3D heat transfer analysis in a loop heat pipe evaporator with a fully saturated wick

A practical quasi three-dimensional numerical model is developed to investigate the heat and mass transfer in a square flat evaporator of a loop heat pipe with a fully saturated wicking structure. The conjugate heat transfer problem is coupled with a detailed mass transfer in the wick structure, and incorporated with the phase change occurring at the liquid–vapor interface. The three-dimensional governing equations for the heat and mass transfer (continuity, Darcy and energy) are developed, with specific attention given to the wick region. By comparing the results of the numerical simulations and the experimental tests, the local heat transfer mechanisms are revealed, through the obtained temperature distribution and the further derived evaporation rates along the liquid–vapor interface. The results indicate that the model developed herein can provide an insight in understanding the thermal characteristics of loop heat pipes during steady-state operation, especially at low heat loads.     

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.     

Visualization and performance measurement of operating mesh-wicked heat pipes

This work presents visualization of the evaporation/boiling process and thermal measurements of operating horizontal transparent heat pipes. The heat pipes consisted of a two-layered copper mesh wick consisting of 100 and/or 200 mesh screens, a glass tube and water as the working fluid. Experimental results indicated that nucleate boiling was prompted for a wick having a fine 200-mesh bottom layer. When the fluid charge approximately equaled the pore volume in the wick, the water–vapor interface receded into more curved menisci with increasing heat load Q. Thus, larger capillary forces and evaporation areas were attained to meet the increasing need of liquid supply and evaporation rate at the water–vapor interface. At Q = 40 and 45 W, the water film became less than 100 μm and the nucleate boiling observed at lower heat loads disappeared. Optimal thermal characteristics with smallest thermal resistances across the evaporator and lowest overall temperature distributions were found for such a wick/charge combination. Under a smaller charge, partial dry-out was observed in the evaporator. Under a larger charge, liquid recession with increasing heat load was limited and bubbles grew and burst violently at high heat loads. The effects of different wicks and fluid charges on the evaporation/boiling characteristics were discussed.     

Heat transfer with flow and evaporation in loop heat pipe’s wick at low or moderate heat fluxes

An axisymmetric two-dimensional mathematical model of the cylindrical evaporator’s wick of loop heat pipes is developed to simulate heat transfer with flow and evaporation in the capillary porous structure. Effect of the interaction between the flow field and the liquid–vapor interface on the position of the interface and the curvature of menisci is adequately considered in this model. The flow fields of transient and steady states are obtained at low or moderate heat fluxes. The dynamic and thermodynamic behavior is discussed in this paper. The auto-driving mechanism of “inverted meniscus type” evaporators is validated. Effect of heat flux is investigated in detail.     

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 vapor flow model for analysis of liquid-metal heat pipe startup from a frozen state

A free-molecular, transition and continuum vapor flow model, based on the dusty gas model, is developed and incorporated in HPTAM, a two-dimensional heat pipe transient analysis model, to analyze the startup of a radiatively-cooled sodium heat pipe from a frozen state. The calculated wall temperatures at different times during the startup transient are in good agreement with measurements. Results showed that minimal sublimation and resolidification of sodium occurred in the early time of the transient, during which the vapor flow is free molecular. The melting of sodium in the wick occurred initially in the radial direction, then axially after the complete thaw of the evaporator section. Subsequent evaporation of liquid sodium caused the vapor flow in the evaporator to transition to the continuum regime. A continuum vapor flow front propagated axially toward the condenser, following the melt front in the wick region. The heat rejection capability of the heat pipe increased gradually as the continuum vapor flow front traveled along the condenser.     

Heat transfer with flow and phase change in an evaporator of miniature flat plate capillary pumped loop

An overall two-dimensional numerical model of the miniature flat plate capillary pumped loop (CPL) evaporator is developed to describe the liquid and vapor flow, heat transfer and phase change in the porous wick structure, liquid flow and heat transfer in the compensation cavity and heat transfer in the vapor grooves and metallic wall. The entire evaporator is solved with SIMPLE algorithm as a conjugate problem. The effect of heat conduction of metallic side wall on the performance of miniature flat plate CPL evaporator is analyzed, and side wall effect heat transfer limit is introduced to estimate the performance of evaporator. The shape and location of vapor-liquid interface inside the wick are calculated and the influences of applied heat flux, liquid subcooling, wick material and metallic wall material on the evaporator performance are investigated in detail. The numerical results obtained are useful for the miniature flat plate evaporator performance optimization and design of CPL.     

