Modeling for heat and mass transfer with phase change in porous wick of CPL evaporator

A mathematic model is developed to describe heat and mass transfer with phase change in the porous wick of evaporator of capillary pumped loop (CPL). This model with six field variables, including temperature, liquid content, pressure, liquid velocity, vapor velocity and phase-change rate, is closed mathematically with additional pressure relationships introduced. The present model is suitable to the numerical computation, as the established equations become comparatively easy to solve, which is applied to CPL evaporator. The numerical results are obtained and the parameter effects on evaporator are discussed. The study demonstrates that instead of an evaporative interface, there exists an unsaturated two-phase zone between the vapor-saturated zone and the liquid-saturated zone in the wick of CPL evaporator.     

Evaporator critical heat flux in the double-wall artery heat pipe

The fact that heat is transferred into a heat pipe through the liquid-saturated evaporator wick gives rise to the so-called boiling limit on the heat pipe capacity. The composite nature of the double-wall artery heat pipe (DWAHP) wick structure makes the prediction of the evaporator superheat (Δ T_crit) and the critical radial heat flux (q_r) very difficult. The effective thermal conductivity of the wick, the effective radius of critical nucleation cavity, and the nucleation superheat, which are important parameters for double-wall wick evaporator heat transfer, have been evaluated based on the available theoretical models. Empirical correlations are used to corroborate the experimental results of the 2 m DWAHP. A heat choke mounted on the evaporator made it possible to measure the evaporator external temperatures, which were not measured in the previous tests. The high values of the measured evaporator wall temperatures are explainable with the assumption of a thin layer of vapor blanket at the inner heating surface. It has been observed that partial saturation of the wick (lean evaporator) causes the capillary limit to drop even though it may be good for efficient convective heat transfer through the wick. The 2 m long copper-water heat pipe had a peak performance of 1850 W at 23 W/cm² with a horizontal orientation.     

Numerical simulation of heat transfer in a micro channel heat sinks using nanofluids

In this study, a numerical simulation of copper microchannel heatsink (MCHS) using nanofluids as coolants is presented. The nanofluid is a mixture of pure water and nanoscale metallic or nonmetallic particles with various volume fractions. Also, the effects of various volume fractions, volumetric flow rate and various materials of nanoparticles on the performance of MCHS have been developed. A three-dimensional computational fluid dynamics model was developed using the commercial software package FLUENT, to investigate the conjugate fluid flow and heat transfer phenomena in micro channel heatsinks. The results show that the cooling performance of a microchannel heat sink with water based nanofluid containing Al₂O₃ (vol 8%) is enhanced by about 4.5% compared with micro channel heatsink with pure water. Nanofluids reduce both the thermal resistance and the temperature difference between the top (heated) surface of the MCHS and inlet nanofluid compared with that pure water. The cooling performance of a micro channel heat sink with metal nanofluids improves compared with that of a micro channel heat sink with oxide metal nanofluids because the thermal conductivity of metal nanofluid is higher than oxide metal nanofluids. Micro channel heat sinks with nanofluids are expected to be good candidates as the next generation cooling devices for removing ultra high heat flux.     

Investigation on Heat and Mass Transfer in a Evaporator of a Capillary-Pumped Loop with the Lattice Boltzmann Method: Pore Scale Simulation

A two-dimensional transient numerical model based on the lattice Boltzmann method (LBM) for the global evaporator of a capillary-pumped loop (CPL) is proposed to describe heat and mass transfer with evaporation in the porous wick, heat conduction in the cover plate, and heat transfer in the vapor groove. To indicate the stochastic phase distribution characteristics of most porous wick, the quartet structure generation set (QSGS) is introduced for generating more realistic microstructures of porous media. By using the present lattice Boltzmann algorithm along with the porous structure, the heat and mass transfer of an evaporator on pore scale can be predicted without resorting to any empirical parameters determined case by case. The energy equations for entire evaporator are solved as a conjugate problem, which are solved by means of a spatially varying relaxation time in the lattice Boltzmann model and the liquid flow is driven via the interfacial mass flux. A convective boundary condition considering the latent heat during the evaporation on the interface is introduced into the lattice Boltzmann model based on the nonequilibrium extrapolation rule. Especially, the bounce-back rule and the equilibrium rule of the LBM are, respectively, introduced to deal with the momentum boundary conditions inside the porous wick and on the evaporation interface in order to ensure the stability and the efficiency of the LBM model. Numerical results corresponding to different working conditions and different working fluids are presented, which provide guidance for the evaporator design of a CPL system.     

Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure

This article presents a numerical study of natural convection cooling of a heat source embedded on the bottom wall of an enclosure filled with nanofluids. The top and vertical walls of the enclosure are maintained at a relatively low temperature. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, location and geometry of the heat source, the type of nanofluid and solid volume fraction of nanoparticles on the cooling performance is studied. The results indicate that adding nanoparticles into pure water improves its cooling performance especially at low Rayleigh numbers. The type of nanoparticles and the length and location of the heat source proved to significantly affect the heat source maximum temperature.     

Boiling heat transfer characteristics of nanofluids in a flat heat pipe evaporator with micro-grooved heating surface

An experimental study was performed to understand the nucleate boiling heat transfer of water–CuO nanoparticles suspension (nanofluids) at different operating pressures and different nanoparticle mass concentrations. The experimental apparatus is a miniature flat heat pipe (MFHP) with micro-grooved heat transfer surface of its evaporator. The experimental results indicate that the operating pressure has great influence on the nucleate boiling characteristics in the MFHP evaporator. The heat transfer coefficient and the critical heat flux (CHF) of nanofluids increase greatly with decreasing pressure as compared with those of water. The heat transfer coefficient and the CHF of nanofluids can increase about 25% and 50%, respectively, at atmospheric pressure whereas about 100% and 150%, respectively, at the pressure of 7.4 kPa. Nanoparticle mass concentration also has significant influence on the boiling heat transfer and the CHF of nanofluids. The heat transfer coefficient and the CHF increase slowly with the increase of the nanoparticle mass concentration at low concentration conditions. However, when the nanoparticle mass concentration is over 1.0 wt%, the CHF enhancement is close to a constant number and the heat transfer coefficient deteriorates. There exists an optimum mass concentration for nanofluids which corresponds to the maximum heat transfer enhancement and this optimum mass concentration is 1.0 wt% at all test pressures. The experiment confirmed that the boiling heat transfer characteristics of the MFHP evaporator can evidently be strengthened by using water/CuO nanofluids.     

Characteristics of low-temperature short heat pipes with a nozzle-shaped vapor channel

This paper presents the results of experimental and numerical studies of heat transfer and swirling pulsating flows in short low-temperature heat pipes whose vapor channels have the form of a conical nozzle. It has been found that as the evaporator of the heat pipe is heated, pressure pulsations occur in the vapor channel starting at a certain threshold value of the heat power, which is due to the start of boiling in the evaporator. The frequency of the pulsations has been measured, and their dependence on the superheat of the evaporator has been determined. It has been found that in heat pipes with a conical vapor channel, pulsations occur at lower evaporator superheats and the pulsation frequency is greater than in heat pipes of the same size with a standard cylindrical vapor channel. It has been shown that the curve of the heat-transfer coefficient versus thermal load on the evaporator has an inflection corresponding to the start of boiling in the capillary porous evaporator of the heat pipe.     

Inverse thermal analysis of the drying zone of the evaporator of an axially grooved heat pipe

An inverse approach is performed to characterize the thermal behaviour of an axially grooved heat pipe, in steady state, for various operating conditions. For this purpose, an experimental set up, as well as a network conduction model, are developed to simulate the heat transfer in the wall at the evaporator section. The minimization of an objective function, taking into account the discrepancy between measured temperatures and computed ones, allows then the estimation of a heat transfer coefficient as well as the drying out front positions for all the axial grooves. Hence, at the burnout point, the significant temperature increase in the evaporator extremity is considered to be a direct consequence of the restriction of the evaporative zone. Therefore, the distribution of liquid phase in the capillary structure of the heat pipe can be obtained through the analysis of the measured temperature gradient in the evaporator section where the dry out front was expected to occur. Furthermore, the dry out front expansion can be observed when the input heat load is increased or when the adiabatic temperature is decreased. Introducing an adverse tilt angle also shows the effect of the puddle.     

