Geometry-driven analysis of capillary flow in wick structures using a coupled analytical–numerical framework

A combined analytical and numerical framework is developed to investigate capillary-driven flow in wick structures with arbitrary cross-sectional geometries. The formulation incorporates geometric effects through the wetted perimeter-to-area ratio for capillary pressure and the Poiseuille number for viscous resistance, enabling consistent comparison across different configurations. Fully developed laminar flow simulations are used to evaluate geometry-dependent viscous resistance, which is then integrated into a reduced-order transient capillary rise model. Baseline geometries, including triangular, circular, and rectangular cross sections, are analyzed, showing that despite identical hydraulic diameter and capillary pressure, significant differences in transient behavior arise due to variations in viscous resistance. The triangular geometry exhibits the fastest rise and lowest resistance, while the circular geometry shows the slowest response. Geometric modifications to the triangular configuration increase the wetted perimeter and capillary rise; however, the associated increase in viscous resistance leads to a slower transient response, highlighting a trade-off between capillary enhancement and flow resistance. A parametric study on hydraulic diameter reveals a similar trade-off, where smaller diameters increase capillary height but reduce flow velocity, while larger diameters enhance transport at the expense of reduced rise. The influence of working fluid properties is also examined, showing that capillary performance is governed by the ratio of surface tension to density, while contact angle variations highlight the critical role of wettability. Overall, the results demonstrate that capillary-driven flow is governed by the coupled effects of geometry, fluid properties, and surface wettability, providing a systematic basis for analyzing wick performance in heat pipe applications.