## 1 Introduction  
Thermal management has become a crucial topic in contemporary engineering applications. Ensuring efficient heat dissipation across a wide range of domains, from electronic devices to architectural elements, is extremely important for optimal system performance, increasing energy efficiency, and reducing adverse thermal effects. Consequently, the development of a comprehensive and effective thermal management strategy constitutes a key factor in the successful implementation of engineering solutions [1, 2, 3]. In this context, heat exchangers are one of the widely used solutions to optimize heat transfer [4]. In recent years, the search for innovative and more efficient structures beyond traditional heat exchanger designs has continued. TPMS is one of the prominent structures in this study. TPMS are cellular structures that have mathematically defined, regular, and minimal surface properties, with complex and continuously curved surfaces [5]. TPMS structures provide several benefits for heat transfer applications. These include low pressure drop, adjustable porosity, and improved heat transfer characteristics. These advantageous properties are attributed to the ability of structures to resemble biological structures found in nature [6; 7]. In recent years, researchers have actively explored TPMS applications across various domains. These include materials science, biomedical engineering, and heat transfer. The focus is primarily on their unique structural and thermal properties. Multiscale topology optimization enhances cellular structures through simulations and experiments. This optimization provides high thermal conductivity, large convective surface area, and rapid cooling capability [8]. Furthermore, comprehensive analyses of the thermal performance and potential applications of TPMS structures have been conducted, particularly proposing an innovative heat exchanger design that incorporates the Gyroid TPMS structure, which demonstrates higher heat transfer efficiency compared to conventional designs [9]. Gyroid structures offer effective heat transfer due to their high surface areas; however, they may present production challenges due to their complex geometries. Conversely, I-graph-and-wrapped-packages (IWP) sheet structures provide advantages for rapid cooling applications by ensuring high temperature homogeneity, although their structural durability may be lower compared to solid alternatives [10]. [PERSON] et al. (2019) [11] performed an extensive analysis of the essential characteristics of TPMS architectures and their prospective utilization across multiple engineering domains. The investigation emphasized the promising potential of TPMS structures in diverse fields, including thermal management, structural mechanics, sound absorption, and medical implants. The authors elucidated the beneficial attributes of TPMS designs, such as elevated surface area-to-volume ratios, reduced relative densities, and the ability to adjust mechanical properties based on specific requirements [11]. The performance of heat exchangers designed with TPMS structures significantly depends on material selection. [PERSON] et al. (2019) [12] demonstrated the potential of these structures, which have various types such as Schwarz P, Gyroid, and I-WP, in many applications, including heat exchangers, due to their high mechanical performance and large surface area properties [12]. [PERSON] et al. (2018) [13] conducted a study on TPMS structures fabricated using titanium alloy. Their research focused on evaluating the mechanical and thermal characteristics of these structures. The findings revealed that TPMS structures exhibit a favorable strength-to-weight ratio, highlighting their potential for lightweight and high-performance applications [13]. The choice of coolant is also an important factor affecting the performance of TPMS structures used in heat exchangers with nanofluids. While water has been a common choice traditionally, the use of nanofluids has started to attract attention in recent years.