On the quenching of steel and zircaloy spheres in water-based nanofluids with alumina,silica and diamond nanoparticles

The quenching curves (temperature vs time) for small (∼1 cm) metallic spheres exposed to pure water and water-based nanofluids with alumina, silica and diamond nanoparticles at low concentrations (?0.1 vol%) were acquired experimentally. Both saturated (ΔT_sub = 0 °C) and highly subcooled (ΔT_sub = 70 °C) conditions were explored. The spheres were made of stainless steel and zircaloy, and were quenched from an initial temperature of ∼1000 °C. The results show that the quenching behavior in nanofluids is nearly identical to that in pure water. However, it was found that some nanoparticles accumulate on the sphere surface, which results in destabilization of the vapor film in subsequent tests with the same sphere, thus greatly accelerating the quenching process. The entire boiling curves were obtained from the quenching curves using the inverse heat transfer method, and revealed that alumina and silica nanoparticle deposition on the surface increases the critical heat flux and minimum heat flux temperature, while diamond nanoparticle deposition has a minimal effect on the boiling curve. The possible mechanisms by which the nanoparticles affect the quenching process were analyzed. It appears that surface roughness increase and wettability enhancement due to nanoparticle deposition may be responsible for the premature disruption of film boiling and the acceleration of quenching. The basic results were also confirmed by quench tests with rodlets.     

Experimental and theoretical research on capillary limit of micro heat pipe with compound structure of sintered wick on trapezium-grooved substrate

Since heat flux increases sharply yet cooling space in microelectronic and chemical products gradually decreases, a micro heat pipe has been an ideal device for heat transfer for high heat-flux products, and its performance depends largely on its capillary limit. This study proposed an integrated utilization of the advantages of lower backflow resistance to working fluid in trapezium-grooved-wick micro heat pipes and greater capillary force in sintered-wick micro heat pipes; first the factors that are crucial to both types’ heat transfer performances were analyzed, and then mathematical modeling was built for capillary limit of a micro heat pipe with the compound structure of sintered wick on trapezium-grooved substrate, and finally heat transfer limits for micro heat pipes with a trapezium-grooved wick, a sintered wick and with a compound structure were tested through experiments. Both the theoretical analysis and experimental results show that for a micro heat pipe with proposed compound structure, its capillary limit is superior to that of a micro heat pipe with a simplex sintered wick or trapezium-grooved wick.     

The direct effect of interfacial nanolayers on thermal conductivity of nanofluids

One of the most important features of nanofluids is their thermal conductivity. In this article, a new model for thermal conductivity is proposed based on the combination of a statistical model and thermal convection caused by Brownian motion of nanoparticles with considering the effect of interfacial nanolayers among nanoparticles and base fluids. This model is compared with Al₂O₃ in deionized water and CuO in deionized water (based nanofluids of spherical particles) using a number of theoretical and experimental thermal conductivity models, after that the experimental results have been made available in the open literature. In this model, an interfacial nanolayer is influenced directly on both parts of static and dynamic effective thermal conductivity. The present model shows good agreement with the experimental result of nanofluids and gives better predictions compared to models used for nanofluids in this article. This model is purely theoretical and in order to achieve it, experimental results have no effect.     

The effect of real viscosity on the heat transfer of water based Al2O3 nanofluids in a two-sided lid-driven differentially heated rectangular cavity

The heat transfer and fluid flow behavior of water based Al₂O₃ nanofluids are numerically investigated inside a two-sided lid-driven differentially heated rectangular cavity. Physical properties which have major effects on the heat transfer of nanofluids such as viscosity and thermal conductivity are experimentally investigated and correlated and subsequently used as input data in the numerical simulation. Transport equations are numerically solved with finite volume approach using SIMPLEC algorithm. It was found that not only the thermal conductivity but also the viscosity of nanofluids has a key role in the heat transfer of nanofluids. The results show that at low Reynolds number, increasing the volume fraction of nanoparticles increases the viscosity and has a deteriorating effect on the heat transfer of nanofluids. At high Reynolds number, the increase in the viscosity is compensated by force convection and the increase in the volume fraction of nanoparticles which results in an increase in heat transfer is in coincidence with experimental results.     

