Laminar film condensation on an elliptical tube embedded in porous media

Laminar film condensation of saturated vapor flowing over an isothermal elliptical tube embedded in a porous medium is analyzed for conditions of free and forced convection. The flow field in the porous medium is described by the Darcy–Brinkman–Forchheimer model. The effect of vapor shear on condensation is determined by simultaneous solution of the two phase vapor boundary layer and condensate film momentum equations. The numerical results, which are presented in the form of local film thickness and local Nusselt number, show a dependence of these physical parameters on practical dimensionless parameters such as Reynolds number, Darcy number, Bond number and eccentricity.     

Examination of minimum-heat-flux-point condition for film boiling on a sphere in terms of the limiting liquid superheat and the critical vapor film thickness

Previously proposed theories of the minimum-heat-flux-point (MHF-point) condition were examined using available experimental data obtained from the immersion cooling of spheres in water. The sphere diameter ranged from 9.5 to 30 mm and the liquid subcooling from 0 to 85 K. The limiting liquid superheat predicted by the Lienhard equation was compared with the liquid–solid interface superheat at the instant of liquid–solid contact at the MHF-point. The results showed that the liquid–solid interface superheat was not limited by the limiting liquid superheat and its value was connected with the collapse mode of vapor film. The collapse mode was a coherent collapse at a low interface superheat and the mode changed to a propagative collapse as the interface superheat increased. The critical vapor film thickness obtained from the linear stability analysis of vapor film was compared with the calculated value of average vapor film thickness at the MHF-point. For all data, the ratio of the average vapor film thickness to the critical vapor film thickness was correlated well as a function of liquid subcooling. The ratio decreased with increasing liquid subcooling and tended to about 0.8 to 1 depending on the experiments. This indicated that the MHF-point at a high liquid subcooling was determined by the critical vapor film thickness. A physical consideration was given to the effect of liquid–solid contact that occurred in the film boiling region on the calculated value of the vapor film thickness and the stability of vapor film.     

Effect of uniform suction on laminar filmwise condensation on a finite-size horizontal flat surface in a porous medium

The theoretical analysis of filmwise condensation outside a finite-size horizontal flat surface embedded in a porous medium filled with a dry saturated vapor has been solved by a boundary layer treatment. The Newton-Raphson scheme was employed to solve the finite-size horizontal flat plate in porous medium. Results turns out that the average Nusselt number for condensation heat transfer is expressed in terms of Darcy number, Jakob number, film liquid Prandtl number, Darcy-modified Rayleigh number and the parameter of suction, as well as are given for the condensate layer thickness profiles.     

Thermoeconomic optimization of subcooled and superheated vapor compression refrigeration cycle

An exergy-based thermoeconomic optimization application is applied to a subcooled and superheated vapor compression refrigeration system. The advantage of using the exergy method of thermoeconomic optimization is that various elements of the system—i.e., condenser, evaporator, subcooling and superheating heat exchangers—can be optimized on their own. The application consists of determining the optimum heat exchanger areas with the corresponding optimum subcooling and superheating temperatures. A cost function is specified for the optimum conditions. All calculations are made for three refrigerants: R22, R134a, and R407c. Thermodynamic properties of refrigerants are formulated using the Artificial Neural Network methodology.     

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.     

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.     

Study on Characteristics of Steady Flow Condensation Heat Transfer in a Fube Under Zero—Gravitation

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Analysis of heat transfer with liquid-vapor phase change in a forced-flow fluid moving through porous media

This study focuses on the experimental analysis of transient-regime heat transfer with liquidvapor phase change in a fluid as it flows through a porous media composed of small bronze spheres. Three distinct zones can be observed: liquid, two-phase and superheated vapor. The boundaries between these zones are determined using temperature and pressure fields. An N-shaped profile is observed for the temperature values along the main flow axis. The first local maximum value on the temperature curve corresponds to the boundary between the liquid zone and the two-phase zone. When a local minimum temperature exists, it corresponds to the boundary between the two-phase and the vapor zones. A finite element numerical simulation is used to predict the saturation field, which is numerically determined from the boundaries of the two-phase zone and of the experimental temperature field. The liquid and vapor pressure fields are then deduced for all three phase zones of the porous medium.     

