A mathematical model for analyzing the thermal characteristics of a flat micro heat pipe with a grooved wick

A mathematical model is developed for predicting the thermal performance of a flat micro heat pipe with a rectangular grooved wick structure. The effects of the liquid–vapor interfacial shear stress, the contact angle, and the amount of liquid charge are accounted for in the present model. In particular, the axial variations of the wall temperature and the evaporation and condensation rates are considered by solving the one-dimensional conduction equation for the wall and the augmented Young–Laplace equation, respectively. The results obtained from the proposed model are in close agreement with several existing experimental data in terms of the wall temperatures and the maximum heat transport rate. From the validated model, it is found that the assumptions employed in previous studies may lead to significant errors for predicting the thermal performance of the heat pipe. Finally, the maximum heat transport rate of a micro heat pipe with a grooved wick structure is optimized with respect to the width and the height of the groove by using the proposed model. The maximum heat transport rate for the optimum conditions is enhanced by approximately 20% compared to existing experimental results.     

Analytical and Experimental Investigations on Axially Grooved Aluminum-Ethane Heat Pipe

Heat pipes are promising devices to meet the needs of thermal management in spacecraft. In the present work, a dual core axially grooved aluminum-ethane heat pipe was developed and tested for its heat transport characteristics over the temperature range 150–240 K. An analytical model has also been developed to yield maximum heat transport, taking into account the effect of liquid-vapor interfacial shear stress, liquid meniscus variation, and the amount of working fluid in the heat pipe. The model results were compared with experimental results and are found to be in reasonably good agreement.     

Study on flow and heat transfer characteristics of heat pipe with axial “Ω”-shaped microgrooves

A theoretical model of fluid flow and heat transfer in a heat pipe with axial “Ω”-shaped grooves has been conducted to study the maximum heat transport capability of these types of heat pipes. The influence of variations in the capillary radius, liquid–vapor interfacial shear stress and the contact angle are all considered and analyzed. The effect of vapor core and wick structure on the fluid flow characteristics and the effect of the heat load on the capillary radius at the evaporator end cap, as well as the effect of the wick structure on the heat transfer performance are all analyzed numerically and discussed. The axial distribution of the capillary radius, fluid pressure and mean velocity are obtained. In addition, the calculated maximum heat transport capability of the heat pipe at different working temperatures is compared with that obtained from a traditional capillary pressure balance model, in which the interfacial shear stress is neglected. The accuracy of the present model is verified by experimental data obtained in this paper.     

Performance degradation of flattened heat pipes

The performance degradation of flattened heat pipes is studied experimentally under a horizontal orientation. The original cylindrical copper/water heat pipes are ?6 mm and 30 cm in length. Tested are the sintered-powder wick and the groove wick. The maximum heat load (Q_max), the evaporator resistance (R_e), the condenser resistance, the overall thermal resistance, and the longitudinal temperature distributions are measured under incremented heat loads. After flattening, R_e is slightly reduced. Q_max is hardly affected when only the evaporator is flattened; but it is greatly reduced for fully flattened heat pipes. Different mechanisms of performance degradation are observed for flattened powdered and grooved heat pipes. With a thicker wick and larger saturate charge, the main degradation mechanism of flattened powdered heat pipes is liquid clogging at the condenser end. This causes malfunction of a powdered heat pipe flattened to 2.5 mm. When flattened to 3 mm, the powdered heat pipe exhibits milder Q_max degradation than a grooved heat pipe because the liquid flow is better protected against the vapor–liquid interfacial shear. In contrast, the serious Q_max degradation of a flattened grooved heat pipe is mainly caused by the interfacial shear which leads to greatly prompted dryout at the evaporator.     