Effect of pore size distribution in bidisperse wick on heat transfer in a loop heat pipe

The purpose of this article is to experimentally investigate the effect of different pore size distributions in bidisperse wicks upon the heat transfer performance in a LHP. Three bidisperse wicks and one monoporous wick were tested in a loop heat pipe. The pore size distributions of the bidisperse wicks were measured, and the results reflected the three different large/small pore size ratios. The experiments showed that the maximum heat load of the monoporous wick reached about 400 W; and the three bidisperse wicks showed improvements on the maximum heat load up to 570 W. For the monoporous wick, the evaporator heat transfer coefficients of 10 kW/m² K and total thermal resistance of 0.19°C/W were achieved at a high heat load of 400 W. For the better bidisperse wick, the evaporator heat transfer coefficients could attain about 23 kW/m² K and total thermal resistance of 0.13°C/W. The results also indicated that a smaller cluster size in a bidisperse structure created a small pore size ratio. It was also found that the bidisperse wick with smaller clusters had a better enhancement in terms of the evaporator heat transfer coefficient.     

Numerical Investigation of Magnetic Nanoparticles Distribution Inside a Cylindrical Porous Tumor Considering the Influences of Interstitial Fluid Flow

A numerical simulation of interstitial fluid flow and blood flow and diffusion of magnetic nanoparticles (MNPs) are developed, based on the governing equations for the fluid flow, i.e., the continuity and momentum and mass diffusion equations, to a tissue containing two-dimensional cylindrical tumor. The tumor is assumed to be rigid porous media with a necrotic core, interstitial fluid and two capillaries with arterial pressure input and venous pressure output. Blood flow through the capillaries and interstitial fluid flow in tumor tissues are carried by extended Poiseuille’s law and Darcy’s law, respectively. Transvascular flows are also described using Starling’s law. MNPs diffuse by interstitial fluid flow in tumor. The finite difference method has been used to simulate interstitial fluid pressure and velocity, blood pressure and velocity and diffusion of MNPs injected inside a biological tissue during magnetic fluid hyperthermia (MFH). Results show that the interstitial pressure has a maximum value at the center of the tumor and decreases toward the first capillary. The reduction continues between two capillaries, and interstitial pressure finally decreases in direction of the tumor perimeter. This study also shows that decreasing in intercapillary distance may cause a decrease in interstitial pressure. Furthermore, multi-site injection of nanoparticles has better effect on MFH.     

Stimulated adsorption and capillary condensation

The joint adsorption of silver and water vapors on an ideal substrate is studied in a numerical experiment using a modified Langmuir adsorption model. The calculations reveal a number of previously unknown phenomena. It is established that the adsorption and condensation of silver vapor stimulate the adsorption of water vapor, resulting in its capillary condensation at the molecular level even at low saturation. It is shown that the rate of capillary condensation depends on the wetting angle of water on silver, and there is a characteristic wetting angle at which the rate of capillary condensation changes radically. It is also found that water vapor has a significant effect on the adsorption of silver vapor and the structure of its condensate on the substrate: the presence of water vapor reduces the adsorption of silver atoms on the substrate and weakens the adhesion of silver condensate to the substrate. The results can be used to study two-component adsorption and capillary condensation and to develop technologies for growing thin films in a gas phase.     

Three-dimensional numerical analysis of heat and mass transfer in heat pipes

A three-dimensional finite-element numerical model is presented for simulation of the steady-state performance characteristics of heat pipes. The mass, momentum and energy conservation equations are solved for the liquid and vapor flow in the entire heat pipe domain. The calculated outer wall temperature profiles are in good agreement with the experimental data. The estimations of the liquid and vapor pressure distributions and velocity profiles are also presented and discussed. It is shown that the vapor flow field remains nearly symmetrical about the heat pipe centerline, even under a non-uniform heat load. The analytical method used to predict the heat pipe capillary limit is found to be conservative.     

