Simplified approach of turbulent film condensation on an inclined elliptical tube

The present theoretical study investigates turbulent film condensation on an inclined elliptical tube. Adopting the assumption of an isothermal wall surface, the energy equation, forced balance equations and thermal balance equations are derived to describe the phenomena of the condensate film. Results are obtained for the heat transfer coefficient over a wide range of vapor velocities, i.e. low condensation parameter to high condensation parameter. The optimal inclination angle of the tube in different length–radius ratios and eccentricity can be obtained in the present results. This study also discusses the influence of the degree of eccentricity of the elliptical tube on the heat transfer coefficient. Finally, a comparison is provided between the results of the present study and those reported in a previous theoretical study. It is found that a good agreement exists between the two sets of results.     

Laminar film condensation heat transfer of hydrogen and nitrogen inside a vertical tube

There have been a number of experimental investigations on condensing heat transfer to cryogenic fluids. The investigations with nitrogen and oxygen have shown reasonable agreement between experimental data and those predicted by Nusselt's theory. On the other hand, in the previous investigations with much colder fluids, such as hydrogen, deuterium, and helium, the experimental condensing heat transfer coefficients are smaller than those predicted by Nusselt's theory, and these differences become much larger when the film Reynolds number or decreasing temperature difference across the condensate film is decreased. In the present investigation, hydrogen and nitrogen were condensed inside a vertical tube (d = 15 mm, L = 30 mm) under steady‐state conditions, respectively, and condensing heat transfer coefficients were precisely measured. From the experimental results, the condensing heat transfer coefficients for saturated hydrogen and nitrogen vapors agree with those predicted by Nusselt's theory within ±20%. The results of the present study suggest that deuterium and helium might also behave as predicted by Nusselt's theory. © 2001 Scripta Technica, Heat Trans Asian Res 30(7): 542–560, 2001     

Entropy generation minimization of free convection film condensation on an elliptical cylinder

This paper aims to perform thermodynamic analysis of saturated vapor flowing slowly onto and condensing on an elliptical cylinder. This analysis provides us how the geometric parameter-ellipticity affects entropy generation during film-wise condensation heat transfer process. The results observe that local condensate film thickness decreases with an increase in ellipticity of a cylinder. From the first law point of view, the local heat transfer coefficient enhances as ellipticity increases. Meanwhile, from the second law point of view, entropy generation increases with increasing the value of ellipticity. We derive an expression for entropy generation, which accounts for the combined action of the specified irreversibilities. The result demonstrates that thermal irreversibility dominates over film flow friction irreversibility. Finally, an expression of minimizing entropy generation in laminar film condensation heat transfer is obtained.     

Thermodynamic optimization of free convection film condensation on a horizontal elliptical tube with variable wall temperature

This study focuses on the thermodynamic analysis of saturated vapor flowing slowly onto and condensing on an elliptical tube with variable wall temperature. An entropy generation minimization (EGM), technique is applied as a unique measure to study the thermodynamic losses caused by heat transfer and film-flow friction for the laminar film condensation on a non-isothermal horizontal elliptical tube. The results provide us how the geometric parameter ellipticity and the amplitude of non-isothermal wall temperature variation affect entropy generation during filmwise condensation heat-transfer process. The optimal design can be achieved by analyzing entropy generation in film condensation on a horizontal elliptical tube with further account for the amplitude of non-isothermal wall temperature variation.     

Laminar film condensation on a finite-size horizontal wavy plate

A theoretical analysis of two-dimensional, steady laminar film condensation on a finite-size horizontal wavy plate is studied for the case in which a cold plate faces upwards. The present study considers that the wavy characteristic length, amplitude and the depth of boundary layer at the plate edge is equal to a minimum depth. The dimensionless heat transfer coefficients and the dimensionless film thickness along the surface are found to be functions of five parameters: dimensionless wave length and amplitude, Pr, Ja and Ra.     

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.     

Laminar flow with combustion in inert porous media

This work presents one-dimensional numerical results for combustion of an air/methane mixture in inert porous media using laminar and radiation models. Comparisons with experimental data are reported. The burner is composed by a preheating section followed by a combustion region. Macroscopic equations for mass, momentum and energy are obtained based on the volume average concept. Distinct energy equations are considered for the porous burner and the flowing gas. The numerical technique employed for discretizing the governing equations was the control volume method with a boundary-fitted non-orthogonal coordinate system. The SIMPLE algorithm was used to relax the entire equation set. Inlet velocity, excess air, porosity and solid-to-fluid thermal conductivity ratio were varied in order to investigate their effect on temperature profiles. Results indicate that higher inlet velocities result in higher gas temperatures, following a similar trend observed in the experimental data used for comparisons. Burning of mixtures close to the stoichiometric conditions also increased temperatures, as expected. Increasing the thermal conductivity of the preheating section reduced peak temperature in the combustion region. The use of porous material with very high thermal conductivity on the combustion region did not affect significantly temperature levels in the combustion section.     

