Adiabatic-section flow in axial-groove heat pipes with varying meniscus curvature

Via asymptotics and numerics, we develop a semi-analytical procedure to capture the effect of slowly varying (streamwise) meniscus curvature on the flow resistance of the adiabatic section of an axial-groove heat pipe (AGHP). The small parameter is the pitch of the grooves divided by the length of the section. The geometry of the AGHP, its orientation with respect to gravity and relevant thermophysical properties (and, thus, the maximum capillary pressure) are prescribed. The deviation of the radius of curvature of the menisci from that of the lands (raised ridges protruding into the heat pipe bounding the axial grooves through which liquid flows) is captured numerically. (Alternatively, a boundary perturbation approach using a second small parameter, a protrusion angle of the meniscus into the groove, is outlined.) A local analysis ensures that the singularities at the triple-contact lines are resolved. Our procedure enables more accurate prediction of the capillary limit of an AGHP and the thermal resistance of its adiabatic section because, as shown, it causes the flow resistance in the adiabatic section in an AGHP representative of a commercial one to change by as much as 70 %. Instructions to access our code to semi-analytically compute the capillary limit when the radii of the menisci and lands are equal but, unlike in previous literature, shear stress and velocity are matched along the meniscus in the adiabatic section, are provided.