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In this paper, a numerical study has been performed to investigate the effect of geometrical parameters of a viscous micro-pump on the flow rate and entropy generation. The present research has been carried out for three geometrical parameters of micro-pump including eccentricity (), sizes (S) of rotors and also their distance from each other (L) in the range of 0.1 to 0.9, 1.5 to 3.5 and 0.85 to 4.5, respectively. The results show that with increasing , the micro-pump flow rate also increases. On size variation effects, it is observed that decreasing the downstream rotor diameter, while keeping constant the upstream rotor diameter, the flow rate decreases exponentially. By increasing L, a steep increase in flow rate is initially observed, which becomes almost constant, when rotors are sufficiently far apart. With regard to entropy analysis, the effect of above geometrical parameters has been investigated on the entropy generation. The parameter RS indicating the ratio of the gradient of the entropy production rate to the related flow rate is introduced as a tool for entropy analysis. Also in this paper, for obtaining the maximum flow rate at the minimum frictional dissipation, optimal geometrical parameters are extracted. In this regard, the values of L=2, ε=0.5, S_1=1.5 and S_2=2.5 are selected as the optimum geometrical parameters of viscous micro-pump.

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In the present paper, a numerical study is performed for analysis of 3D effects of geometrical parameters namely microchannel depth, eccentricity and sizes of rotors and operational parameter namely pressure difference on flow flux and efficiency by LBM. In investigation of simultaneously variation effect of geometrical parameters namely rotors eccentricity and microchannel depth is observed in all depths, increasing the eccentricity, both flow flux and efficiency increased. Also, in a constant eccentricity both flow flux and efficiency increased. In the next investigation that simultaneously effect of geometrical parameters namely rotors sizes and microchannel depth is discussed determined that in all depths, decreasing the rotors sizes, flow flux decreased. But for efficiency, it became less in the lower depths and increasing depth the efficiency increased. In final, the effects of operational parameter of pressure difference and geometrical parameter of microchannel depth on flow flux and efficiency has been studied. As the results show, increasing the pressure difference, flow flux linearly decreased so that it became zero at the certain pressure. Moreover, efficiency variations vs. pressure difference parabolically is observed.

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In the present paper a numerical simulation based on the LBM is performed to analyze a viscous micropump with a single elliptic rotor. The effects of three important geometric parameters including aspect ratio of rotor, micropump height and rotor eccentricity are investigated on the average flow rate and entropy generation. The obtained results from the simulations are analyzed by response surface method (RSM). The results indicate that the average flow rate increases by increasing the aspect ratio and rotor eccentricity and decreases by increasing the micropump height. Moreover, the sensitivity of the average flow rate to changes of aspect ratio and eccentricity is more than the change of microchannel height. The results also show that by increasing all three geometric parameters, the average entropy generation increases and is sensitive to changes of three geometric parameters. Finally, the optimal geometric parameters are determined by RSM that for maximizing the flow rate, the optimum values of 1, 1.5 and 0.9 are for aspect ratio, height and eccentricity respectively and for minimizing the entropy generation, the optimum values of 0.2, 1.5 and 0.1 are achieved.