Thermal resistance of screen mesh wick heat pipes using the water-based Al2O3 nanofluids

In the present study, the effect of nanofluids on the thermal performance of heat pipes is experimentally investigated by testing circular screen mesh wick heat pipes using water-based Al₂O₃ nanofluids with the volume fraction of 1.0 and 3.0 Vol.%. The wall temperature distributions and the thermal resistances between the evaporator and the adiabatic sections are measured and compared with those for the heat pipe using DI water. The averaged evaporator wall temperatures of the heat pipes using the water-based Al₂O₃ nanofluids are much lower than those of the heat pipe using DI water. The thermal resistance of the heat pipe using the water-based Al₂O₃ nanofluids with the volume fraction of 3.0 Vol.% is significantly reduced by about 40% at the evaporator-adiabatic section. Also, the experimentally results implicitly show that the water-based Al₂O₃ nanofluids as the working fluid instead of DI water can enhance the maximum heat transport rate of the heat pipe. Based on the two clear evidences, we conclude that the major reason which can not only improve the maximum heat transport rate but also significantly reduce the thermal resistance of the heat pipe using nanofluids is not the enhancement of the effective thermal conductivity which most of previous researchers presented. Especially, we experimentally first observe the thin porous coating layer formed by nanoparticles suspended in nanofluids at wick structures. Based on the observation, it is first shown that the primary mechanism on the enhancement of the thermal performance for the heat pipe is the coating layer formed by nanoparticles at the evaporator section because the layer can not only extend the evaporation surface with high heat transfer performance but also improve the surface wettability and capillary wicking performance.     

Thermal performance of flat-shaped heat pipes using nanofluids

Analytical models are utilized to investigate the thermal performance of rectangular and disk-shaped heat pipes using nanofluids. The liquid pressure, liquid velocity profile, temperature distribution of the heat pipe wall, temperature gradient along the heat pipe, thermal resistance and maximum heat load are obtained for the flat-shaped heat pipes utilizing a nanofluid as the working fluid. The flat-shaped heat pipe’s thermal performance using a nanofluid is substantially enhanced compared with one using a regular fluid. The nanoparticles presence within the working fluid results in a decrease in the thermal resistance and an increase in the maximum heat load capacity of the flat-shaped heat pipe. The existence of an optimum nanoparticle concentration level and wick thickness in maximizing the heat removal capability of the flat-shaped heat pipe was established.     

Modulated wick heat pipe

In heat pipes, modulation of evaporator wick thickness provides extra cross-sectional area for enhanced axial capillary liquid flow and extra evaporation surface area, with only a moderate increase in wick superheat (conduction resistance). This modulated wick (periodic stacks and grooves over a thin, uniform wick) is analyzed and optimized with a prescribed, empirical wick superheat limit. A thermal-hydraulic heat pipe figure of merit is developed and scaled with the uniform wick figure of merit to evaluate and optimize its enhancement. The optimal modulated wick for the circular and flat heat pipes is found in closed-form expressions for the viscous-flow regime (low permeability), while similar results are obtained numerically for the viscous-inertial flow regime (high permeability which is also gravity sensitive). The predictions are compared with the experimental result of a prototype (low permeability, titanium/water pipe with the optimal design) heat pipe which gives a scaled figure of merit of 2.2. Good agreement is found between the predicted and measured performance. The maximum enhancement is limited by the pipe inner radius (tapering of the stacks), the wick effective thermal conductivity, and the prescribed wick superheat limit.     

A numerical model for transport in flat heat pipes considering wick microstructure effects

A 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.     

A three-dimensional thermal-fluid analysis of flat heat pipes

A detailed, three-dimensional model has been developed to analyze the thermal hydrodynamic behaviors of flat heat pipes without empirical correlations. The model accounts for the heat conduction in the wall, fluid flow in the vapor chambers and porous wicks, and the coupled heat and mass transfer at the liquid/vapor interface. The flat pipes with and without vertical wick columns in the vapor channel are intensively investigated in the model. Parametric effects, including evaporative heat input and size on the thermal and hydrodynamic behavior in the heat pipes, are investigated. The results show that, the vertical wick columns in the vapor core can improve the thermal and hydrodynamic performance of the heat pipes, including thermal resistance, capillary limit, wall temperature, pressure drop, and fluid velocities due to the enhancement of the fluid/heat mechanism form the bottom condenser to the top evaporator. The results predict that higher evaporative heat input improves the thermal and hydrodynamic performance of the heat pipe, and shortening the size of heat pipe degrades the thermal performance of the heat pipe.     

