Mathematical Model of Heat Transfer Characteristics of Miniature Heat Pipe with Sintered–Grooved Wick with Empirical Correlation of Evaporation Rate from Wick Surface

Accurate prediction of the thermal performance of bent and flattened miniature heat pipes remains challenging due to the complex evaporation behavior of working fluids within porous wick structures, especially the calculation of evaporation rate from the surface of different wick structures. This study aims to experimentally develop an empirical correlation for the evaporation rate from a sintered–grooved wick structure and employ it in a three-dimensional (3D) mathematical model to predict the heat transfer characteristics of flattened-bent miniature heat pipes with two heat sources. Experiments were conducted with the test rig consisting of a composite sintered–grooved copper wick attached to a heater block. The wick structure comprised sintered copper powder combined with grooves to facilitate liquid transport through capillary action. Heat was supplied from the bottom of the wick through the heater block to promote evaporation of the working fluid. The chosen working fluid was distilled water. The heat input was increased in a stepwise manner, starting from 5 W with increments of 5 W, to investigate the effects of heat input and wick porosity on the evaporation rate. The results showed that increasing the heat input from 5 to 15 W produced an approximately linear increase in the evaporation rate, with a coefficient of determination (R2) of 0.9669. Further increasing the wick porosity from 0.61 to 1.00 enhanced the evaporation rate by 11.9%. The empirical correlation was subsequently employed in a 3D numerical model based on the Receding and Excess Fluid (REF) concept to account for working-fluid redistribution within deformed wick structures caused by bending and flattening used in miniature heat pipes subjected to two heat sources. The predicted thermal resistances agreed well with experimental measurements within a ±7.43% accuracy range. These findings show that the proposed 3D modeling can be utilized as an effective tool in predicting the heat transfer characteristics, enhancing predictive accuracy and providing a useful approach for evaluating the thermal performance of geometrically deformed miniature heat pipes in compact electronic cooling applications.