On the hydrostatic limit for thin film flow with applications to thermosyphons

Heat pipes frequently encounter challenges in effectively returning condensed liquid from the condenser to the evaporator through capillary pumping, which limits their overall efficacy. When capillary pumping becomes irrelevant due to factors like an absent wick or overfilling, the heat pipe is more properly termed a thermosyphon. In a close-to-horizontal orientation, the driving force for liquid return in a thermosyphon relies on the difference in liquid pool depth between the evaporator and condenser. An excessively deep liquid pool in the condenser can hinder radial heat transfer, necessitating a design that favors intermediate-depth liquid pools. This study utilizes a theoretical approach based on the lubrication approximation to the Navier–Stokes equations to determine the fill ratio that maximizes thermosyphon performance. We explore the relationship between this fill ratio and factors such as the axial temperature difference along the thermosyphon. Our analysis thereby highlights the hydrostatic-driven flow limit in the thermosyphon as an analogue to the capillary limit in heat pipes. Regarding the hydrostatic limiting curve as an alternative to the capillary limiting curve offers valuable insights for enhancing thermosyphon performance and provides a means of comparing the performance of one vs. the other passive heat transfer device.