Ma and Peterson 2 performed a series of experiments to determine the heat transport in triangular grooves, similar to those used in heat pipes, purely based on the capillary rise limit. They concluded that heat pipes with deep and narrow capillary grooves produce the best results while most of their data showed that the heat flux bottleneck of the evaporator was the capillarity limitation. 1 experimented with flat miniature heat pipes to determine the maximum heat flow rate and heat flux for different operating temperatures. In fact, the capillary rise is one of the important factors in designing heat pipes. These two-phase heat transfer devices are a crucial part of any modern power electronic device. One main application of capillary action in micro-grooves is in heat pipes. The self-driving flow of a liquid in a capillary micro-groove is an important feat of engineering with a wide range of applications, from space applications due to microgravity to power electronics and heat pipes, to sorption technology and capillary-assisted evaporators. This study can be used for a unified approach in designing heat pipes, capillary-assisted evaporators for sorption systems, drug delivery micro-fluidic devices, etc. The effect of the grooves’ height, width, and contact angle is investigated and reported. The proposed model is compared against data from the literature and can capture the experimental results with less than 10% relative difference. In this study, a unified non-dimensional model for capillary rise is proposed that can accurately predict the capillary rise for any given groove geometry and condition and only depends on two parameters: contact angle and characteristic length scale, defined as the ratio of the liquid–vapor to the solid–liquid interface. Although the capillary action is well studied, all the available equations for the capillary rise are case-specific and depend on the geometry of the groove, surface properties, and the transport liquid. Micro-grooves utilize capillary action to deliver a liquid, with no need for an extra pumping device, which makes them unique and desirable for numerous systems. Micro-grooves are a crucial feature in many applications, such as microelectro-mechanical systems, drug delivery, heat pipes, sorption systems, and microfluidic devices.
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