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.     

Conjugate numerical analysis of flow and heat transfer with phase change in a miniature flat plate CPL evaporator

Two-dimensional numerical model for the global evaporator of miniature flat plate capillary pumped loop (CPL) is developed to describe heat and mass transfer with phase change in the porous wick, liquid flow and heat transfer in the compensation cavity and heat transfer in the vapor grooves and metallic wall. The governing equations for different zones are solved as a conjugate problem. The side wall effect heat transfer limit is introduced to estimate the heat transport capability of evaporator. The influences of liquid subcooling, wick material, metallic wall material and non-uniform heat flux on the evaporator performance are discussed in detail.     

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.     

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 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.     

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.     

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.     

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.     

Simulation of flow and heat transfer with evaporation in a porous wick of a CPL evaporator on pore scale by lattice Boltzmann method

A three-dimensional transient double-population thermal lattice Boltzmann BGK scheme for the global evaporator of a CPL is proposed to describe the heat and mass transfer in the porous wick, the cover plate and the vapor groove. The lattice BGK D3Q6 model, developed on passive-scalar approach, is proposed to represent the energy distribution function. The D3G15 incompressible lattice BGK model is chosen to represent the pressure distribution function to calculate the pressure and velocity fields. The random porous structure is reconstructed by the quartet structure generation set (QSGS) and is coupled to the lattice Boltzmann method (LBM) by some special boundary schemes for pore scale simulation. The numerical results of different working conditions and different working fluids are presented, which can improve the understandings of heat and mass transport mechanisms in a CPL evaporator and provide guidance for the evaporator design in a CPL system.     

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.     

Numerical simulation of transient heat and mass transfer in a cylindrical evaporator of a loop heat pipe

The paper investigates the transient processes of heat and mass transfer in a cylindrical evaporator of a loop heat pipe (LHP) during the device start-up. One of the most “arduous” prestart situations, which is characterized by the absence of a liquid in the evaporator central core and filled vapor removal channels, has been considered. With such liquid distribution a successful start-up of an LHP becomes possible only after formation of the vapor phase in the vapor removal channels and their liberation from the liquid. The aim of the investigations is to determine conditions that ensure the boiling-up of a working fluid in vapor removal channels. The problem was solved by a numerical method. Simulation of start-up regimes has been performed for different heat loads and different structural materials of the evaporator. Copper, titanium and nickel wick have been examined. Calculations have been made for three different working fluids; water, ammonia and acetone. Account has been taken of the conditions of heat exchange between the compensation chamber and surrounding medium.     

Heat transfer analysis of a loop heat pipe with biporous wicks

Because the evaporative heat transfer of a wick structure in a loop heat pipe is exceedingly sensitive to the internal volume fractions of liquid and vapor phases, the purpose of this study was to investigate the evaporative heat transfer of various biporous wick parameters by controlling the particle size of pore former, the pore former content, and the sintering temperature. A statistical experiment was carried out to analyze the evaporative heat transfer of the biporous wicks and to understand the effects of the parameters more effectively. The statistical analysis indicated a clear and strong relationship between the effect of the pore former content and the evaporative heat transfer of a biporous wick. This is because the pore former content had a great influence on the probability of large interconnecting pores and an extended surface area for liquid film evaporation in a biporous wick. Experimental results also showed that, at the sink temperature of 10 °C and the allowable evaporator temperature of 85 °C, the evaporative heat transfer coefficient of the biporous wick, which reached a maximum value of 64,000 W/m² K, was approximately six times higher than that of the monoporous wick.     

Numerical study of bubble growth and wall heat transfer during flow boiling in a microchannel

A numerical study has been performed to analyze the wall heat transfer mechanisms during growth of a vapor bubble inside a microchannel. The microchannel is of 200 μm square cross section and a vapor bubble begins to grow at one of the walls, with liquid coming in through the channel inlet. The complete Navier–Stokes equations along with continuity and energy equations are solved using the SIMPLER method. The liquid vapor interface is captured using the level set technique. Experiments have been conducted to validate the numerical model. The bubble growth rate and shapes show good agreement between numerical and experimental results. The numerical results show that the wall heat transfer increases with wall superheat but stays almost unaffected by the liquid flow rate. The liquid vapor surface tension value has little influence on bubble growth and wall heat transfer. However, the bubble with the lowest contact angle resulted in the highest wall heat transfer.     

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.     

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.     

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.     

Three-dimensional simulation of saturated film boiling on a horizontal cylinder

Three-dimensional simulations of film boiling on a horizontal cylinder have been performed. A finite difference method is used to solve the equations governing the conservation of mass, momentum and energy in vapor and liquid phases. A level set formulation for tracking the liquid–vapor interface is modified to include the effect of phase change at the liquid–vapor interface and to treat the no-slip condition at the fluid–solid interface. From the numerical simulations, the effects of cylinder diameter and gravity on the interfacial motion and heat transfer in film boiling are quantified. The heat transfer coefficients obtained from numerical analysis are found to compare well with those predicted from empirical correlations reported in the literature.     

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.     

3-D modeling of the dynamics and heat transfer characteristics of subcooled droplet impact on a surface with film boiling

The impact of a subcooled water and n-heptane droplet on a superheated flat surface is examined in this study based on a three-dimensional model and numerical simulation. The fluid dynamic behavior of the droplet is accounted for by a fixed-grid, finite-volume solution of the incompressible governing equations coupled with the 3-D level-set method. The heat transfer inside each phase and at the solid–vapor/liquid–vapor interface is considered in this model. The vapor flow dynamics and the heat flux across the vapor layer are solved with consideration of the kinetic discontinuity at the liquid–vapor and solid–vapor boundaries in the slip flow regime. The simulated droplet dynamics and the cooling effects of the solid surface are compared with the experimental findings reported in the literatures. The comparisons show a good agreement. Compared to the water droplet, it is found that the impact of the n-heptane droplet yields much less surface temperature drop, and the surface temperature drop mainly occurs during the droplet-spreading stage. The effects of the droplet’s initial temperature are also analyzed using the present model. It shows that the droplet subcooling degree is related closely to the thickness of the vapor layer and the heat flux at the solid surface.     

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.