Capillary Limit Research Articles

Enhancing heat pipe performance through hybrid wick structures: Balancing pore size and permeability

This study investigates the impact of wick structures on heat pipe performance by optimizing the balance between effective pore radius and permeability for efficient heat dissipation. It addresses the challenge of enhancing capillary pumping forces while maintaining optimal liquid replenishment to the evaporator. A novel hybrid wick structure is proposed, strategically integrating sintered and screened elements within the heat pipe to improve thermal performance. Experimental tests include varying inclination angles (antigravity up to 60°) to assess thermal resistance and liquid return capabilities. Results show a 13.31 % reduction in thermal resistance compared to conventional sintered heat pipes, particularly at higher power levels (40 W– 60 W). At a 40° inclination angle, optimal evaporation and liquid flow improve thermal performance, with thermal resistance for sintered and hybrid heat pipes decreasing by 14.05 % and 27.72 %, respectively. However, at 60° inclination, the hybrid’s thermal resistance increases significantly due to local dry-out. The study identifies limitations beyond 45° inclination, which is attributed to increased receding contact angles, and the influence of gravity becomes more pronounced, affecting capillary limits. This research underscores the importance of innovative wick designs in advancing heat pipe technology for diverse applications.

Study on the permeability and capillary pressure of spiral woven mesh for flat-plate heat pipes

Due to its excellent capillary characteristics, spiral woven mesh is widely used as the wick structure in ultra-thin flat-plate heat pipes. The performance of these heat pipes surpasses that of conventional ones using sintered powder or multi-layer mesh structures. However, precise quantitative studies on the permeability and capillary pressure characteristics of this unique porous structure are lacking. In this work, we systematically investigated its permeability and capillary pressure, as well as their relationship with the structure. Based on experimental results, we demonstrated that numerical simulation of periodic microelements and subsequent area weighting can accurately predict the permeability of actual structures. Additionally, a parametric study was conducted, yielding a unified empirical relationship between permeability and the structural parameters. In the part of capillary pressure, U-shape tube gravity method was utilized and the relationship between capillary pressure and structure was also disclosed. This study will provide reliable data and theoretical guidance for calculating the capillary limit in heat pipes using spiral woven mesh as the wick.

Theoretical and experimental analysis of evaporative cooling with hydrophilic screen mesh on condenser surface

In this study, we theoretically and experimentally analyzed the effect of evaporative cooling on the external thermal resistance of a condenser with a water-filled hydrophilic screen mesh. To calculate the external thermal resistance of the condenser theoretically, the external thermal resistance model was developed, considering evaporative cooling in the screen mesh. The evaporative mass flow rate in the screen mesh was calculated using the Lewis number, which can convert heat transfer to mass transfer. Especially, the maximum flow rate absorbed by the screen mesh was theoretically determined by the capillary limit. In experimental approach, hydrophilic screen meshes with mesh numbers M100, M150, and M200 were manufactured and attached to an aluminum plate simulating the condenser surface. The external thermal resistance of the condenser was measured. Based on the results, the theoretical model was well matched with experimental results. The effects of the air velocity, mesh number, and heat flux on the external thermal resistance of the condenser with evaporative cooling in the water-filled hydrophilic screen mesh were investigated. Finally, it is shown that the external thermal resistance of the condenser with evaporative cooling using the water-filled hydrophilic screen mesh can be reduced up to an average of 92 %.

Comparison of Maximum Heat Transfer Rate of Thin Vapor Chambers with Different Wicks under Multiple Heat Sources and Sinks

In this paper, we present a new analytical model to investigate the maximum heat transfer rate of a thin vapor chamber (TVC) with multiple heat sources and sinks. The model can specifically consider different heat flux conditions for each heat source. Both capillary limitations and allowable maximum temperature constraints were employed to determine the maximum heat transfer rate. The liquid and vapor pressure distributions within the TVC were analytically derived using the Brinkman-extended Darcy equation and the Hagen–Poiseuille equation, respectively. Additionally, the theoretical wall temperature distribution was calculated based on the 3D energy equation, considering different heat flux conditions for multiple heat sources with a weighting factor. Our results demonstrate that the heat flux conditions applied to the heat sources significantly impact the internal flow pattern of the TVC. These changes in flow patterns influence the pressure distributions of the liquid and vapor, thereby affecting the maximum heat transfer rate. Furthermore, the effects of wick parameters on the maximum heat transfer rate under various heat flux conditions were examined.