Extensive study on laminar free film condensation from vapor–gas mixture

The dimensionless velocity component method was successfully applied in a depth investigation of laminar free film condensation from a vapor–gas mixture, and the complete similarity transformation of its system of governing partial differential equations was conducted. The set of dimensionless variables of the transformed mathematical model greatly facilitates the analysis and calculation of the velocity, temperature and concentration fields, and heat and mass transfer of the film condensation from the vapor–gas mixture. Meanwhile, three difficult points of analysis related to the reliable analysis and calculation of heat and mass transfer for the film condensation from the vapor–gas mixture were overcome. They include: (i) correct determination of the interfacial vapor condensate saturated temperature; (ii) reliable treatment of the concentration-dependent densities of vapor–gas mixture, and (iii) rigorously satisfying the whole set of physical matching conditions at the liquid–vapor interface. Furthermore, the critical bulk vapor mass fraction for condensation was proposed, and evaluated for the film condensation from the water vapor–air mixture, and the useful methods in treatment of temperature-dependent physical properties of liquids and gases were applied. With these elements in place, the reliable results on analysis and calculation of heat and mass transfer of the film condensation from the vapor–gas mixture were achieved.The laminar free film condensation of water vapor in the presence of air was taken as an example for the numerical calculation. It was confirmed that the presence of the non-condensable gas is a decisive factor in decreasing the heat and mass transfer of the film condensation. It was demonstrated that an increase of the bulk gas mass fraction has the following impacts: an expedited decline in the interfacial vapor condensate saturation temperature; an expedited decrease in the condensate liquid film thickness, the condensate liquid velocity, and the condensate heat and mass transfer. It was found that an increase of the wall temperature will increase the negative effect of the non-condensable gas on heat and mass transfer of the film condensation from the vapor–gas mixture.     

Theoretical research of convective condensation heat transfer for mixture gas on a horizontal tube

The mechanism of convective condensation heat transfer of moist mixed gas across a horizontal tube was studied in this paper. The models referring to how the liquid film flows and the heat transfers on the tube are set up by combining modified film model and Nusselt condensation theory. The effects of Re number, wall temperature, and water vapor concentration on condensation heat transfer are discussed. Results predict that the film thickness profile on the tube is influenced greatly by vapor shear force on liquid film. Local Nusselt number depends remarkably on gas phase heat resistance, which is different from pure vapor and very similar to single‐phase gas. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(6): 324–333, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20169     

Dynamics of a vapor bubble on a heated substrate

The dynamics of a vapor bubble between its liquid phase and a heated plate is studied in relation to the breakdown and recovery of the film boiling. By examining the expansion and the contraction of the vapor bubble the film boiling and transition boiling states are predicted. Conservation laws in the vapor, solid, and liquid phases are invoked along with fully nonlinear, coupled, free boundary conditions. These coupled system of equations are reduced to a single evolution equation for the local thickness of the vapor bubble by using a long-wave asymptotics, which is then solved numerically to yield the transient motion of the vapor bubble. Of the numerous parameters involved in this complex phenomenon we focus on the effects of the degree of superheat from the solid plate, that of the supercooling through the liquid, and the wetting/dewetting characteristics of the liquid on the solid plate. A material property of the substrate thus is incorporated into the criteria for the film boiling based on hydrodynamic models.     

Vapor condensation onto a turbulent liquid—II. Condensation burst instability at high turbulence intensities

The process of vapor condensation onto a turbulent, subcooled liquid is shown to become unstable when the liquid-side turbulence intensity exceeds a threshold value which depends on liquid subcooling. Above the threshold, very short, high-intensity bursts of condensation occur intermittently. Data are presented on the nature of the bursts and the conditions for their onset.     

Film boiling heat transfer around a vertical finite‐length cylinder with a convex hemispherical bottom

The film boiling heat transfer around a vertical silver cylinder with a convex hemispherical bottom was investigated experimentally in quiescent water at atmospheric pressure. The experiments have been carried out using a quenching method. The diameter and length of the test cylinder are 32 mm and 48 mm, respectively. The test cylinder was heated to about 600 °C in an electric furnace and then cooled in saturated or subcooled water with an immersion depth of about 100 mm. The degree of liquid subcooling was varied from 0 K to 30 K. The analytical solutions for saturated and subcooled boiling are obtained by applying a two‐phase boundary layer theory for vapor film with a smooth interface. The experimental data correlates within ±15% based on the proposed prediction method. Also, the lower limit of film boiling was examined in terms of wall heat flux and degree of superheating. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20289     

A numerical study of film condensation on a metallic foam-sintered plate with considering convection and super-cooling effects