Numerical investigation of an evaporating meniscus in a channel

A detailed numerical model is developed that describes heat and mass transfer from a meniscus to open air. The model accounts for the effects of evaporation at the interface, vapor transport through air, thermocapillary convection, and natural convection in air. Evaporation at the interface is modeled using kinetic theory, while vapor transport in air is computed by solving the complete species transport equation. Since the vapor pressure at the liquid–gas interface depends on both evaporation and the vapor transport in air, the equations are solved in an iterative manner. Evaporation is strongest at the triple line due to the highest local vapor diffusion gradient in this region. This differential evaporation, coupled with the low thermal resistance near the triple line, results in a temperature gradient along the interface that creates thermocapillary convection. The numerical results obtained show satisfactory agreement with experimental data for the evaporation rate and the temperature profile. Additionally, results from a simplified model neglecting thermocapillary convection are compared with the full solution, thus delineating the importance of thermocapillary convection-induced mixing in the energy transfer process. The present generalized model may easily be extended to other geometries and hence may be used in the design of two-phase cooling devices.     

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.     

Interfacial temperature measurements,high-speed visualization and finite-element simulations of droplet impact and evaporation on a solid surface

The objective of this work is to investigate the coupling of fluid dynamics, heat transfer and mass transfer during the impact and evaporation of droplets on a heated solid substrate. A laser-based thermoreflectance method is used to measure the temperature at the solid–liquid interface, with a time and space resolution of 100 μs and 20 μm, respectively. Isopropanol droplets with micro- and nanoliter volumes are considered. A finite-element model is used to simulate the transient fluid dynamics and heat transfer during the droplet deposition process, considering the dynamics of wetting as well as Laplace and Marangoni stresses on the liquid–gas boundary. For cases involving evaporation, the diffusion of vapor in the atmosphere is solved numerically, providing an exact boundary condition for the evaporative flux at the droplet–air interface. High-speed visualizations are performed to provide matching parameters for the wetting model used in the simulations. Numerical and experimental results are compared for the transient heat transfer and the fluid dynamics involved during the droplet deposition. Our results describe and explain temperature oscillations at the drop–substrate interface during the early stages of impact. For the first time, a full simulation of the impact and subsequent evaporation of a drop on a heated surface is performed, and excellent agreement is found with the experimental results. Our results also shed light on the influence of wetting on the heat transfer during evaporation.     

Two-phase flow of refrigerants during evaporation under constant heat flux in a horizontal tube

This paper presents the results of simulations using a two-phase separated flow model to study the heat transfer and flow characteristics of refrigerants during evaporation in a horizontal tube. A one-dimensional annular flow model of the evaporation of refrigerants under constant heat flux is developed. The basic physical equations governing flow are established from the conservation of mass, energy and momentum. The model is validated by comparing it with the experimental data reported in literature. The present model can be used to predict the variation of the temperature, heat transfer coefficient and pressure drop of various pure refrigerants flowing along a horizontal tube. It is found that the refrigerant temperature decreases along the tube corresponding to the decreasing of its saturation pressure. The liquid heat transfer coefficient increases with the axial length due to the reducing thickness of the liquid film. The evaporation rate of liquid refrigerant tends to decrease with increasing axial length, due to the decreasing latent heat transfer through the liquid–vapor interface. The developed model can be considered as an effective tool for evaporator design and can be used to choose appropriate refrigerants under designed conditions.     

