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

A transient, three-dimensional model for thermal transport in heat pipes and vapor chambers is developed. The Navier–Stokes equations along with the energy equation are solved numerically for the liquid and vapor flows. A porous medium formulation is used for the wick region. Evaporation and condensation at the liquid–vapor interface are modeled using kinetic theory. The influence of the wick microstructure on evaporation and condensation mass fluxes at the liquid–vapor interface is accounted for by integrating a microstructure-level evaporation model (micromodel) with the device-level model (macromodel). Meniscus curvature at every location along the wick is calculated as a result of this coupling. The model accounts for the change in interfacial area in the wick pore, thin-film evaporation, and Marangoni convection effects during phase change at the liquid–vapor interface. The coupled model is used to predict the performance of a heat pipe with a screen-mesh wick, and the implications of the coupling employed are discussed.     

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

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

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.     

Multi-artery,heat-pipe spreader

Multiple, columnar liquid vapor chamber allows for effective heat removal from finite, concentrated heat source by heat spreading via lateral vapor flow, while minimizing conduction resistance through thinner evaporator wick. The individual liquid arteries are designed by wick coated solid pillar. We optimize the artery geometry, numbers, and distribution, for both liquid and air-cooled, finned condensers, and show that the overall thermal resistance is substantially lower than the uniform wick vapor chamber.     

Performance degradation of flattened heat pipes

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

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.     

Rapid vaporization of subcooled liquid in a capillary structure

A novel process is introduced for rapid vaporization of subcooled liquid in a capillary structure. The process consists of a low-thermal-conductivity porous wick, heated from a downward-facing grooved heating block that is in intimate contact with the upper surface of the wick structure. For such a specially configured heat transfer device, measurements show that vapor can be generated rather quickly once a sufficient amount of heat was applied. The mechanisms leading to the rapid vaporization of liquid are numerically investigated. It is found that the low thermal conductivity of the capillary structure and the presence of the extremely steep temperature gradients at the fin/porous structure interface due to the rather weak natural convection, reflected by small-scale secondary flow cells below the heated fins, are responsible for the rapid vaporization of subcooled liquid.     

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

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

A study of condensation on a vertical internally cooled pipe embedded in porous medium

This paper reports a theoretical study of film condensation on the outside of a vertical pipe containing a cold fluid and imbedded in a porous medium. Two distinct cases are considered. In the first case the collant in the pipe and the falling film of condensate are in parallel flow. In the second case the two forthmentioned fluid streams are in counterflow. The flow in the porous medium is modeled by using both the Brinkman-Darcy model and the Darcy model. The main results of the problem document the effect of the condensation phenomenon on the heat gain in the pipe for a host of the problem parameters.     

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.     

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.     

Characterization of evaporation and boiling from sintered powder wicks fed by capillary action

The thermal resistance to heat transfer into the evaporator section of heat pipes and vapor chambers plays a dominant role in governing their overall performance. It is therefore critical to quantify this resistance for commonly used sintered copper powder wick surfaces, both under evaporation and boiling conditions. The objective of the current study is to measure the dependence of thermal resistance on the thickness and particle size of such surfaces. A novel test facility is developed which feeds the test fluid, water, to the wick by capillary action. This simulates the feeding mechanism within an actual heat pipe, referred to as wicked evaporation or boiling. Experiments with multiple samples, with thicknesses ranging from 600 to 1200 μm and particle sizes from 45 to 355 μm, demonstrate that for a given wick thickness, an optimum particle size exists which maximizes the boiling heat transfer coefficient. The tests also show that monoporous sintered wicks are able to support local heat fluxes of greater than 500 W cm^?2 without the occurrence of dryout. Additionally, in situ visualization of the wick surfaces during evaporation and boiling allows the thermal performance to be correlated with the observed regimes. It is seen that nucleate boiling from the wick substrate leads to substantially increased performance as compared to evaporation from the liquid free surface at the top of the wick layer. The sharp reduction in overall thermal resistance upon transition to a boiling regime is primarily attributable to the conductive resistance through the saturated wick material being bypassed.     

Feasibility study of a vapor chamber with a hydrophobic evaporator substrate in high heat flux applications

A novel vapor chamber was fabricated to assess the feasibility of combining hydrophobic and hydrophilic wettabilities in the evaporator to optimize thermal performance. The proposed vapor chamber included a separate layer of hydrophilic sintered copper powder wick that was pressed in intimate contact with a hydrophobic evaporator substrate with a water contact angle around 140°. The contact between the wick layer and the evaporator was provided by sixteen posts implemented on the condenser, which pushed the wick layer toward the evaporator. The thermal performance was evaluated based on the thermal resistance, source temperature, and temperature uniformity across the condenser. Results were compared with those of a baseline vapor chamber that was fabricated by sintering hydrophilic copper particles on a hydrophilic copper evaporator substrate. The wick size and the copper powders used to fabricate the wick structure were the same in both vapor chambers. Overall, the performance of the proposed vapor chamber was lower than that of the baseline vapor chamber, possibly due to microscale gaps between the wick layer and the evaporator substrate. However, the concept of using a hydrophilic wick to force liquid in contact with a hydrophobic evaporating surface could enable a new family of vapor chambers with low thermal resistance, if more efficient techniques for improving the mechanical contact between the wick layer and the evaporator are introduced through further detailed research. If successful, the fabrication cost of vapor chambers would be reduced as well, by using prepared wick structures, which do not require high-temperature sintering processes on evaporators.     

