Flow resistance of grooved heat pipes with axially varying meniscus curvature

We present a semi-analytical procedure to capture the effect of slowly-varying (streamwise) meniscus curvature on the flow resistance of an axial-groove heat pipe (AGHP). The relevant small parameter in the geometry of an AGHP is the ratio of the groove period to the length of the adiabatic section. Prescribed are the AGHP geometry, its orientation with respect to gravity and relevant thermophysical properties (and, by implication, the capillary pressure driving the flow in the grooves). We focus on meniscus variation in the adiabatic region due to pressure gradients using an asymptotic expansion, and invoke the standard assumptions in the evaporator and condenser sections, i.e., that the meniscus curvature is constant and equal to that of the cylinder. In the adiabatic section, the deviation of the meniscus from this curvature is captured using a boundary perturbation. A local analysis at the contact lines ensures the flow singularities are fully resolved. Our procedure enables more accurate prediction of the capillary limit in an AGHP, and the results are compared to those in the literature.