numerically. The side walls of the cavity are insulated, the top lid is cold and moving toward right or left and bottom wall is hot and the side walls angle from the horizon is 45˚. The results showed that with imposing the magnetic field and enhancing it, the nanofluid convection and the strength of flow decrease and the flow tends toward natural convection and finally toward pure conduction. For this reason, for all of the considered Reynolds numbers and volume fractions, by increasing the Hartmann number the average Nusselt number decreases. Furthermore, for any case with constant Reynolds and Hartmann numbers by increasing the volume fraction of nanoparticles the maximum stream function decreases. For all of the studied cases, entropy generation due to friction is negligible and the total entropy generation is mainly due to irreversibility associated with heat transfer and variation of the total entropy generation with Hartmann number is similar to that of the average Nusselt number. With change in lid movement direction at Reynolds number of 30 the average Nusselt number and total entropy generation are changed, but at Reynolds number of 1000 it has a negligible effect.

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In this paper, numerical investigation was carried out for the sake of identifying optimum geometry for variable geometry ejector using in solar refrigeration system as the prerequisites to experimental tests. Variable geometry was made by using a movable primary nozzle and movable spindle in it. Vacuum tube collector was postulated as heat source and R600a used as working fluid. Condenser temperature based on Middle East area temperature and evaporator based on operative condition in HVAC system selected. Generator, condenser and evaporator operating temperatures have severe effects on the optimum geometry of ejector. Therefore, for maximum entrain ratio it is necessary to identify optimum geometry to cope with variations in operating condition. The results showed that using a variable geometry ejector is a requirement for cooling during the day. The following fluid structure was compared by entropy generation during mixing and shock phenomena. The results showed there is optimum back pressure to minimize fluid exit entropy. It coincides with critical back pressure. It was found that depending on back pressure maximum entropy generation happen by two reasons, mixing and shock phenomena.

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In this paper the mixed convection and entropy generation in a square cavity filled with Al2O3-water nanofluid with the presence of a constant axial magnetic field, is analyzed. The upper and bottom walls are adiabatic. Discretization of the governing equations were achieved through a finite volume method and solved with SIMPLE algorithm. In this research the effects of the Rayleigh number (103- 106), Hartmann number (0 - 100) and also inclination angle (0 - 90°) are investigated. When the cavity is rotated, it is observed that the mean Nusselt number and total entropy generation increase when the Rayleigh number increases in cavity. In square cavity, regardless of the Ha number, by increasing of the inclination angel, the mean Nusselt number and entropy generation rate, increase until inclination angel 30°, then decreases. Also when the magnetic field is rotated, it is observed that the mean Nusselt number decrease when the Hartmann number increases. The mean Nusselt number when the cavity rotates with specific inclination angel is less than state that the cavity rotates with specific magnetic field. For finding optimum condition of heat transfer, Artificial Neural networks (ANN) were used. The results from optimization show that as the Rayleigh number increases, the optimum angel decreases. Whatever the Rayleigh number more increases, the decrement in optimum angel more intenses. Also in low the Rayleigh number, as the Hartmann number increases, the optimum angel decreases firstly then increases. In high Rayleigh number, as the Hartmann number increases, the optimum angel increases too.

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In this study, generated entropy of mixed convection of Al2O3–water nano fluids in a vertical channel with sinusoidal walls under a constant and uniform magnetic field was numerically investigated. The effects of various parameters such as volume fraction of nanoparticles, amplitude of sine wave, Reynolds, Grashof and Hartman numbers were studied. This study was carried out by assuming the laminar, steady state and incompressible flow. Also, the thermo physical properties of nanoparticles were assumed constant. The Boussinesq approximation was used to calculate the variations of the density caused by buoyancy force and the finite volume method and two phase mixture model were used to simulate the flow. The results showed that the entropy generation due to heat transfer and viscous effects increase by adding nanoparticles to the base fluid. Also, the results showed that the entropy generation due to heat transfer increases by increasing the Grashof number and decreasing the Reynolds number, while a reverse trend is observed for entropy generation due to viscous effects. By increasing the Hartman number, the entropy generation due to heat transfer increases at first and then decreases and entropy generation due to viscous effects reduces. For all studied intensities of magnetic fields, the entropy generation decreases using corrugated channels.