Investigation of Boiling Heat Transfer of Binary Mixture from Vertical Tube Embedded in Porous Media

ＩｎｖｅｓｔｉｇａｔｉｏｎｏｆＢｏｉｌｉｎｇＨｅａｔＴｒａｎｓｆｅｒｏｆＢｉｎａｒｙＭｉｘｔｕｒｅｆｒｏｍＶｅｒｔｉｃａｌＴｕｂｅＥｍｂｅｄｄｅｄｉｎＰｏｒｏｕｓＭｅｄｉａＨａｉｌｏｎｇＭｏ；ＴｏｎｇｚｅＭａ；ＺｈｅｎｇｆａｎｇＺｈａｎｇ（Ｉｎｓｔｉ...     

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 eddy diffusivity in film condensation on a horizontal tube

It is an investigation into turbulent film condensation on a horizontal tube. In order to forecast the results more exactly, a new theory model of local film shear stress (τ / τ_w) is presented in the paper. In the study, four models of different eddy diffusivity are considered. The numerical calculation is obtained by using Visual C⁺⁺. The result shows that among the four models, the difference between the higher value and the lower value of the mean Nusselt number is about 10.1%. Besides, the results developed in the current study are compared with those generated by previous theoretical results. The result shows that the present paper considering film local shear has a higher mean Nusselt number than the previous ones that exclude the film local shear.     

Laminar film condensation in tubes; calculation of local film resistance and local adiabatic mixing temperature

For combined gravity and shear forces between turbulent vapour and laminar condensate (co-current or counter-current flow) the local thickness of the film and its adiabatic mixing temperature were calculated.

For the accurate calculation of the film thickness the condensate viscosity profile was taken into account, resulting in three different reference temperatures for the viscosity.

For the calculation of the local adiabatic mixing temperature constant local condensate properties and a linear condensate temperature profile was assumed. Then, when taking gravity and shear forces into account the local mixing temperature is no longer constant (for given local wall and film surface temperatures) but a function of many variables.

From the analytical (though iterative) solution approximating equations were derived for the local film resistance, facilitating calculation “by hand”.     

Prediction of onset of boundary layer transition in film condensation on a horizontal elliptical cylinder

This article is devoted to a numerical study of prediction of the onset of the boundary layer transition in film condensation of pure saturated vapor on a horizontal elliptical tube, under the simultaneous effects of gravity, shear stress, and the imposed pressure gradients, caused by the vapor flow and curvature, on the condensate film. The inertia and convection terms are retained in the analysis. The hypothesis of Shekriladze and Gomelauri is used at the liquid-vapor interface. Outside the boundary layer, the vapor phase velocity is obtained from potential flow. Temperature, velocity distribution, and dimensionless apparent turbulent stress of the fully developed flow are carried out using the implicit Keller method. The effects of pressure gradients characterized by Froude number, ellipticity, and Bond number on the transition position have been evaluated. The transition criterion has been given in terms of the critical film Reynolds number ( {bf Re}_{bGamma} ) C .     

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.     

Numerical heat transfer analysis of laminar film condensation on a vertical fluted tube

The purpose of this study is to find a convenient and practical procedure for calculating heat transfer of laminar film condensation on a vertical fluted tube. The condensate film on the tube surface along the axial direction was divided into two portions: the initial portion and the developing portion. The developing portion was analyzed in details. The film thickness equation of condensate film over the crest and the momentum equation of condensate film in the trough were established respectively after some simplifications and coupled with two-dimensional thermal conduction equation. The relationship between the heat transfer rate and the length of the flute was obtained through solving the equations numerically. The present procedure was tested on a sinusoidal fluted tube. The amount of heat transfer rates Q_t of the tube were calculated at different temperature differences by using this procedure. The calculation was compared with the experimental data quoted. The results were in good agreement with a maximum deviation of 18%. So the present procedure is reliable and can be used in the parameter design of sinusoidal fluted tubes.     

Conjugate film condensation and natural convection along the interface between a porous and an open space

This paper reports a theoretical investigation focusing on the interaction between film condensation and natural convection along a vertical wall separating a fluid reservoir from a fluid-saturated porous reservoir. The two reservoirs are maintained at different temperatures. The study consists of two parts: in the first part the condensation phenomenon takes place in the fluid reservoir and the natural convection phenomenon in the porous layer. In the second part, the opposite situation is considered. The main heat transfer and flow characteristics in the two counterflowing layers, namely, the condensation film and the natural convection boundary layer are documented for a wide range of the problem parameters. These parameters appear after boundary layer scaling of the governing equations. Important engineering results regarding the overall heat flux from the condensation side to the natural convection side are summarized in the course of the study. Finally, the effect of the thermal resistance of the wall constituting the interface separating the two reservoirs, on the overall heat flux from the condensation side to the natural convection side is determined.