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.     

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.     

A novel oxidized composite braided wires wick structure applicable for ultra-thin flattened heat pipes

This present study proposed a novel low-cost and high performance braided wire wick structure having superhydrophilic treatment applicable for ultra-thin heat pipe. The test wick structures include mono and composite wick structure. The composite braided wire adopts two different diameter wire design, using a large diameter (0.1 mm) in the core while the exterior of the core is covered by smaller diameter copper wire (0.05 mm). The mono design contains only one uniform wire diameter (0.1 mm) in core region. Test results indicate that via oxidizing the surface of the braided wires can largely enhance the surface roughness and result in a much higher capillary force as comparing to the un-oxidized one. In addition, both mono (m-FHP) and composite braided wire (c-FHP) with oxidization could possess a maximum heat transfer capability over 15 W under horizontal operation, and test results showed that the heat transfer capability of composite design outperforms mono one by more than 32.5% in all orientations. It is also found that the filling loading ratio plays essential role on the overall performance of FHP. Either a low filling loading ratio or a high filling loading ratio may yield a lower maximum heat transfer capability and a higher thermal resistance. An optimum filling loading ratio of 125% yields the lowest thermal resistance around 0.12 K/W with the best heat transfer capability of 20 W.     

A numerical model for seasonal storage of solar heat in the ground by vertical pipes

We present a three-dimensional numerical model for seasonal heat storage in the ground using vertical heat exchanger pipes. The model also accounts for convective heat flows in the ground. The storage is employed in a district solar heating system with a heat pump. The effects of storage volume, storage medium, collector area, and collector type on system performances are studied for the Helsinki (60°N) climate. Economic optimization of the storage and collector installation is also briefly discussed. For a 500-house community, a collector area of 35 m² per house and a rock storage volume of 550 m³ per house would provide a solar fraction of 70%.     

3-D numerical and experimental models for flat and embedded heat pipes applied in high-end VGA card cooling system

The present study utilizes the three-dimension numerical and experimental methods to investigate the optimum thermal performance of a flat heat pipe-thermal module application in high-end VGA card cooling system, and compares that with a traditional copper metal based plate embedded three 6 mm diameter heat pipe-thermal module under three dissimilar inclination angles of 0°, 90° and 180°. The optimization for the thermal modules researches into various fin material, thickness and gap. Results show that the flat heat pipe-thermal module has the best thermal performance at high power GPU of 180 W and inclination angle of 180°. Simulation results show in good agreement with experimental results within 5%. Therefore, the thermal performance of a flat heat pipe-thermal module can be accurately simulated and analyzed by employed the manner introduced in this paper and is able to cope with the higher heat flux GPU over 62.5 W/cm² in the future.     

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.     

A 2D transient numerical model combining heat/mass transport effects in a tubular solid oxide fuel cell

The purpose of this study is to present a 2D transient numerical model to predict the dynamic behavior of a tubular SOFC. In this model, the transient conservation equations (momentum, species and energy equations) are solved numerically and electrical and electrochemical outputs are calculated with an equivalent electrical circuit for the cell. The developed model determines the cell electrical and thermal responses to the variation of load current. Also it predicts the local EMF, state variables (pressure, temperature and species concentration) and cell performance for different cell load currents. Using this comprehensive model the dynamic behavior of Tubular SOFC is studied. First an initial steady state operating condition is set for the SOFC model and then the time response of the fuel cell to changes of some interested input parameters (like electrical load) is analyzed. The simulation starts when the cell is at the steady state in a specific output load. When the load step change takes place, the solution continues to reach to the new steady state condition. Then the cell transient behavior is analyzed. The results show that when the load current is stepped up, the output voltage decreases to a new steady state voltage in about 67 min.     

Experimental validation of an analytical model for predicting the thermal and hydrodynamic capabilities of flat micro heat pipes

An analytical model by Lefèvre and Lallemand [F. Lefèvre, M. Lallemand, Coupled thermal and hydrodynamic models of flat micro heat pipes for the cooling of multiple electronic components, Int. J. Heat Mass Transfer 49 (2006) 1375–1383] that couples a 2D hydrodynamic model for both the liquid and the vapor phases inside a flat micro heat pipe (FMHP) and a 3D thermal model of heat conduction inside the FMHP wall has been modified. It consists of superposing two independent solutions in order to take into account the impact of evaporation or condensation on the equivalent thermal conductivity of the capillary structure. The temperature, pressure and velocity fields can be determined using Fourier solutions. The model has been experimentally validated based on literature data from a grooved FMHP. Two new correlations for the equivalent thermal conductivities during evaporation and condensation inside rectangular micro-grooves have been proposed based on a numerical database. The influence of the saturation temperature and geometry on the maximum heat flux transferred by the system is presented.     