Thermal performance of screen mesh wick heat pipes using water-based copper nanofluids

Fairly stable surfactant free copper–distilled water nanofluids are prepared using prolonged sonication and homogenization. Thermal conductivity of the prepared nanofluid displays a maximum enhancement of ～15% for 0.5 wt% of Cu loading in distilled water at 30 °C. The wall temperature distributions and the thermal resistances between the evaporator and the condenser sections of a commercial screen mesh wick heat pipe containing nanofluids are investigated for three different angular position of the heat pipe. The results are compared with those for the same heat pipe with water as the working fluid. The wall temperatures of the heat pipes decrease along the test section from the evaporator section to the condenser section and increase with input power. The average evaporator wall temperatures of the heat pipe with nanofluids are much lower than those of the heat pipe with distilled water. The thermal resistance of the heat pipe using both distilled water and nanofluids is high at low heat loads and reduces rapidly to a minimum value as the applied heat load is increased. The thermal resistance of the vertically mounted heat pipe with 0.5 wt% of Cu–distilled water nanofluid is reduced by ～27%. The observed enhanced thermal performance is explained in light of the deposited Cu layer on the screen mesh wick in the evaporator section of the heat pipe.     

Thermofluid Characteristics in Microporous Structure With Different Flow Channels for Loop Heat Pipe

The use of two-phase heat transfer devices using capillary action in a microscale porous structure such as a loop heat pipe (LHP) is a promising heat transport technology. This is because they have characteristics of higher heat transfer power and longer heat transport distances with no electrical power compared with conventional heat pipes. The thermal performance of an LHP is governed by the thermofluid behavior in a microscale porous structure called the wick. In this research, high-performance wicks made of polymer have been developed, and their pore distribution and permeability were evaluated. The effects of the vapor channel's shape on the loop's thermal performance have been investigated by calculation and experiment to enhance evaporator performance. A mathematical model of the evaporator considering super heat in the channel, pressure drop across the wick, and two-phase pressure loss on the boundary face between the wick and the evaporator case was newly developed. The experiment was also conducted as a function of the groove shapes. From calculations and test results, it was found that in order to increase the maximum heat transport capability and decrease the operating temperature, the groove should be well distributed.     

Thermal performance and operational attributes of the startup characteristics of flat-shaped heat pipes using nanofluids

Thermal performance, transient behavior and operational start-up characteristics of flat-shaped heat pipes using nanofluids are analyzed in this work. Three different primary nanofluids namely, CuO, Al₂O₃, and TiO₂ were utilized in our analysis. A comprehensive analytical model, which accounts in detail the heat transfer characteristics within the pipe wall and the wick within the condensation and evaporation sections, was utilized. The results illustrate enhancement in the heat pipe performance while achieving a reduction in the thermal resistance for both flat-plate and disk-shaped heat pipes throughout the transient process. It was shown that a higher concentration of nanoparticles increases the thermal performance of either the flat-plate or disk-shaped heat pipes. We have also established that for the same heat load a smaller size flat-shaped heat pipe can be utilized when using nanofluids.     

Mathematical modeling of heat transfer, condensation, and capillary flow in porous insulation on a cold pipe

Porous insulation used on pipes carrying cold fluids suffers thermal degradation due to condensation of water vapor and the build up of water in the insulation. Recently, it has been suggested that the thermal degradation can be significantly reduced by wrapping a hydrophilic wick fabric on the cold pipe. The capillary action of the fabric, aided by gravity, allows the condensed moisture to move to the outer surface of the insulation, from where, if ambient conditions are right, it evaporates. This paper presents the details of a mathematical model for condensation in the insulation in the presence of the wick fabric. The model is based on the volume-averaged equations for unsteady transport of heat, water vapor, and liquid water in a porous medium. The wick is modeled as an anisotropic porous medium. The model also allows for the presence of a vapor retarder jacket that is used to reduce the ingress of water vapor into the insulation. The model has been applied to an insulation layer around a horizontal pipe. The presence of the wick is shown to significantly reduce the amount of liquid water in the insulation. The results of the model have been verified using laboratory experiments and field tests.     