A numerical solution was presented for film condensation on a vertical plate sintered with metallic foam. In the metallic foam region, the Brinkman-Darcy model was employed to establish the fluid flow equation, and the thermal equilibrium model was used to describe local heat transfer. Through introduction of dimensionless distance, namely, the ratio of the coordinate normal to the plate and the local film thickness, the computational domain was regularized in a rectangular zone. The effects of convection and explicit heat of super-cooled liquid on the condensation film were considered. The temperature and velocity profile, film thickness, and the local and average Nu number were obtained. The effects of Ja and Da number on the velocity profile and heat transfer performance were investigated. The numerical model was verified through comparison of the predicted results with those in the literature, which neglected convection and explicit heat of super-cooling effects. Convection and explicit heat of super-cooling can play a positive role in reducing the velocity level in the film. The two effects played a positive role in heat transfer improvement when the dimensionless location along the gravity direction (X) was > 0.15, which was associated with reduced film thickness. The two effects also had a mild influence on the linear distribution of dimensionless temperature. The heat transfer performance deteriorated with an increase in Ja number or Da number.     

Turbulent film condensation on a half oval body

The paper is an investigation of turbulent film condensation on a half oval body. The high tangential velocity of the vapor flow at the boundary layer is determined from potential flow theory. The Colburn analogy is used to define the local liquid-vapor interfacial shear which occurs when the high velocity vapor flows across the body surface. The paper then presents a discussion of the results obtained for the local dimensionless film thickness and heat transfer characteristics. Furthermore, the present paper discusses the influence of Froude number, sub-cooling temperature and system pressure on mean Nusselt number.     

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.     

Film condensation with lateral mass flux about a body of arbitrary shape in a porous medium

Under an appropriate distribution of lateral mass flux at the boundary, similarity solution is obtained to the problem of film condensation in a porous medium along the surface of a body of arbitrary shape. The thickness of the liquid layer, the temperature profiles, and the Nusselt number are calculated. It is found that the results depend strongly on the lateral mass flux at the boundary.     

Laminar film condensation driven latent thermal energy storage in rectangular containers

This paper focuses on numerically analyzing the thermal transport phenomena in the transient conjugate problem of melting and laminar film condensation. The key focus is to identify an optimum container aspect ratio/shape and conditions for which the heat storage time and the storage capacity are minimum and maximum respectively. Since most solid–liquid phase change materials (PCMs) suffer from poor thermal conductivities, the major resistance to heat transfer comes from PCM. Hence, high thermal conductivity, low-cost metal foam is suggested for use along with PCM to minimize this resistance. The conjugate transient problem of film condensation driven solid–liquid phase change of PCM impregnated inside porous metal foam is numerically analyzed. An effective heat capacity formulation is employed for modeling the transient PCM phase change in porous foam and is solved using finite element method. It is coupled with laminar film condensation on the outside of the storage container. The model is then used for selecting the best aspect ratio for thermal energy storage (TES) containers that enables to store comparatively the maximum heat. The results of the developed model showed that the major resistance to heat transfer and hence efficient thermal energy storage depends strongly on the aspect ratio of the PCM storage containers.     

Effects of uniform suction and surface tension on laminar filmwise condensation on a horizontal elliptical tube in a porous medium

This study performs a theoretical investigation into the problem of steady filmwise condensation flow over the external surface of a horizontal elliptical tube embedded in a porous medium with suction at the tube surface. The combined effects of the surface tension force and the gravitational force in driving the flow of the liquid film within the porous medium are modeled using Darcy's law. An effective suction function, f, is introduced to model the effect of the suction force at the wall on the thickness of the condensate film. The theoretical results presented in this study show that the heat transfer performance can be enhanced by applying a suction effect at the wall. Furthermore, it is shown that the surface tension force has a negligible effect on the mean Nusselt number.     

Analysis of Infiltration,Solidification, and Remelting of a Pure Metal in Subcooled Porous Preform

The parts fabricated by selective laser sintering of metal powders are usually not fully densified and have porous structure. Fully densified parts can be obtained by infiltrating liquid metal into the porous structure and solidifying the liquid metal. When the liquid metal is infiltrated into the subcooled porous structure, the liquid metal can be partially solidified. Remelting of the partially solidified metal can also take place and a second moving interface can be present. Infiltration, solidification, and remelting of metal in a subcooled porous preform obtained by laser sintering of metal powders are analytically investigated in this article. The governing equations are nondimensionalized and the problem is described using six dimensionless parameters. The temperature distributions in the remelting and uninfiltrated regions were obtained by an exact solution and an integral approximate solution, respectively. The effects of porosity, Stefan number, subcooling parameter, and dimensionless infiltration pressure are investigated.