Experimental study of the characteristics and mechanism of pool boiling CHF enhancement using nanofluids

The pool boiling critical heat flux (CHF) performance of aqueous nanofluids was investigated using various nanoparticles of TiO₂, Al₂O₃, and SiO₂. The usage of a nanofluid as a working fluid can significantly enhance the pool boiling CHF, which was found to be strongly dependent on the kind of nanoparticle, as well as its concentration. A nanoparticle surface coating was observed on the heating surface after the experiment. The CHF of pure water on the nanoparticle-coated surface was higher than that of nanofluids for all cases. This revealed that the cause of the CHF enhancement using nanofluids is due to the fact that the heater surface is modified by the nanoparticle deposition. The mechanism of CHF enhancement due to the nanoparticle coating was discussed, relating it to surface wettability, surface roughness, and maximum capillary wicking height of the nanoparticle-coated surface.     

Flow and migration of nanoparticle in a single channel

A numerical simulation based on a combined Euler and Lagrange method is investigated in this work to simulate the flow and migration of nanoparticles in a single channel. The motion of discrete nanoparticles is determined by the Lagrangian trajectory method based on the Newton’s second law that includes the influence of the body force, various hydrodynamic forces, the Brownian motion and the thermophoresis force. The coupling of discrete particles with continuous flow is realized through the modification of the source term of the continuous equation. The results reveal the two-phase flow nature of nanoparticle suspensions and their implications to the convective heat transfer of nanofluids.     

Experimental studies on heat transfer and friction factor characteristics of CuO/water nanofluid under laminar flow in a helically dimpled tube

An experimental investigation on the convective heat transfer and friction factor characteristics in the plain and dimpled tube under laminar flow with constant heat flux is carried out with distilled water and CuO/water nanofluids. For this, CuO nanoparticles with an average size of 15.3 nm were synthesized by sol–gel method. The nanoparticles are then dispersed in distilled water to form stable suspension of CuO/water nanofluid containing 0.1, 0.2 and 0.3% volume concentration of nanoparticles. It is found that the experimental Nusselt numbers for 0.1, 0.2 and 0.3% volume concentration of CuO nanoparticles are about 6, 9.9 and 12.6%, respectively higher than those obtained with distilled water in plain tube. However, the experimental Nusselt numbers for 0.1, 0.2 and 0.3% volume concentration of CuO nanoparticles are about 3.4, 6.8 and 12%, respectively higher than those obtained with distilled water in dimpled tube. The friction factor of CuO/water nanofluid is also increased due to the inclusion of nanoparticles and found to increase with nanoparticle volume concentration. The experimental results show that there exists a difference in the enhancement levels of Nusselt numbers obtained with nanofluids in plain tube and dimpled tube. Hence it is proposed that the mechanism of heat transfer enhancement obtained with nanofluids is due to particle migration from the core of fluid flow to tube wall.     

Operational characteristics of miniature loop heat pipe with flat evaporator

Loop heat pipes are heat transfer devices whose operating principle is based on the evaporation and condensation of a working fluid, and which use the capillary pumping forces to ensure the fluid circulation. A series of tests have been carried out with a miniature loop heat pipe (mLHP) with flat evaporator and fin-and-tube type condenser. The loop is made of pure copper with stainless mesh wick and methanol as the working fluid. Detailed study is conducted on the start-up reliability of the mLHP at high as well as low heat loads. During the testing of mLHP under step power cycles, the thermal response presented by the loop to achieve steady state is very short. At low heat loads, temperature oscillations are observed throughout the loop. The amplitudes and frequencies of these fluctuations are large at evaporator wall and evaporator inlet. It is expected that the extent and nature of the oscillations occurrence is dependent on the thermal and hydrodynamic conditions inside the compensation chamber. The thermal resistance of the mLHP lies between 0.29 and 3.2°C/W. The effects of different liquid charging ratios and the tilt angles to the start-up and the temperature oscillation are studied in detail.