Mathematical modeling of steady-state operation of a loop heat pipe

A steady-state mathematical model of a loop heat pipe is established and compared with experimental results in this work. The modeling of the evaporator wick includes not only the single-layer wick, but also the two-layer compound wick. The annular flow model is adopted in the modeling of the condenser, in which the effect of surface tension of liquid and the interaction between the liquid and vapor phases including both frictional and momentum-transfer shear stresses are considered. The model can predict the decreasing length of the condenser two-phase zone under the constant conductance mode caused by the volume expansion of the liquid in the compensation chamber, and is in good agreement with the experimental data. It also shows that the application of the two-layer compound wick can improve the performance of the loop heat pipe operating under the variable conductance mode, due to the reduction of heat leak from the evaporator to the compensation chamber. A parametric study of the effect of heat sink temperature, ambient temperature, adverse elevation, and working fluid inventory on the operating temperatures of the loop heat pipe is also conducted, which further contributes to the understanding of the steady-state operating characteristics of loop heat pipes.     

Analysis and optimization of a latent thermal energy storage system with embedded heat pipes

Latent thermal energy storage system (LTES) is an integral part of concentrating solar power (CSP) plants for storing sun’s energy during its intermittent diurnal availability in the form of latent heat of a phase change material (PCM). The advantages of an LTES include its isothermal operation and high energy storage density, while the low thermal conductivity of the PCM used in LTES poses a significant disadvantage due to the reduction in the rate at which the PCM can be melted (charging) or solidified (discharging). The present study considers an approach to reducing the thermal resistance of LTES through embedding heat pipes to augment the energy transfer from the heat transfer fluid (HTF) to the PCM. Using a thermal resistance network model of a shell and tube LTES with embedded heat pipes, detailed parametric studies are carried out to assess the influence of the heat pipe and the LTES geometric and operational parameters on the performance of the system during charging and discharging. The physical model is coupled with a numerical optimization method to identify the design and operating parameters of the heat pipe embedded LTES system that maximizes energy transferred, energy transfer rate and effectiveness.     

Comparative study of the effect of hybrid nanoparticle on the thermal performance of cylindrical screen mesh heat pipe

The thermal performance of a cylindrical screen mesh heat pipe with hybrid nanofluid was experimentally investigated. The hybrid nanofluid was prepared by mixing Al2O3 and CuO nanoparticles with deionised water. The heat pipe was fabricated with straight copper tube of dimensions 300 mm length, 12.5 mm outer diameter and 1 mm thickness. The wick structure in the heat pipe was created by a three layer copper screen mesh of 100 mesh size. The heat input to the heat pipe was varied from 50 W to 250 W in five equal steps. The heat pipe was tested with three hybrid nanofluids made with combinations of Al2O3 and CuO nanoparticle in DI water (Al2O3 75%–CuO 25%, Al2O3 50%–CuO 50% and Al2O3 25%–CuO 75%). The tested hybrid nanofluids were made with 0.1% volume concentration of Al2O3 and CuO nanoparticle combination in deionised water. The results of the investigation showed that for the maximum heat load of 250 W considered in this work, the thermal resistance of the hybrid nanofluid with combination, Al2O3 25%–CuO 75%, showed 44.25% reduction compared to deionised water. The reduction in thermal resistance is due to the formation of porous coating on the wick surface which increases the wettability and surface roughness thereby creating more nucleation sites as seen in the SEM images. From the experimental investigation, it was observed that hybrid nanofluids are alternative to the conventional working fluids in heat pipes for electronic cooling applications.     