Computing Relative Permeability and Capillary Pressure of Heterogeneous Rocks Using Realistic Boundary Conditions

Relative permeability and capillary pressure are key parameters in multiphase flow modelling. In heterogeneous porous media, flow direction- and flow-rate dependence result from non-uniform saturation distributions that vary with the balance between viscous, gravitational, and capillary forces. Typically, relative permeability is measured using constant inlet fractional-flow—constant outlet fluid pressure conditions on samples mounted between permeable porous plates to avoid capillary end-effects. This setup is replicated in numeric experiments but ignores the extended geologic context beyond the sample size, impacting the saturation distribution and, consequently, the upscaled parameters. Here, we introduce a new workflow for measuring effective relative permeability and capillary pressure at the bedform scale while considering heterogeneities at the lamina scale. We harness the flexibility of numeric modelling to simulate continuum-REV-scale saturation distributions in heterogeneous rocks eliminating boundary artefacts. Periodic fluid flux boundary conditions are applied in combination with arbitrarily oriented, variable-strength pressure gradient fields. The approach is illustrated on a periodic model of cross-bedded sandstone. Stepping saturation while applying variable-strength pressure-gradient fields with different orientations, we cover the capillary-viscous force balance spectrum of interest. The obtained relative permeability and capillary pressure curves differ from ones obtained with traditional approaches highlighting that the definition of force balances needs consideration of flow direction as an additional degree of freedom. In addition, we discuss when the common viscous and the capillary limits are applicable and how they vary with flow direction in the presence of capillary interfaces.

Demonstration of heat switch function of loop heat pipe controlled by electrohydrodynamic conduction pump

Loop heat pipes (LHPs) are attractive devices to cool electronic devices in spacecraft. The LHP operation must be shut down in some cases to avoid considerable reductions in the temperature of such electric devices. A new active technology capable of heat switching is developed for LHPs using an electrohydrodynamic (EHD) conduction pump that operates to facilitate liquid flow in the reverse direction against the normal LHP flow. To demonstrate our proposed approach, an EHD conduction pump with rod–ring electrodes was developed and evaluated to obtain generated pressure with varying applied voltages. The LHP with R134a as a working fluid was shut down successfully when a sufficiently high voltage was applied. The LHP shutdown continued until the EHD conduction pump was turned off. A comparison with a test in which a manually controlled mechanical valve caused the capillary limit showed that the EHD pump worked differently from the valve: the shutdown by the EHD pump involved a reverse flow. The consumed electric power for the EHD pump was 10–30 mW for 6–8 kV of applied voltage during the LHP shutdown. Furthermore, pressure loss through the EHD pump during normal LHP operation was approximately 0.5 % of the capillary pressure.

Dry-out limit enhancement strategy in sodium heat pipes: Overfilling effect and modified capillary limit model

Despite the significant impact of the filling ratio on dry-out of heat pipe, current operating limit models do not adequately address this factor. This study proposes an advanced capillary limit model that incorporates the effect of the filling ratio. An experimental study was conducted to compare the operating limits of sodium heat pipes with filling ratios of 107 % and 246 %. The results showed that the existing capillary model is difficult to predict the operating limits based on filling ratios, leading to significant deviations between theoretical predictions and actual outcomes. Specifically, a heat pipe filled to 107 % experienced dry-out at a point 31.1 % lower than expected, while a heat pipe filled to 246 % reached dry-out at 20.2 % higher than expected. Notably, the overfilled heat pipe maintained a steady state even at 10.5 % above the expected dry out point. The key point of the proposed model, based on optical imaging and temperature data at dry-out, is that the excess liquid in vapor region travels and forms a liquid plug at the end of the condenser, which shortens the length required for capillary transport. Based on this insight, the Chi model was modified to predict the operating limit of overfilled heat pipes more accurately within a 5 % margin of error. The study highlights the critical role of filling ratio in heat pipe design, noting that overfilling can shorten the effective capillary length through liquid plug formation, thereby increasing the dry-out limit. However, these pools also limit the reach of sodium vapor and potentially reduce the effective area of the condenser.

