Multi-objective optimization of twisted tri-lobed tube geometry for enhanced heat transfer and reduced resistance in turbulent flow

•Introduced a multi-objective optimization for twisted tri-lobed tubes.•Used LINMAP and TOPSIS to select the best solution from Pareto optimals.•Analyzed parameter interactions with 3D response surface methodology. This study presents a detailed multi-objective optimization analysis of turbulent flow and heat transfer within a twisted tri-lobed tube, employing an integrated approach that combines Central Composite Design (CCD), Response Surface Methodology (RSM), Non-dominated Sorting Genetic Algorithm II (NSGA-II), Pareto frontier analysis, Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP), and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The investigation focuses on optimizing key design parameters: Reynolds number (Re), twist pitch (P), and minor circle radius (r), targeting Nusselt number (Nu), Poiseuille number (fRe), and Performance Evaluation Criterion (PEC) as optimization objectives. Our major findings reveal that the developed second-order regression model precisely predicts the influences of these parameters on Nu, fRe, and PEC, with sensitivity analysis showing Re's strong positive impact on Nu and fRe, P's negative effect on fRe, and r's minimal impact. The study notably highlights the significant Nu enhancement with Re increase. Utilizing multi-objective optimization, we identified a Pareto optimal set, and through LINMAP and TOPSIS methods, derived compromise solutions that optimally balance heat transfer efficiency, flow resistance, and overall performance. These outcomes underscore the critical importance of parameter selection to meet specific engineering needs, offering a strategic framework for enhancing twisted tri-lobed tube designs.