Multi-optimization of vortex generators and tube profiles for thermo-hydraulic performance enhancement of compact fin-and-tube heat exchangers using RSM-NSGA-II

This study develops a multi-objective optimization framework integrating computational fluid dynamics (CFD), response surface methodology (RSM), and the NSGA-II genetic algorithm for a finned-tube heat exchanger equipped with vortex generators. A three-dimensional steady-state numerical model is established using the finite volume method, assuming incompressible air with constant thermophysical properties, while natural convection and thermal radiation are neglected. Three design variables—transverse offset ( A ), offset angle ( B ), and major-axis length of the heat exchange tube ( C )—are investigated with respect to the Nusselt number ( Nu ), friction factor ( f ), and performance evaluation criterion ( PEC ). A central composite design is employed to construct second-order response surface models, and the optimal solution is identified from the Pareto front using the TOPSIS decision-making method. Results reveal that tube cross-sectional shape exerts the most pronounced influence on both heat transfer and flow resistance: the elliptical tube increases Nu by approximately 23% and reduces f by approximately 12.8% compared with the circular tube. The optimal parameter combination is determined as A = 3 mm, B = 45°, and C = 15 mm (elliptical tube). Relative to the baseline design, the optimized configuration yields a 0.71% decrease in Nu , an 8.02% reduction in f , and a 2.62% increase in PEC , confirming the effectiveness of the proposed framework. This methodology provides a theoretical foundation for designing high-efficiency, low-pressure-drop compact heat exchangers and is extendable to other heat transfer intensification problems involving multi-parameter coupling.