On the hydrostatic limit for thin film flow with applications to thermosyphons

Heat pipes frequently encounter challenges in effectively returning condensed liquid from the condenser to the evaporator through capillary pumping, which limits their overall efficacy. When capillary pumping becomes irrelevant due to factors like the absence of wick, or overfilling, the heat pipe is more properly termed as thermosyphon. In a close-to-horizontal orientation, the driving force for liquid return in a thermosyphon relies on the difference in liquid pool depth between the evaporator and condenser. An excessively deep liquid pool in the condenser can hinder radial heat transfer, necessitating a design that favours intermediate-depth liquid pools. This study utilizes a theoretical approach based on the lubrication approximation to the Navier–Stokes equations to determine the fill ratio that maximizes thermosyphon performance. We explore the relationship between this fill ratio and factors such as the axial temperature difference along the thermosyphon. Our analysis thereby highlights the hydrostatic-driven flow limit in the thermosyphon as an analogue to the capillary limit in heat pipes. Regarding the hydrostatic limiting curve as an alternative to the capillary limiting curve offers valuable insights for enhancing thermosyphon performance and provides means of comparing the performance of one vs. the other passive heat transfer device.

Numerical study on the characteristics of sodium heat pipes for space application at operation limits

Sodium heat pipes are important thermal conductive components in space nuclear power sources. They efficiently transfer heat within the range of 500–1000 °C by utilizing the latent heat of phase change. However, their maximum heat transfer capacity is limited by various factors. In this study, numerical simulations were conducted to investigate the operating conditions of sodium heat pipes when encountering different heat transfer limits, with a focus on analyzing the vapor–liquid distribution and axial temperature distribution in evaporator section. It is revealed that as reaching the heat transfer limits, sodium heat pipes exhibit wall temperature fluctuations in evaporator section. When encountering the viscous limit, liquid aggregation occurs within the wick, causing discontinuous flow. As reaching the sonic limit, a vapor blockage zone forms at the outlet of evaporator section, disrupting the flow circulation within heat pipe. For the entrainment limit, the liquid inside wick is carried away by vapor flow, reducing the amount of liquid involved in phase change cycle. As in the capillary limit, inadequate liquid reflux leads to thinner liquid layer, weakening the flow circulation. During the transition from the viscous limit to the sonic limit, no significant phenomena of phase distribution occur in the evaporator section. As the sonic limit and the entrainment limit act together, both vapor blockage and liquid entrainment occur, accompanied by liquid accumulation. The phenomena when the entrainment limit and the capillary limit act together differ from those occurring individually. The simulation results provide references for a deeper understanding of heat transfer limit mechanism and other operating characteristics.

A special-shaped sodium heat pipe with a “bridge-type” artery for coupling free-piston Stirling generator and fission reactor

The nuclear-powered free-piston Stirling generator (FPSG) by using heat pipes as heat transfer devices has significant potential for future applications in the deep space exploration. Due to the compact size of the FPSG, it is very difficult to directly insert the cylindrical heat pipe into the heat head to transfer heat, which has been a challenge for application in such a system. Here, a special-shaped heat pipe is designed to match the heat head. In this design, the surface of the heat head was used as the condensing surface and a “bridge-type” composite artery was used to transfer the liquid sodium from the condensing surface to the evaporating surface, which could greatly simplify the structure and improve the capillary limit. A simplified model for arterial wick was proposed to predict the artery geometrical parameters and capillary limit and the performance of the startup and steady state were experimentally investigated. It successfully transmitted about 4 kW of heat with a tilt angle of −35°, verifying the feasibility of the new structure. The effect of different cooling conditions and inclinations were also investigated. To ensure that the heat pipe was fully activated, it was necessary to meet the minimum input power under different cooling conditions.

