A numerical model is developed for the evaporating liquid meniscus in wick microstructures under saturated vapor conditions. Four different wick geometries representing common wicks used in heat pipes, viz., wire mesh, rectangular grooves, sintered wicks and vertical microwires, are modeled and compared for evaporative performance. The solid-liquid combination considered is copper-water. Steady evaporation is modeled and the liquid-vapor interface shape is assumed to be static during evaporation. Liquid-vapor interface shapes in different geometries are obtained by solving the Young-Laplace equation using Surface Evolver. Mass, momentum and energy equations are solved numerically in the liquid domain, with the vapor assumed to be saturated. Evaporation at the interface is modeled by using heat and mass transfer rates obtained from kinetic theory. Thermocapillary convection due to non-isothermal conditions at the interface is modeled for all geometries and its role in heat transfer enhancement from the interface is quantified for both low and high superheats. More than 80% of the evaporation heat transfer is noted to occur from the thin-film region of the liquid meniscus. The very small Capillary and Weber numbers resulting from the small fluid velocities near the interface for low superheats validate the assumption of a static liquid meniscus shape during evaporation. Solid-liquid contact angle, wick porosity, solid-vapor superheat and liquid level in the wick pore are varied to study their effects on evaporation from the liquid meniscus.

The topology and geometry of microstructures play a crucial role in determining their heat transfer performance in passive cooling devices such as heat pipes. It is therefore important to characterize microstructures based on their wicking performance, the thermal conduction resistance of the liquid filling the microstructure, and the thin-film characteristics of the liquid meniscus. In the present study, the free-surface shapes of the static liquid meniscus in common microstructures are modeled using SURFACE EVOLVER for zero Bond number. Four well-defined topologies, viz., surfaces with parallel rectangular ribs, horizontal parallel cylinders, vertically aligned cylinders, and spheres (the latter two in both square and hexagonal packing arrangements), are considered. Nondimensional capillary pressure, average distance of the liquid free-surface from solid walls (a measure of the conduction resistance of the liquid), total exposed area, and thin-film area are computed. These performance parameters are presented as functions of the nondimensional geometrical parameters characterizing the microstructures, the volume of the liquid filling the structure, and the contact angle between the liquid and solid. Based on these performance parameters, hexagonally-packed spheres on a surface are identified to be the most efficient microstructure geometry for wicking and thin-film evaporation. The solid-liquid contact angle and the nondimensional liquid volume that yield the best performance are also identified. The optimum liquid level in the wick pore that yields the highest capillary pressure and heat transfer is obtained by analyzing the variation in capillary pressure and heat transfer with liquid level and using an effective thermal resistance model for the wick.

a b s t r a c tA transient, three-dimensional model for thermal transport in heat pipes and vapor chambers is developed. The Navier-Stokes equations along with the energy equation are solved numerically for the liquid and vapor flows. A porous medium formulation is used for the wick region. Evaporation and condensation at the liquid-vapor interface are modeled using kinetic theory. The influence of the wick microstructure on evaporation and condensation mass fluxes at the liquid-vapor interface is accounted for by integrating a microstructure-level evaporation model (micromodel) with the device-level model (macromodel). Meniscus curvature at every location along the wick is calculated as a result of this coupling. The model accounts for the change in interfacial area in the wick pore, thin-film evaporation, and Marangoni convection effects during phase change at the liquid-vapor interface. The coupled model is used to predict the performance of a heat pipe with a screen-mesh wick, and the implications of the coupling employed are discussed.

The thermal and hydrodynamic performance of passive two-phase cooling devices such as heat pipes and vapor chambers is limited by the capabilities of the capillary wick structures employed.The desired characteristics of wick microstructures are high permeability, high wicking capability and large extended meniscus area that sustains thin-film evaporation. Choices of scale and porosity of wick structures lead to trade-offs between the desired characteristics. In the present work, models are developed to predict the capillary pressure, permeability and thin-film evaporation rates of various micropillared geometries. Novel wicking geometries such as conical and pyramidal pillars on a surface are proposed which provide high permeability, good thermal contact with the substrate and large thin-film evaporation rates. A comparison between three different micropillared geometriescylindrical, conical and pyramidal -is presented and compared to the performance of conventional sintered particle wicks. The employment of micropillared wick structure leads to a ten-fold enhancement in the maximum heat transport capability of the device. The present work also demonstrates a basis for reverse-engineering wick microstructures that can provide superior performance in phase-change cooling devices.

The major factors limiting the thermal performance of passive two-phase heat-spreading devices are the ability of the wick structures to transport liquid by means of capillary forces and the thermal resistance posed by the wicks. Nano-scale geometric enhancements to the wick structure, through the use of carbon nanotubes and metallic nanowires, promise to enhance the capillary transport while at the same time decreasing the thermal resistance due to their high intrinsic thermal conductivity. We analyze the performance of nanostructured wicks in heat-spreading applications. We report that the flow resistance of nanostructures constitutes a major barrier to § Author to whom correspondence should be addressed. Phone: +1 (765) 494-5621 2 their use as passive flow-conveying media, and identify geometrical parameters which yield high rates of thin-film evaporation while minimizing the flow resistance. The analysis shows that the use of nanostructures as the sole wicking element in a two-phase thermal spreader restricts its footprint area to a size of 4 cm 2 for heat flux inputs as low as 1 W/cm 2 due to the large flow resistance in the nanowick. To overcome nanowick flow resistance, we propose a nanostructureenhanced sintered particle wick microstructure which leads to a decrease in the wick thermal resistance by 14% relative to the corresponding wick with the same flow resistance and without nanostructures.

No abstract

C E Ergun's coefficient, 0.55.

The topology and geometry of microstructures play a crucial role in determining heat transfer performance in passive cooling devices such as heat pipes. It is therefore important to characterize microstructures based on their wicking performance, the thermal conduction resistance of the liquid filling the microstructure, and the thin-film characteristics of the liquid meniscus. In the present study, the free-surface shapes of the static liquid meniscus in common microstructures have been modeled using the program, Surface Evolver, for zero Bond number. Four well-defined topologies, viz., surfaces with parallel rectangular ribs, horizontal parallel cylinders, vertically aligned cylinders, and spheres (the latter two in both square and hexagonal packing arrangements), have been modeled. Non-dimensional capillary pressure, average distance of the free liquid surface from solid walls (a measure of the conduction resistance of the liquid), total exposed area and thin-film percentage of surface area of the liquid meniscus have been computed. These parameters are presented as functions of the non-dimensional geometrical parameters of the microstructures, volume of the liquid filling the structure, as well as the contact angle between the liquid and solid. Based on these non-dimensional performance parameters, the microstructure, contact angle and non-dimensional liquid volume for the best performance are identified.