A modified Reynolds analogy for the Gyroid TPMS in laminar flow: Thermal-hydraulic correlations, numerical validation and multi-objective optimisation

Triply Periodic Minimal Surfaces (TPMS) are increasingly adopted as heat-transfer structures thanks to their smooth curvature, tunable porosity and high surface-to-volume ratio. In the present work, we focus on the Gyroid topology in laminar flow (20≤Re≤100) and develop a modified Reynolds analogy linking thermal and hydraulic behaviour through compact engineering correlations. Using CFD datasets obtained under both prescribed wall temperature and imposed wall heat-flux boundary conditions, we analyse the friction factor, Nusselt number and Stanton number over the porosity range 0.3≤φ≤0.7. A Darcy–Forchheimer interpretation of the hydraulic behaviour shows that the investigated operating window spans the transition from a predominantly Darcian regime to a mixed viscous–inertial regime while remaining entirely laminar. Three alternative forms of modified Reynolds analogy are calibrated, yielding correlations that reproduce the CFD data with residual deviations of 10%–15%. The resulting correlations are then employed for reduced-order thermo–hydraulic optimisation based on heat-transfer enhancement and pumping-power minimisation. Among the three formulations, only the correlation including a porosity-dependent Reynolds-number correction generates an internal Pareto front, highlighting the role of inertial transport in determining the optimal thermo–hydraulic trade-off. The proposed framework enables the prediction of thermal performance directly from hydraulic information and provides a reduced-order design tool for Gyroid-based heat-transfer applications.