The aim of this study was to utilize thermodynamic laws analysis to optimize the geometric parameters of a double-tube heat exchanger that incorporates water-graphene nanofluid. The heat exchanger was outfitted with novel type of twisted conical fins on the tube side and ribs on the annular side. The realizable k − ε model with enhanced wall treatment function was utilized to simulate a counter-current flow in which nanofluid passes on the tube side and water passes on the annular side in a turbulent regime. The heat exchanger’s design parameters, including the number of twisted conical fins, number of ribs on the annular side, pitch, and height of the elliptical ribs were investigated. Multi-objective optimization was then conducted to achieve the dual objectives of maximizing heat transfer and minimizing both friction coefficient and entropy generation. To determine objective functions based on decision variables in the multi-objective optimization, the group method of data handling was employed. Through a parametric study, it was found that increasing the pitch, number, and height of ribs on the annular side results in enhanced heat exchange between the two fluids and an increase in entropy and friction coefficient. Conversely, increasing the number of conical fins leads to increased heat transfer and friction coefficient while decreasing entropy production on the tube side. According to the obtained results, in the average values of other variables of the problem, in the changes of conical fins from 1 to 2 compared to 2 to 3, the values of the changes in the overall heat transfer coefficient and the friction coefficient were 1.9 times and 1.4 times higher, respectively, while it is 2.4 times less in total entropy production, which shows the greater effect of changing the number of conical fins from 1 to 2 compared to 2 to 3, as well as a greater effect on the overall entropy production. The optimal state for the given decision variables was specified using the multi-objective optimization method. The results of the three-objective optimization revealed that the optimal state was achieved when the pitch, number of ribs, and fins parameters were set to approximately the middle of their range of variation. Furthermore, the most optimal state possible was achieved with the minimum rib height. The optimal geometry leads to entropy production 15.7% more than the lowest entropy production and 73.9% less than the highest entropy production.
