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The main aim in current work is to optimize TiO 2 /W-EG nano-fluid (with 60 vol% of water and 40 vol% of ethylene glycol) flow within the inner tube of the double-pipe heat exchangers with helical coil inserts. The entropy generation is selected as the target function and is to be minimized. To reach this goal, at the first step, a comprehensive sensitivity analysis is carried out taking into account all of the nano-fluid flow conditions (including nanoparticle volume fraction , Reynolds number Re and Prandtl number Pr) and geometric parameters of the helical coil inserts (including thepitch-to-diameter ratio of coil Π). Afterward, the genetic algorithm (GA) is utilized in the optimization process. The results of sensitivity analysis reveal that and Π , respectively, have the highest and lowest impact on the thermodynamics characteristics. Also, the addition of up to 0.02 vol% nanoparticles leads to a maximum of 13.93% improvement in dimensionless entropy generation (DEG). The outputs of the GA are opt = 0.0198%, Re opt = 8421.173, Pr opt = 32.833, Π opt = 2.437 and DEG opt = 0.005086. Furthermore, based on the optimization results, a useful correlation is proposed to find the optimum geometry of the helical coil based on the nano-fluid flow conditions.

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