An integrated optimization methodology for heat transfer enhancement: A case study on nanofluid flow in a pipe equipped with inserts

A hybrid approach that combines Multi-objective Optimization (MOO) and Multiple-criteria Decision-making (MCDM) techniques has been introduced in the present paper for heat transfer augmentation in pipes. The combination of two passive heat transfer enhancement techniques namely the nanofluid and insert employment have been applied in the representative problem. In this context, the performance of water-based CuO, Fe₃O₄, and CNT-Fe₃O₄ nanofluids and two different inserts as twisted tape (TT) and wire coil (WC) were evaluated and their optimum design and flow parameters were determined. The methodology introduced here has two major parts. Firstly, a MOO study was conducted employing the experimentally obtained correlations for the Nusselt number (Nu) and the friction factor (f) as objective functions. The optimum values of the selected design parameters (the Reynolds number (Re), nanoparticle volume fraction ((ϕ)), twist ratio (h/d), wire coil pitch ratio (p/d), and the Prandtl number (Pr)) that maximizes Nu while minimizing f were found as Pareto front. Secondly, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method was used to help decision-makers making an optimal choice among the Pareto optimal solutions that meet their requirements. In the MCDM problems, two criteria (Nu and f) and fifteen alternatives were evaluated for each case. A sensitivity analysis was also conducted by changing the weights of criteria. It was found that the combination of TT and CNT-Fe₃O₄ with the values of design parameters (Re; ϕ; h/d; Pr)=(20,000; 0.27%; 10; 5.50) exhibited the best thermal-hydraulic performance for the equal weights of criteria.