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.     

Effects of capillary forces on laminar filmwise condensation on horizontal disk in porous medium

This study investigates the problem of steady filmwise condensation on a horizontal disk embedded in a porous medium. The disk surface is cold and faces upwards into the porous medium, which is filled with a dry vapor. Due to the effects of capillary forces in the porous medium, a two-phase zone is formed between the liquid film and the vapor zone. As in the classical filmwise condensation problem, this study assumes that the inertia within the liquid film is negligible and that the properties of the porous medium, dry vapor, and condensate are constant. Darcy’s law is used to analyze the liquid flow in both the liquid film and the two-phase zone. A capillary parameter, Bo_c, is introduced to characterize the liquid flow caused by capillary forces in the porous medium. It is shown that the mean Nusselt number, , increases at higher values of the capillary parameter, Bo_c. Finally, this study derives a simple closed form correlation for the Nusselt number for the case where the capillary forces are neglected.     

Theoretical study of superheated vapor effect on liquid film condensation in a saturated porous medium using Forchheimer's model

In this work, the superheated vapor effect on liquid film condensation in a saturated porous medium using Forchheimer's model has been investigated analytically and numerically. The applied governing equations, the continuity equation, the Forchheimer equation, and the energy equation were transformed using the similarity transformation technique into a dimensionless form using a set of suitable variables and then solved numerically using the Runge–Kutta method. Results obtained were graphically drawn to illustrate the effects of superheated vapor and subcooled liquid on the liquid film condensation, temperature, and heat transfer rate through the porous medium. It was found that the film thickness is a function of dimensionless parameters related to the degree of subcooling and Grashof number without a superheating effect. Consequently, the Nusselt number depends on the square root of the Rayleigh number, the Grashof number, and the dimensionless film thickness. It was also found that if superheating exists, the liquid film thickness then depends on four dimensionless parameters related to the Grashof number, the degree of subcooling of the liquid, the extent of the superheating of the surrounding vapor, and a property ratio of the liquid and the vapor phase.     

Analytical model of heat transfer in porous insulation around cold pipes

A thermal insulation system is analysed that consists of a cold tube insulated with a porous material faced with a vapour retarding foil.Water vapour will diffuse through the vapour retarding foil and condense on the cold tube. To avoid build-up of water in the insulation a hydrophilic wicking cloth is wrapped around the cold tube and extended through a slit in the tubular insulation and a slot in the facing to the ambient so that condensed water can evaporate into the air. Some of the moisture in that part of the wicking cloth situated in the slit in the tubular insulation will diffuse backwards to the cold pipe and contribute to the heat uptake of the cold tube. This part is calculated for the stationary case and compared with the sensible heat transfer through the tubular shaped insulation material, using measured dry λ values and measured fictitious moist λ values.     

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.     

Thermal response of a flat heat pipe sandwich structure to a localized heat flux

The temperature distribution across a flat heat pipe sandwich structure, subjected to an intense localized thermal flux has been investigated both experimentally and computationally. The aluminum sandwich structure consisted of a pair of aluminum alloy face sheets, a truncated square honeycomb (cruciform) core, a nickel metal foam wick and distilled water as the working fluid. Heat was applied via a propane torch to the evaporator side of the flat heat pipe, while the condenser side was cooled via natural convective and radiative heat transfer. A novel method was developed to estimate experimentally, the heat flux distribution of the torch on the evaporator side. This heat flux distribution was modeled using a probability function and validated against the experimental data. Applying the estimated heat flux distribution as the surface boundary condition, a finite volume analysis was performed for the wall, wick and vapor core regions of the flat heat pipe to obtain the field variables in these domains. The results were found to agree well with the experimental data indicating the thermal spreading effect of the flat heat pipe.     

TRANSIENT TWO-DIMENSIONAL COMPRESSIBLE ANALYSIS FOR HIGH-TEMPERATURE HEAT PIPES WITH PULSED HEAT INPUT

Abstract

A complete mathematical model for transient two-dimensional heat pipes is presented. The numerical results for both simulated compressible vapor flow with high Mach numbers and the vapor flow of a high-temperature heat pipe are compared with the experimental data in the literature. The transient responses of heat pipes to a pulsed heat input are also investigated. It is very important to include the porous wick and the wall in the numerical calculations for the transient analysis of heat pipes and to treat the entire heat pipe as a single system rather than to analyze the vapor flow alone.