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

Thermosyphons are passive heat exchangers that combine phase change and flow in achieving rates of heat transfer well in excess of those due to conduction. The flow of liquid that develops within a moderately-inclined thermosyphon is driven primarily by the hydrostatic force associated with the elevation difference between the deep liquid pool within the (raised) condenser vs the shallow liquid pool at evaporator. Such considerations ostensibly favor a deep liquid pool in the condenser, however, any gain of axial (convective) heat transfer may be offset by a corresponding decrease of radial heat transfer by conduction. Finding the optimum balance between these two competing effects is a surprisingly rich problem that requires from a theoretical perspective the application of the Navier Stokes equations in conjunction with thermodynamical considerations. For prescribed working fluid, inclination angle and heat load, the theoretical model in question can predicts the liquid fill ratio required to maximize thermosyphon performance. We juxtapose our results with those associated with a capillarity driven heat pipe. On the basis of this comparison we can predict, with particular reference to the liquid flow, parametric combinations where one vs the other engineering design is favored