Analysis of Fluid Flow in Axial Re-entrant Grooves with Application to Heat Pipes

Thefullydevelopedlaminar∞owwithinare-entrantgroovehasbeenanalyzedusing a flnite element model. Re-entrant grooves have been used in both axially-grooved heat pipes and in monogroove heat pipes. The main beneflt to using this type of wick structure is the reduction of the liquid pressure drop along the length of the grooveduetocountercurrentliquid-vaporinteractionatthemeniscus. Allprevious researchers assumed that the pressure drop within the liquid could be modelled as ∞ow within a smooth tube, but the results of the current analysis show that this assumption can lead to signiflcant errors in the pressure drop prediction. An extensive literature survey was completed and the results of flve previous studies were used to validate the current numerical model. It was found that the present flnite element model is both more accurate and consumes less computer resources than a flnite difierence based model developed previously by one of the authors of the current manuscript. A parametric analysis was carried out to determine the Poiseuille number, Po = fRe, the dimensionless mean velocity, v ⁄ , and the dimensionlessvolumetric∞owrate, _ V ⁄ ,asfunctionsofthegeometryofthere-entrant groove (groove height 1:0 • H ⁄ • 4:0, slot half-width 0:05 • W ⁄ =2 • 0:9, flllet radius 0:0• R ⁄ •1:0),andtheliquid-vaporshearstress(0:0•i? ⁄ lv •2:5). Itwasdetermined that the ∞ow variables were strongly afiected by the groove height, slot half-width and liquid-vapor shear stress, but were relatively unafiected by the flllet radius. The case in which the meniscus recedes into the re-entrant groove was examined, whichcouldbearesultofevaporatordry-outorinsu‐cientliquidflllamount. The cross-sectionalareaoftheliquidinthegroove, A ⁄ ,themeniscusradius, R ⁄,andthe above-mentioned∞owvariableswerecalculatedasfunctionsofthemeniscuscontact angle(0 ‐ • `•40 ‐ )andmeniscusattachmentpoint(0:0• H ⁄