A numerical study of flow and heat transfer in internally finned rotating straight pipes and stationary curved pipes

In this article the effects of internal fins on laminar incompressible fluid flow and heat transfer inside rotating straight pipes and stationary curved pipes are numerically studied under hydrodynamically and thermally fully developed conditions. The fins are assumed to have negligible thickness with the same conditions as the pipe walls. Two cases, constant wall temperature and constant heat flux at the wall, are considered. First the accuracy of the numerical code written by a finite volume method based on SIMPLE algorithm is verified by the available data for the finless rotating straight pipes and stationary curved pipes, and then, the numerical results for those internally finned pipes are investigated in detail. The numerical results for different sizes and numbers of internal fins indicate that the flow and temperature field analogy between internally finned rotating straight pipes and stationary curved pipes still prevail. The effects of Dean number (K_L) versus friction factor, Nusselt number, and other non-dimensional parameters are studied in detail. From the numerical results obtained, an optimum fin height about 0.8 of pipe radius is determined for Dean numbers less than 100. At this optimum value, the heat transfer enhancement is maximum, and the heat transfer coefficient appears to be 6 times as that of corresponding finless pipes.     

Fluid flow and heat transfer model for high-speed rotating heat pipes

A new complete model has been developed to predict the performance of high-speed rotating heat pipes with centrifugal accelerations up to 10 000 g. The flow and heat transfer in the condenser is modeled using a conventional modified Nusselt film condensation approach. The heat transfer in the evaporator has previously been modeled using a modified Nusselt film evaporation approach. It was found, however, that natural convection in the liquid film becomes more significant at higher accelerations and larger fluid loadings. A simplified evaporation model including the mixed convection is developed and coupled with the film condensation model. The predictions of the model are in reasonable agreement with existing experimental data. The effects of working fluid loading, rotational speed, and pipe geometry on the heat pipe performance are reported here.     

Evaporative heat transfer model of a loop heat pipe with bidisperse wick structure

A mathematical model of evaporative heat transfer in a loop heat pipe was developed and compared with experiments. The steady-state thermal performance was predicted for different sintered nickel wicks, including monoporous and bidisperse structures. The effect of wick pore size distribution on heat transfer was taken into consideration. The wick in the evaporator was assumed to possess three regions during vaporization from an applied heat load: a vapor blanket, a two-phase region, and a saturated liquid region. The evaporator wall temperature and the total thermal resistance at different heat loads were predicted using ammonia as the working fluid. The predictions showed distinct heat transfer characteristics and higher performance for the bidisperse wick in contrast with monoporous wick. A bidisperse wick was able to decrease the thickness of the vapor blanket region, which presents a thermal resistance and causes lower heat transfer capacity of the evaporator. Additionally, a validation test presented good agreement with the experiments.     

A microscale model for thin-film evaporation in capillary wick structures

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.     

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.     

A numerical model for thermoelectric generator with the parallel-plate heat exchanger

This paper presents a numerical model to predict the performance of thermoelectric generator with the parallel-plate heat exchanger. The model is based on an elemental approach and exhibits its feature in analyzing the temperature change in a thermoelectric generator and concomitantly its performance under operation conditions. The numerical simulated examples are demonstrated for the thermoelectric generator of parallel flow type and counter flow type in this paper. Simulation results show that the variations in temperature of the fluids in the thermoelectric generator are linear. The numerical model developed in this paper may be also applied to further optimization study for thermoelectric generator.     

Theoretical and numerical analysis of convective heat transfer in the rotating helical pipes

In terms of the tensor analysis technique, the relative N-S equations and the energy equation in a rotating helical coordinate system are presented in this paper. Convective heat transfer in the rotating helical pipes with circular cross-section is investigated employing theoretical and numerical method. A perturbation solution up to the secondary order is obtained for a small Dean number. Variations of the temperature distribution with the force ratio (the ratio of the Coriolis force to the centrifugal force), the curvature and the torsion are discussed in detail. Present studies also show the natures of the Nusselt number, as well as the effects of the force ratio, the curvature, and the torsion. This study explores many new characteristics of convective heat transfer in the rotating helical pipes and covers wide ranges of parameters.     