The experimental and numerical investigation of a grooved vapor chamber

An effective thermal spreader can achieve more uniform heat flux distribution and thus enhance heat dissipation of heat sinks. Vapor chamber is one of highly effective thermal spreaders. In this paper, a novel grooved vapor chamber was designed. The grooved structure of the vapor chamber can improve its axial and radial heat transfer and also can form the capillary loop between condensation and evaporation surfaces. The effect of heat flux, filling amount and gravity to the performance of this vapor chamber is studied by experiment. From experiment, we also obtained the best filling amount of this grooved vapor chamber. By comparing the thermal resistance of a solid copper plate with that of the vapor chamber, it is suggested that the critical heat flux condition should be maintained to use vapor chamber as efficient thermal spreaders for electronics cooling. A two-dimensional heat and mass transfer model for the grooved vapor chamber is developed. The numerical simulation results show the thickness distribution of liquid film in the grooves is not uniform. The temperature and velocity field in vapor chamber are obtained. The thickness of the liquid film in groove is mainly influenced by pressure of vapor and liquid beside liquid–vapor interface. The thin liquid film in heat source region can enhance the performance of vapor chamber, but if the starting point of liquid film is backward beyond the heat source region, the vapor chamber will dry out easily. The optimal filling ratio should maintain steady thin liquid film in heat source region of vapor chamber. The vapor condenses on whole condensation surface, so that the condensation surface achieves great uniform temperature distribution. By comparing the experimental results with numerical simulation results, the reliability of the numerical model can be verified.     

Computational fluid dynamics simulations of direct contact heat and mass transfer of a multicomponent two-phase film flow in an inclined channel at sub-atmospheric pressure

A method for simultaneous heat and multicomponent mass transfer incorporated with the volume of fluid surface tracking method was developed in a two-dimensional inclined channel. The process in the channel includes direct contact condensation of hydrocarbon mixtures with and without noncondensable gas, and distillation effect is also considered. Interfacial transport was performed by a multicomponent phase change model in kinetic forms considering the assumption of thermodynamic equilibrium at the vapor–liquid or vapor/gas–liquid interface using Peng–Robinson equations. The shear-stress transport k–ω turbulence model damped near the vapor–liquid or vapor/gas–liquid interface was used. The hydrocarbon mixtures in both phases were described by five pseudo-components, and Stefan–Maxwell equations were used to describe diffusional interactions in the multicomponent system. Parametric studies were performed to investigate further the model with various boundary conditions. Simulations for a binary system were also performed for a preliminary validation. For the liquid phase, similar trends of the Sherwood numbers were found between the results by simulations and predicted by the Penetration Theory. For the vapor phase, good agreement was observed between the results by empirical correlation and simulations.     

Parametric effects on heat transfer in loop heat pipe’s wick

The capillary-driven flow with conductive, convective and evaporative heat transfer occurs in the capillary wick of a loop heat pipe, so-called the inverted meniscus evaporator. An axisymmetric two-dimensional mathematical model is developed to investigate the effects of heat flux and porous structure parameters on wick’s working states and performances. The full effects of the interaction between the flowfield and the liquid–vapor interface are adequately considered in this model, as well as the capillary effect of evaporation and the combined effect of conductive, convective and evaporative heat transfer. Wick’s performances are introduced and discussed while parametric effects are discussed in detail. Wick’s working states are classified into three operating modes while all operating modes are discussed in detail. Furthermore, the phase-diagrams on the q–k_t,l plane and the q–K plane are also obtained and discussed.     

Comprehensive experimental and theoretical study of fluid flow and heat transfer in a microscopic evaporating meniscus in a miniature heat exchanger

The complex physicochemical phenomena occurring in the contact line region of an evaporating meniscus are described using a unique combination of high-resolution experimental data and three complementary models. The following were used: (1) high-resolution experimental liquid profile data (thickness, slope, curvature and curvature gradient) to obtain the pressure gradient in the evaporating pentane meniscus in a vertical constrained vapor bubble (VCVB); (2) macroscopic outside surface temperature profile data; (3) a finite element model to obtain the two-dimensional heat conduction profile in the solid substrate wall (macro-model) and the solid–liquid interfacial temperature profile in the evaporating meniscus region; (4) a continuum fluid-dynamics model (micro-model) to obtain the liquid–vapor interfacial temperature, mass flow rate, Marangoni stresses, and evaporative heat flux profiles along the length of the evaporating meniscus; and (5) the Kelvin–Clapeyron model to obtain the vapor temperature profile (liquid–vapor interfacial temperature jump) in the evaporating meniscus region.The retarded dispersion constant and high-resolution thickness, slope, curvature and curvature gradient profiles were obtained from the experimental reflectivity profiles. There was a substantial increase in the measured curvature in the transition region, where the evaporation rate and flux are a maximum. To obtain numerical closure between the three complementary models, the continuum fluid dynamics model (micro-model) required slip at the solid–liquid interface to support the observed high mass flow rates in the evaporating pentane meniscus. Mass flow rates due to Marangoni stresses, capillary pressure and disjoining pressure are compared. Depending on the liquid thickness, Marangoni stresses can either enhance or hinder fluid flow towards the contact line for the evaporating pure pentane meniscus. Due to the high heat removal rate by the evaporating pentane meniscus in the transition region, dips in the vapor, liquid–vapor and solid–liquid interface temperature were obtained. The results demonstrate and describe the sensitivity and complexity of the phase change process in micro-regions.     