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In present paper, a numerical study is performed for analysis of effects of geometrical and operational parameters of viscous micropump with the approach to Entropy Generation Minimization by Lattice Boltzmann Method. In study of effect of change in the geometric parameter L and operational parameters ∆P*, it was found that in all ∆P*s, two range of L=1.2 - 1.6 and L=4.4 - 4.8 at EGM viewpoint and two range of L=1.1 - 1.6 and L=4.4 - 4.9 at the minimum power of rotors viewpoint are introduced as optimum ranges. Due to the full overlap of optimum ranges at the EGM viewpoint with the minimum power of rotors viewpoint, the same range mentioned in the EGM viewpoint is selected as the optimal range. Results of the effect of change in the geometric parameter L and operational parameters Re showed that in all Res, two range of L=1.1 - 1.5 and L=4.5 - 4.9 at the EGM viewpoint and two range of L=1.2 - 1.6 and L=4.4 - 4.8 at the minimum power of rotors viewpoint are introduced as optimum ranges. Therefore, the common range of these viewpoint namely L=1.2 - 1.5 and L=4.5 - 4.8 can be selected as the most optimal range. Regarding the effect of change in the geometric parameter ε and operational parameters Re and ∆P* is determined in all Res and ∆P*s, the range of ε = 0.1 – 0.5 is selected as optimum range in the EGM viewpoint and the minimum power of rotors viewpoint.

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Optimum design and performance improvement of the Heat Recovery Steam Generator (HRSG) have noticeable effects on the thermal efficiency of the combined cycle power plants. Therefore, HRSG must be designed in such way that maximizes the heat recovery and improves the overall performance of the plant.
In this paper, a method for design and optimization of a triple pressure HRSG is proposed. It is shown how to simultaneously optimize the operating and geometric design parameters of the HRSG by using the constructal theory. Considering the minimum total entropy generation as the objective function, the optimum parameters in the HRSG unit are derived by using the genetic algorithm method under the fixed total volume condition. Optimized total volume is derived by converting the exergy destruction to cost of entropy generation in order to compare with the capital cost and the results show that there is a trade-off between them. Also, aspect ratios of the units, the heat transfer area for each component of the HRSG and thermodynamic properties are significant features of the flow configuration inducted by the Constructal design. Furthermore, the effects of changing in the temperature and flow rate of hot gas on the optimal values of the total volume, power and steam production are determined.

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In the present paper, heat transfer and entropy generation in Rayleigh-Bَenard convection of nanofluids subjected to a magnetic field within an enclosed cavity is studied by adopting the lattice Boltzmann Model. The left and the right walls are smooth and insulated against heat and mass. The bottom wavy wall is heated, while the top flat wall is maintained at the cold temperature. The variation of density is slight thus; hydrodynamics and thermal fields equations are coupled using the Boussinesq approximation. The density and energy distribution are both solved by D2Q9 model. The study have been carried out for Rayleigh number 103, 104 and 105, Hartmann number 0, 30, 60 and 90 and volume fractions of 0 up to 0.04 for Cu, CuO and Al2O3 nanoparticles in base pure water fluid. Results show that the Nusselt number and entropy generation increase with the increment of Rayleigh number and nanoparticles volume fraction, but those decrease by the increment of the Hartmann number. The enhancement of magnetic field augments or plummets the effect produced by the presence of nanoparticles on heat transfer and entropy generation at different Rayleigh numbers. In addition, it is shown the greatest effect of nanoparticles on heat transfer and entropy generation is observed by addition of Cu nanoparticles and the least is function of Ra number. This study can, provide useful insight for enhancing the convection heat transfer performance by considering of energy losses within enclosed cavities with Rayleigh–Bَenard convection nanofluid under influence of magnetic field.

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