A mixing-length method for predicting heat transfer in rough pipes

A mixing length formulation which includes a finite value at a hypothetical surface within the roughness is used to predict heat transfer in rough pipes. Several empirical parameters are required in this formulation and these were obtained by making comparisons of predictions, using a range of these parameterzs, with experiments. The experiments were carried out with airflow in pipes roughened internally with screw threads in the Reynolds number range 2 × 10⁴ to 3 × 10⁵. Simple correlations are suggested for the variation of the two most important empirical parameters namely the surface mixing length and the cavity Stanton number. Using these correlations enables the appropriate form of the energy equation for one-dimensional flow to be solved numerically in the thermal entrance region with any form of thermal boundary condition and the Prandtl numbers other than unity. Good agreement is shown for measurements in the thermal entrance region with a uniform wall heat flux.     

A mathematical model to analyze heat and mass transfer characteristics of a CPL evaporator porous wick

A capillary pumped loop (CPL), because of its high power thermal transport character, has been developed as an attractive system for the thermal discharge of electronic chips with high power loads, especially on spacecrafts. A working fluid having relatively larger heat of evaporation, methanol for example, may transfer significant heat flux. In this paper a new mathematic model is constructed, in which the most important character is the treatment or the unsaturated region of the evaporator porous wick. Numerical simulation of heat and mass transfer in the evaporator porous wick is carried out with a new three‐layer model. The importance of unsaturated layer to simulate the present problem is clear. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(4): 209–218, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20066     

Prediction of the temperature field in flat plate heat pipes with micro-grooves – Experimental validation

A liquid and vapour flow model coupled to a thermal model is presented for a flat plate heat pipe with micro-grooves. This model allows the calculation of the liquid and vapour pressures and velocities, the meniscus curvature radius in the grooves and the temperature field in the heat pipe wall from the heat source to the heat sink. The meniscus curvature radius is introduced in the thermal model to take into account the heat transfer at the liquid–vapour interface. Experimental measurements of the meniscus curvature radius as well as temperature measurements along a grooved heat pipe are compared to the model results. Both comparisons show the good ability of the numerical model to predict the maximum heat transport capability and the temperature field in the heat pipe. The model is used to optimize the heat pipe dimensions in order to improve its thermal performances.     

A numerical study of algebraic flux models for heat and mass transport simulation in complex flows

A numerical study of heat and mass transport based on the Reynolds-Averaged Navier–Stokes and scalar transport equations is presented to establish the predictive capabilities of algebraic flux models compared to the standard eddy-diffusivity representation. The analysis of scalar transport in simple-shear flows is initially performed to provide a basic validation of numerical techniques and scalar flux closures. The evaluation of algebraic models is carried out by examining the flow and scalar transport phenomena over a wavy wall and comparing the results to reliable direct numerical simulations. Despite the similarities with the standard gradient-diffusion hypothesis and the questionable validity of local-equilibrium conditions, the results show that algebraic models provide an efficient way to improve heat and mass transport predictions in complex flows with respect to the standard eddy-diffusivity model. The impact of abandoning the isotropic eddy-diffusivity in favor of a tensorial representation is found particularly significant in the analysis of scalar dispersion from a point source over the wavy wall, where lateral transport comes into play. While it is found that algebraic closures also represent a reasonable approximation for the spanwise scalar flux, the lateral spread of scalar concentration is considerably under-estimated by the standard gradient-diffusion model.     

Effect of nanofluids on the thermal performance of a flat micro heat pipe with a rectangular grooved wick

In this paper, the effect of water-based Al₂O₃ nanofluids as working fluid on the thermal performance of a flat micro-heat pipe with a rectangular grooved wick is investigated. For the purpose, the axial variations of the wall temperature, the evaporation and condensation rates are considered by solving the one-dimensional conduction equation for the wall and the augmented Young–Laplace equation for the phase change process. In particular, the thermophysical properties of nanofluids as well as the surface characteristics formed by nanoparticles such as a thin porous coating are considered. From the comparison of the thermal performance using both DI water and nanofluids, it is found that the thin porous coating layer formed by nanoparticles suspended in nanofluids is a key effect of the heat transfer enhancement for the heat pipe using nanofluids. Also, the effects of the volume fraction and the size of nanoparticles on the thermal performance are studied. The results shows the feasibility of enhancing the thermal performance up to 100% although water-based Al₂O₃ nanofluids with the concentration less than 1.0% is used as working fluid. Finally, it is shown that the thermal resistance of the nanofluid heat pipe tends to decrease with increasing the nanoparticle size, which corresponds to the previous experimental results.