Experimental investigation of forced convective heat transfer and fluid flow in a mini heat pipe with rectangular micro grooves

In the present study, the convective heat transfer coefficient of water in a laminar flow regime under constant inlet temperature conditions inside a flat mini heat pipe was investigated ex-perimentally. Heat flux ranged from 20-50W and various horizontal heat sink temperatures (operating temperature) ranged from 15-35°C with liquid flow rate (3.563E-8 m3/sec) used during the experiments. The rectangular microchannels performance is evaluated in terms of the temperature profile, heat transfer coefficient, Nusselt number and thermal resistance. The results emphasized that the mini heat pipe temperature gradients are less than the tempera-ture of the copper plate and the heat resistance gradually decreases to its lowest value when the heat flux value reaches its highest value if it does not exceed the capillary limits. The data also demonstrated that the coefficient of heat transfer in the condensation zone is lower than in the evaporation zone at different heat sink temperatures. The augmentation rate for the flat mini heat pipe thermal conductivity reached about 240% at a heat load 30W for the positions of thermosyphon and horizontal, while the rate of increase in the case of the anti-gravity situ-ation at a heat load 30W reaches 210%, then the improvement percentage begins to decrease to 200%. A generalized regression equation is developed for the estimation of the Nusselt number valid for water in a flat mini heat pipe.

Thermal management of Li-ion batteries in electric vehicles by nanofluid-filled loop heat pipes

An analytical model is developed to determine the thermal performance of a Loop Heat Pipe filled (LHP) with copper oxide–water and alumina–water nanofluids for battery thermal management in electric vehicles. The thermal performances of the LHP are predicted for different heat loads and nanoparticle concentrations. It is demonstrated that for fast charging operation corresponding to a heat load of 150 W, the LHP ensures evaporator temperatures of less than 60 °C for a heat sink temperature of 40 °C. The heat transport capacity of the LHP is enhanced and the evaporator temperature is deceased by augmenting the nanoparticle concentration. The water–CuO nanofluid-filled LHP performs better than the water–Al2O3 nanofluid-filled one. The addition of the nanoparticles increases the LHP total pressure drop and the driving capillary pressure. The capillary limit of the water–CuO nanofluid-filled LHP is hardly affected by CuO nanoparticle concentration until 6% beyond which the capillary limit starts decreasing. For the water–Al2O3 nanofluid-filled LHP, the capillary limit decreases when Al2O3 nanoparticle concentration increases. Beyond 6% Al2O3 nanoparticle concentration, the capillary limit of the Al2O3-filled LHP becomes lower than the water-filled one.

The Effect of Wick Permeability and Porous Radius on Capillary and Entrainment Limit in A Heat Pipe Reactor

For heat extraction in nuclear systems, interest in the design of nuclear reactors with heat pipes has increased. The determination of heat limitations is one of the remarkable factors for safety when heat pipes are used for nuclear systems. In this study, capillary and entrainment limit values for the heat pipe were calculated in a heat pipe reactor with potassium working fluid operating at 650 K. Five different effective porous radii (10.1x10-6, 10.225x10-6, 10.35x10-6, 10.425x10-6 and 10.6x10-6 m) and five different wick permeability (4.75x10-12, 5x10-12, 5.25x10-11, 5.5x10-12 and 5.75x10-12 m2) is considered for sintered copper wick heat pipe. While the effects of effective porosity radius, wick permeability, and wick radius on the capillary barrier were studied, only the effects of effective porosity radius were studied. While the effects of effective porosity radius, wick permeability, and wick radius on the capillary barrier are studied, only the effects of effective porosity radius are studied. The highest values of the capillary and entrainment limits are obtained when the porosity radius is 10.1x10-6 m. Besides, maximum capillary limits are achieved when the wick permeability is 5.75x10-12 m2 and the effective porosity radius is 10.1x10-6. This study aims to determine the optimum effective porous radius and wick permeability for this reactor and investigate the effect of effective porous radius and wick permeability on the heat pipe limitations.

Transient recovery from heat pipe dryout by power throttling

Heat pipes and vapor chambers are passive heat spreaders driven by capillary pumping of an internal working fluid via a porous wick. The capillary limit is the maximum steady-state heat input at which the fluid pressure drop can be supported by the capillary pressure head generated in the wick. However, heat pipes and vapor chambers often find application in devices where the heat input is highly transient and can exceed the capillary limit for brief time intervals. Operating heat pipes briefly above the capillary limit will not result in a dryout if the operating time interval does not exceed a characteristic time-to-dryout. Operation over a duration that exceeds this time-to-dryout can induce transient dryout and may lead to thermal hysteresis, that is, the original heat pipe thermal resistance may not be recovered even after the heat input is lowered back below the capillary limit. To fully recover the heat pipe performance after a transient dryout event, our recent experiments have shown that the heat input must be lowered (or throttled) significantly below the capillary limit. Due to the highly transient nature of power dissipation from electronic devices, it becomes imperative to characterize the throttling power level and duration required to ensure full recovery of a heat pipe from dryout under transient operations. This work experimentally characterizes recovery of heat pipes from dryout by power throttling under transient conditions, where ‘power throttling’ is the act of reducing the operating power level significantly below the capillary limit to eliminate post-dryout thermal hysteresis. We deduce from the experiments that the power must be throttled for longer than a minimum throttling time interval, defined as the time-to-rewet, in order to eliminate dryout-induced thermal hysteresis. The dependence of this time-to-rewet on the throttling power level is explored, and guidelines are presented on the need for throttling and the choice of throttling power under transient conditions.