Numerical Simulation of the Thermal Performance of a Nanofluid-Filled Heat Pipe

Improving the working fluid transport properties is a way to enhance the thermal performance of heat transfer equipment. In this research work, a two-dimensional numerical simulation is used to investigate the thermal performance of a nanofluid-filled cylindrical heat pipe. The considered nanofluid is pure water as the base fluid with dispersed Al₂O₃ nanoparticles. Effects of particle volume fractions, particle diameters, various heat inputs, and wick structures on thermal performance of the heat pipe are investigated and the results are compared with that of the pure water. A comparison is made for the first time between the results of a simulation by considering fluid flow in the liquid-wick region and treating this region as pure conduction. The results show the heat pipe thermal performance enhancement and a decrease in thermal resistance for about 31% when 5% particle volume fraction with a particle diameter of 10 nm is used. Also, an insignificant effect of heat input on thermal resistance and variation of pressure distribution in the presence of nanoparticles are observed.     

Heat Transfer Performance of Heat Pipe Radiator with SiO2/Water Nanofluids

The effect of nanofluids on thermal performance of the miniature heat pipe radiator which was assembled by two heat pipes containing 0.6 vol.% SiO₂/water nanofluids and 30 pieces of rectangular aluminum fins was investigated experimentally and theoretically. The wall temperatures of the miniature heat pipe and fin surface temperatures were measured. Results showed that the utilization of SiO₂/water nanofluids as a working fluid in the heat pipe enhanced the heat performance by reducing wall temperature differences. Compared with Deionized water (DI water), the thermal resistance of the miniature heat pipe with SiO₂/water nanofluids decreased by about 23% to 40%. Furthermore, the theoretical calculation on a basis of one dimension found that the fin heat dissipation in the miniature heat pipe radiator charged SiO₂/water nanofluids was about 1.17 times of that of the DI water radiator.     

Effect of low thermal conductivity wick on the performance of compact loop heat pipe

The existing work deals with the evaluation of compact loop heat pipe by means of a low thermal conductivity sintered chrysotile wick to avoid large heat leaks as of the evaporator to the compensation chamber. Accordingly, a wick with low thermal conductivity (0.068–0.098 W/mK) chrysotile powder of a mean particle diameter of 3.4 μm is fabricated through sintering. Nine chrysotile wicks are sintered with different compositions of binders (bentonite and dextrin) and pore-forming agent NaCl at sintering temperatures of 500°C, 600°C, and 700°C with a sintering time of 30 min. The wick properties, for instance, porosity, permeability, wettability, and capillary rise are studied owing to sintering temperature. Consequently, it is observed that a pure chrysotile powdered wick at a sintering temperature of 600°C exhibits a high porosity of 61.8% with permeability 1.04 × 10⁻¹³ m² and a capillary rise of 4.5 cm in 30 s and is considered optimal. This optimal wick is used for performance evaluation in compact loop heat pipe and a decrease of 36.1% in thermal resistance is found when compared with copper mesh wick in a loop heat pipe. The lowermost thermal resistance originates to be 0.147 K/W at 120 W with wall temperature 57.7°C. This indicates that loop heat pipe with sintered chrysotile wick can operate at lower heat loads efficiently when compared with copper mesh wick and as heat load increases a chance of dry out condition occurs. The highest evaporative heat transfer coefficient obtained is 65.7 kW/m² K at a minimum heat load.     

Thermal performance characteristics of heat pipes

Theoretical and experimental studies are conducted to evaluate the overall thermal performance of single-component and gas-loaded heat pipes. In the analysis, the simple conduction model developed recently for the single-component heat pipes has been extended to predict the wall temperature profiles of gas-loaded heat pipes with phase change occurring in the evaporator wick. Experimental evaluation of the thermal performance is made with two working fluids (water and acetone) under two corresponding sink environments (boiling water and boiling alcohol). The heat pipe system is designed with variable-length heat input and output sections under a wide range of heat input conditions. Measured results agree well with theoretical predictions.