Mass-momentum synergistic transport criterion in gravity-controlled closed phase-change systems: Numerical validation using nanofluid-enhanced heat pipes

In closed phase-change heat transfer system under gravitational control, the essence of coordinating the material basis (mass source) and the driving potential (momentum source) to maintain efficient circulation dynamics lies in the fact that the geometric topology of the liquid pool changes dynamically with the inclination angle, leading to a drift in the mapping relationship between the macroscopic inventory of the working fluid and the actual wetting topology. However, the lack of a quantitative understanding of this nonlinear coupling mechanism has resulted in the absence of a unified criterion to define the physical boundary between local dry-out and efficient operation. To overcome this, the current research paper uses nanofluid two phase closed thermosyphon (TPCT) that is very sensitive to changes in mass and momentum as a common physical model. For the first time, a comprehensive dimensionless transport criterion, Y, was proposed. This criterion unifies the filling ratio (mass source) and the inclination angle (momentum source) through the geometric topology of the liquid pool, thereby establishing a dynamic correspondence between the availability of the working fluid inventory and the actual wetting topology. The results demonstrate that the thermal resistance data under different operating conditions achieve a data collapse for the investigated TPCT configuration based on Y (R 2 ≈ 0.98). The operational states of the TPCT are delineated into three physical regimes: a dry-out dominated regime (Y < 25), limited by insufficient effective wetting area; a synergy enhancement regime (25 ≤ Y ≤ 60), where high-intensity vortices (vorticity >32 s −1 ) induced by interfacial shear significantly reduce thermal resistance; and a thermodynamic limit regime (Y > 60), where performance saturation occurs due to viscous damping of the liquid film. Consequently, the optimal engineering design window for the TPCT is identified as 40 ≤ Y ≤ 60, providing atheoretical basis for the optimized design of efficient closed phase-change systems.