Convection and evaporation of microlayer underneath bubbles under microgravity

The multidimensional heat transfer and fluid flow in the microlayer region below a vapor bubble formed during boiling in microgravity are investigated by numerically solving the Navier–Stokes equations with the energy equation. The flow is driven by Marangoni flow due to the surface tension gradient along the bubble surface that results from the temperature gradient. The model also includes condensation and evaporation at the bubble surface. The flow field and heat transfer are calculated for microlayer thicknesses from 0.01 mm to 10 mm to investigate the effect of microlayer thickness. The results show that the velocities are small and have only a small effect on the temperature distribution as compared to the solution for pure conduction in the liquid. Natural convection is shown to have a negligible effect on heat transfer. For less than ideal evaporative heat transfer at the bubble interface, Marangoni convection caused the heat transfer to increase several percent. The flow in the microlayer is shown to agree with the lubrication analogy only for thin, relatively flat interfaces. © 2000 Scripta Technica, Heat Trans Asian Res, 30(1): 1–10, 2001     

Effect of Hydrothermal Waves on Evaporation Distribution During Drop Evaporation

The objective of this study is to clarify physical mechanisms involved in the evaporation of small (a few microliters) sessile drops. We aim to understand the relation between local thermal information at the solid–liquid interface and overall evaporation. An infrared (IR) camera and a charge-coupled device (CCD) camera were used to determine the temperature and heat flux distribution at the solid–liquid interface and the profile of the evaporating drop, respectively. The temperature distribution at the solid–liquid interface was determined using a multilayer substrate consisting of a silicon wafer coated with a thin thermal insulator that is partially transparent to IR. The liquids used were water and FC-72. The evaporation rate of water drops was found to occur mostly at the contact line. However, the heat transfer distribution at the liquid–solid interface was relatively uniform, indicating the heat transferred from the wall must be transported within the drop to the contact line. The mechanisms by which this occurs have yet to be determined. In contrast, the evaporation rate of FC-72 drops where hydrothermal waves were present was found to be proportional to the liquid–vapor interface area rather than the circumference of the drop, indicating a more uniform distribution of evaporation.     

A New Numerical Approach for Predicting the Two-Phase Flow of Refrigerants during Evaporation and Condensation

This article reports on four finite-volume–based numerical methods developed for predicting the one-dimensional two-phase flow of pure refrigerants in evaporators and condensers during change-of-phase processes. The methods differ in the physical assumptions considered at the interface separating the liquid and vapor phases and in the equation used to predict the variation of the refrigerant flow quality during change of phase. In all methods, numerical predictions are obtained via a locally iterative marching-type solution algorithm. Therefore, the models permit the prediction of the size of the pipe needed to achieve full evaporation/condensation of the saturated refrigerant. The effectiveness and robustness of the numerical procedures in predicting the flow and heat transfer characteristics are assessed by comparing results with published experimental data. Good agreement is obtained. The new approach is used to perform a parametric study analyzing the effect of refrigerant type, pipe diameter, and mass flow rate on the flow and heat transfer characteristics in evaporators.     

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 Novel Approach for Modeling Mixed Convection Film Boiling for a Vertical Flat Plate

A numerical model is developed to study mixed convection film boiling over a vertical flat plate. The integral form of conservation equations for each phase along with the appropriate interface conditions due to phase change is transformed into ordinary differential equation (ODE)-form. The length scale used in the model is based on Rayleigh–Taylor instability wave at the liquid–vapor interface. The heat transfer associated in the process is assessed and results are validated successfully for different available experimental results for natural convection and mixed convection film boiling. The mixed convection film boiling is characterized in terms of relevant nondimensional parameters for each phase.