Design and experimental study of a novel vapor chamber for proton exchange membrane fuel cell cooling

Proper thermal management is the key to the efficient and safe operation of proton exchange membrane fuel cells. In this study, a novel vapor chamber was designed and experimentally tested to verify its potential application for proton exchange membrane fuel cell cooling. The thermal management design scheme of proton exchange membrane fuel cells based on vapor chambers was introduced, and the influence of structural parameters on the theoretical maximum heat transfer of the vapor chamber was discussed. Based on theoretical analysis, a vapor chamber matching the structural characteristics of proton exchange membrane fuel cells was designed and manufactured, and the influence of heat load, tilt angle, and cooling water flow rate on the heat transfer performance of the vapor chamber was investigated experimentally. The results showed that the designed vapor chamber had excellent thermal dispersion performance and temperature equalization ability. When the heat load was less than 35 W, the maximum temperature of the vapor chamber was always less than 33 °C, and the thermal resistance was less than 0.2 °C/W. The tilt angle affected the capillary limit of the vapor chamber, and then significantly affected the thermal performance of the vapor chamber. In addition, the results also indicated that increasing the cooling water flow rate led to an increase in the temperature difference and thermal resistance of the vapor chamber, but this effect was relatively limited. The results of this study will provide a new idea and reference for the efficient thermal management of proton exchange membrane fuel cells.

Experimental and numerical investigation on thermal characteristics of the heat sink integrating 3D vapor chamber heat spreader and liquid cooling fins

The traditional vapor chamber/ heat pipe heat sink in high-power chip heat dissipation structures consists of two separate parts. The contact thermal resistance between these parts leads to an increase in thermal resistance during the heat transfer process. To mitigate the contact thermal resistance and improve the heat dissipation performance of vapor chamber heat sinks, this paper proposes a heat sink integrating a 3D vapor chamber heat spreader and liquid cooling fins. Experiments and simulations were carried out to analyze the heat transfer characteristics under different heating powers. The pressure drop and thermal resistance were calculated to analyze the internal phase-change heat transfer process and capillary heat transfer limit. The simulation results were in close agreement with the experimental data for heating powers ranging from 397 to 795 W, with the thermal resistance of the proposed heat sink of about 0.04℃/W. Compared to three traditional vapor chamber heat sinks operating under the same heat flux, the proposed type exhibited a noteworthy enhancement in the heat transfer performance, leading to a reduction in thermal resistance by approximately 44% to 67%.

Strategies for thermal performance improvements of polymeric thermal ground planes (TGP)

This paper presents a study on the thermal performance and enhancement techniques of polymeric thermal ground planes (TGPs). The literature features a range of polymeric TGPs that exhibit an effective thermal conductivity up to twice that of copper. However, the TGP effective thermal conductivity does not provide insight into the performance and potential improvements that could be made to a specific TGP design and configuration. Relying only on this metric can be limiting to compare different TGPs performances, since effective conductivity is affected by the device size, layout of heated and cooled zones, and the fabrication materials. In this paper, we adapted a model by connecting the TGP pumping capacity to its thermal resistance to predict the polymeric TGP thermal performances as a function of their geometry, test configuration and material used. This approach enables the development of strategies to optimize the polymeric TGPs performances and identify their limitations rather than relying on effective thermal conductivity as a benchmark for comparison. The present model considers vapor flow through a mechanical structure for the first time in TGPs. Indeed, the polymeric TGP in contrast to the metallic one requires a denser mechanical structure to support the vapor core thickness during vacuum due to the flexibility of the polymeric shell. The generated vapor pressure drop along the TGP has a dual impact on its performance as it affects both the capillary limit and vapor resistance resulting in a tradeoff between the TGP pumping capacity and thermal resistance, for a given TGP thickness. To back up the proposed model, experimental characterization was carried out on a one-step assembled polymeric TGP, to extract simultaneously the total and vapor thermal resistances. The model highlighted a trade-off in designing the vapor core and wicking structure, balancing the polymeric TGP pumping capacity and thermal resistance, for a target TGP thickness. Hence, the current study provides guidelines for defining improvement strategies for TGPs thermal performances based on the geometry and the type of material used during the fabrication process. The recommended approach also permits the identification of polymeric TGPs capabilities and limits rather than depending on the thermal metrics, which may be misleading while comparing performances.

