Abstract: The present study aims to systematically investigate and compare the flow and heat transfer characteristics of three typical triply periodic minimal surface (TPMS) heat exchanger architectures, namely Gyroid, Diamond, and Primitive structures. A key objective is to reveal the underlying heat transfer enhancement mechanisms, especially the role of field synergy, and to provide a theoretical basis for the structural selection and engineering application of TPMS-based compact heat exchangers under laminar low-velocity operating conditions. A series of numerical simulations were conducted using the multiphysics simulation software COMSOL. The three-dimensional steady-state Navier-Stokes equations, energy equation, and the shear stress transport (SST) turbulence model were solved to simulate conjugate heat transfer within the TPMS heat exchangers. Computational fluid dynamics (CFD) techniques were employed to analyze the internal flow processes and temperature fields in detail. Three TPMS structures were constructed with identical porosity and wall thickness, and their hydraulic diameters were calculated. The computational domain included extended inlet and outlet sections (80 mm in length) to mitigate inlet effects, although flow development remained complex due to geometric disparity. Water was used as the working fluid. Boundary conditions included a velocity inlet (0.1 m/s) and pressure outlet (0 Pa), with cold inlet temperature at 293.15 K and hot inlet temperature varying from 343.15 K to 358.15 K. A grid independence study was performed, and the numerical model was validated against experimental data from the literature, with relative errors within 2%. Key performance parameters such as Nusselt number (Nu), Fanning friction factor (f), overall heat transfer coefficient, performance evaluation criterion (PEC), and field synergy angle were computed and compared. The simulation results demonstrate that the three TPMS structures exhibit distinctly different flow and thermal fields. For the Gyroid structure, the temperature distribution displays wavy gradients and the pressure field shows periodic strong fluctuations due to its highly disordered and tortuous channels, which induce intense flow mixing and boundary layer disruption. For the Diamond structure, both temperature and pressure fields exhibit regular oblique banded gradients, reflecting its ordered and directional flow passages that guide the fluid along stable paths. For the Primitive structure, the temperature and pressure distributions show ring-shaped gradients around each periodic pore, characteristic of porous-media-like flow with repeated splitting and merging. Quantitative analysis reveals that under the same inlet temperature condition, the Diamond structure achieves the highest overall heat transfer coefficient, which is approximately 32% higher than that of the Gyroid and 147% higher than that of the Primitive structure. The Nusselt number trend is consistent with the overall heat transfer coefficient. The Fanning friction factor is lowest for the Gyroid structure, intermediate for Diamond structure, and highest for Primitive structure. The PEC values for both Gyroid and Diamond structures are greater than unity relative to Primitive structure under the same pumping power, indicating superior comprehensive performance. Field synergy analysis shows that the average cosine of the synergy angle is highest for Diamond structure (≈0.68), followed by Gyroid structure (≈0.55) and Primitive structure (≈0.47), indicating that the Diamond structure achieves the best alignment between velocity and temperature gradient vectors. In laminar low-velocity regimes, the Diamond structure offers the optimal trade-off between heat transfer enhancement and flow resistance penalty among the three structures examined. Its ordered oblique channels promote excellent field synergy, leading to superior thermal performance with moderate pressure drop. The Gyroid structure, while providing strong local heat transfer through flow destabilization, suffers from higher energy dissipation. The Primitive structure minimizes pressure drop but at the cost of reduced heat exchange efficiency. These findings provide valuable guidance for the design and selection of TPMS-based heat exchangers in applications requiring compactness, high efficiency, and controlled pumping power. Further experimental validation is recommended for high-precision engineering implementations.