## 1 Introduction
[PERSON] and [PERSON] (2022) [14] investigated the heat exchanger performance of water-based nanofluids containing metal oxide nanoparticles. In their study, they showed that nanofluids can increase the heat transfer coefficient by up to 45% [14]. Similarly, an additional study explores the effect of magnetized ternary hybrid nanofluid (THNF) flow on heat transfer and shows that the heat transfer capacity of ternary hybrid nanofluid is more enhanced compared to hybrid nanofluids. The shape of the nanoparticles, particularly the blade shape, plays a significant role in enhancing the heat transfer rate [15]. Numerical and experimental methods have been employed to investigate the performance of heat exchangers based on TPMS and Periodic Nodal Surfaces (PNSs). Comparative studies have been conducted on different TPMS and PNS structures to evaluate their advantages over traditional heat exchangers [13]. Supporting these investigations, simulations of flow and heat transfer in 3D-printed TPMS heat exchangers have demonstrated the potential of these structures to offer innovative and efficient solutions [16]. Various numerical studies have been conducted to understand the flow and heat transfer mechanisms in TPMS structures. [PERSON] and [PERSON] (2024) [17] employed computational fluid dynamics (CFD) techniques to analyze the heat transfer and pressure drop behavior in TPMS structures. The performance of these structures was assessed over a range of Reynolds number (\(Re\)) [17]. Numerical investigations using CFD analyses examined flow and heat transfer in TPMS structures. The study tested three different porosity levels under laminar flow conditions. Results showed that increasing \(Re\) enhances heat transfer performance. Different geometries demonstrated varying levels of effectiveness [18]. Various optimization studies have been carried out to further improve the performance of TPMS structures. Recent research focuses on investigating the effects of TPMS structures on turbulence generation, heat transfer, and flow mixing, aiming to evaluate their potential to enhance the efficiency of conventional heat exchangers [19]. In addition to these optimization studies, the thermal and hydraulic performance of TPMS-based heat exchangers has been examined using three-dimensional models of various surfaces with different volume ratios. The findings reveal the significant impact of secondary flows, periodic flow acceleration/deceleration, and continuous flow direction changes on convective heat transfer. This research contributes to the design and implementation of TPMS-based heat exchangers [20]. The performance of TPMS structures is heavily influenced by surface finish quality. [PERSON] et al. (2023) highlighted how advanced soft abrasive flow finishing techniques can enhance the surface characteristics of complex geometries in constraint spaces, which could potentially improve the thermal-hydraulic performance of TPMS heat exchangers by reducing surface roughness and optimizing flow channels [21]. Most studies have focused on the thermal performance of TPMS structures under laminar flow conditions. Nevertheless, recent research has begun to explore the effects of turbulent flow on their heat transfer characteristics. [PERSON] et al. (2019) [22] examined the thermal conductivity of TPMS structures, finding that thermal conductivity decreases as porosity increases. Among the different TPMS topologies, the Gyroid structure demonstrated the highest thermal conductivity. The results suggested that TPMS structures could be effectively employed in thermal management systems, including heat exchangers. In the study, effective thermal conductivity values were measured for different TPMS topologies (Gyroid, Diamond, and Primitive), and the relationship between these values and the \(Re\) was investigated. At high Re (Re > 2000), in the turbulent flow regime, it was observed that the heat transfer performance of TPMS structures significantly increased.