Design and Thermal Performance of Ultra-Thin Flat Plate Heat Pipes with Composite Wick for Electronic Cooling

The rapidly increasing heat load and high-density packaging of electronic devices demand heat dissipation devices that possess miniaturization and high thermal performance. A series of ultra-thin flat plate heat pipes (UPHPs) with thicknesses of 1.2 mm was prepared to satisfy this demand. Strengthening rib optimization and capillary optimization were processed to restrict the entrainment limit and capillary limit of the UPHPs. Furthermore, surface modification technology with composite nanostructure coated was introduced to improve the surface wettability of capillary wick. Finally, the heat transfer capacity of the UPHPs was experimentally tested. The influence of capillary structure and liquid filling ratio on the heat transfer characteristic was investigated in detail. This work provides insight into the design and application of UPHPs for the new generation of electronic devices.

Biomimetic Copper Forest Structural Modification Enhances the Capillary Flow Characteristics of the Copper Mesh Wick

In a two-phase heat transfer device, achieving a high capillarity of the wick while reducing flow resistance within a limited space becomes the key to improving the heat dissipation performance. As a commonly used wick structure, mesh is widely employed because of its high permeability. However, achieving the desired capillary performance often requires multiple layers to be superimposed to ensure an adequate capillary, resulting in an increased thickness of the wick. In this study, an ultra-thin biomimetic copper forest structural modification of copper mesh was performed using an electrochemical deposition to solve the contradiction between the permeability and the capillary. The experiments were conducted on a copper mesh to investigate the effects of various conditions on their morphology and capillary performance. The results indicate that the capillary performance of the modified copper mesh improves with a longer deposition time. The capillary pressure drops can reach up to 1400 Pa when using ethanol as the working fluid. Furthermore, the modified copper mesh demonstrates a capillary performance value (ΔPc·K) of 8.44 × 10−8 N, which is 1.7 times higher than that of the unmodified samples. Notably, this enhanced performance is achieved with a thickness of only 142 μm. The capillary limit can reach up to 45 W when the modified copper mesh is only 180 μm. Microscopic flow analysis reveals that the copper forest modified structure maintains the original high permeability of the copper mesh while providing a greater capillary force, thereby enhancing the overall flow characteristics.

An efficient analytical approach for steady-state upscaling of relative permeability and capillary pressure

Upscaling in petroleum reservoir simulation captures the dynamic behavior of fine-scale models at the coarse-scale in a volume average sense. Traditional upscaling of immiscible two-phase flow can be implemented by solving the fluid flow equations at steady state in the capillary or viscous limit in fine scale, which requires modeling the single-phase flow numerically many times and is computationally demanding. In this study, an analytical approach is proposed, to replace the numerical simulation, for computing the relative permeability. The key idea is to utilize the perturbation expansion technique and Fourier analysis to derive an explicit expression of the equivalent permeability. The analytical expression accounts for spatial correlations and is more accurate than the simple averaging and renormalization methods. It matches well with the numerical method in all cases for the upscaling of the relative permeability and capillary pressure. The developed method is also validated by comparing the pressure and saturation results from the coarse-scale and fine-scale models. In the base case of SPE10 benchmark test, the numerical upscaling takes 436 s, whereas the analytical upscaling takes 13.6 s, which is about 30 times faster than the numerical method. Moreover, the analytical coefficients just need to be computed once for the whole space in a given geostatistical model, which naturally leads to improved efficiency and is clearly favorable for petroleum reservoir simulations.