“Multi-optimization of nanofluid and fractal fin in the plate heat exchanger using RSM and TOPSIS”

• A novel heat exchanger design integrating fractal fins and Oil/MWCNT nanofluids is optimized for superior thermal–hydraulic performance. • Multi-objective optimization reveals a Pareto-optimal solution that increases the Nusselt number by 50% and the Colburn coefficient by 260%, while simultaneously reducing pumping power by 93%. • The fin attack angle is identified as a dominant geometric parameter, with a critical threshold of 60 degrees for significant heat transfer enhancement. • A synergistic effect is demonstrated: combining a high attack angle with a 4% nanoparticle concentration boosts heat transfer performance by up to 60%. This study employs a three-step methodology to conduct a multi-objective optimization of a novel three-stream plate-fin heat exchanger design. The analysis evaluates the thermal performance of the system across attack angles of 30°, 60°, and 100° while integrating an Oil/multi-walled carbon nanotube (MWCNT) nanofluid to enhance heat transfer efficiency. Numerical simulations are conducted using the finite volume method (FVM) to analyze the thermal-fluid performance of a three-layer heat exchanger incorporating fractal fins in its mid-layer. The study spans Reynolds numbers ranging from 10,000 to 40,000, with the pressure–velocity coupling resolved via the SIMPLE algorithm. Subsequently, a multi-objective optimization framework is implemented, combining the Non-dominated Sorting Genetic Algorithm (NSGA-II) with the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for Pareto-front analysis and optimal design selection. The results of this research show that the fractal fin attack corner increases cause more flow deviation from the direct route and better fluid mixing arising from collisions to the internal surfaces of the exchanger. With the flow velocity increase, the thermal boundary layer forms and disappears by collision with the fin surfaces. The temperature distribution is more uniform in the exchanger due to the flow collision with the fractal fins, which have more attack corners. A Reynolds number of 40,000 can improve the heat transfer on average to about 63 percent. Also, adding volume fractions of solid particles to a similar Reynolds number for different attack corners can increase heat transfer by about 48 percent. An increase of the fractal fin’s attack angle to 100 degrees increases the amount of pumping power to about 50 percent in comparison to the fin with a 30-degree attack corner. The fractal fins attack corner increases to 100 degrees, increasing the coefficient of friction to about 45 to 85 percent in comparison to the lower attack corner. The Colburn factor exhibited limited sensitivity to variations in angular orientation and nanoparticle concentration. However, it demonstrated a significant nonlinear decrease of about 1.2 times as the Reynolds number increased to 11,000. In the multi-objective optimization analysis, significant enhancements were observed in the Nusselt number and the Colburn coefficient, which increased by approximately 50 % and 260 %, respectively, compared to the initial state. Conversely, the pumping power was sharply reduced by 93 %, while the Friction factor saw a 43 % increase.