Two-Phase Heat Transfer in Thermosyphon Evacuated-Tube Solar Collectors

1989 ◽  
Vol 111 (4) ◽  
pp. 292-297 ◽  
Author(s):  
Karen R. Den Braven
Keyword(s):  
Heat Transfer ◽  
Surface Waves ◽  
Film Surface ◽  
Detailed Examination ◽  
Film Condensation ◽  
Condensation Process ◽  
Two Phase ◽  
Number Range ◽  
Laminar Film Condensation ◽  
Evacuated Tube

This work analyzes the heat transfer within a tilted thermosyphon and its use in a heat pipe evacuated-tube solar collector. A detailed examination is made of the laminar film condensation process, including the effects of interfacial shear due to the moving vapor. Effects of film surface waves are later included. Including the shear term in the constitutive equations changes the predicted film thickness in the condenser portion of the device by less than one percent, depending on location along the surface. This change causes only a slight increase in the predicted heat transfer. Accounting for surface waves increases the heat transfer rate 10 percent to 50 percent in the Reynolds number range studied. The condenser results are combined with a simple trough model for the evaporator portion of the thermosyphon to give the effective heat-transfer coefficient for the entire tube. Predicted performances of the condenser, the evaporator, and the entire tube compare favorably with available data.

Numerical Investigation of Laminar Filmwise Condensation of Water Vapor in Horizontal Tube With VOF Method in the Presence of Air

2014 ◽  
Author(s):  
Zhan Yin ◽  
Jianjun Wen ◽  
Min Zeng ◽  
Qiuwang Wang
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Volume Fraction ◽  
Horizontal Tube ◽  
Vof Method ◽  
Film Condensation ◽  
Interface Temperature ◽  
Condensation Process ◽  
Laminar Film Condensation

A steady three-dimensional numerical simulation of laminar film condensation of vapor in the presence of air inside a 1 mm horizontal tube is presented. The volume of fluid (VOF) method is used to capture the liquid-vapor interface with a phase change model. According to a generally accepted flow regime map, annular flow pattern is to be expected. Uniform wall temperature and interface temperature are assumed to be boundary condition. The influence of gravity is obvious while the effect of surface tension is neglected. At inlet, the liquid film is thin and evenly distributed around tube wall. Moving downstream the tube, film at the bottom half becomes thicker under the influence of gravity, while film on upper half remains almost constant. Correspondingly, local heat transfer coefficient on bottom half declines gradually and global average heat transfer coefficient shows little difference along axial direction. Existence of air makes heat transfer coefficient decrease sharply compared with that of pure vapor condensation, caused by an existed air layer which increases the thermal resistance during condensation process. As inlet volume fraction of air increases from 0.5% to 3%, the decline trend of heat transfer coefficient slows down.

Laminar Condensation Heat Transfer on a Horizontal Cylinder

1959 ◽  
Vol 81 (4) ◽  
pp. 291-295 ◽  
Author(s):  
E. M. Sparrow ◽  
J. L. Gregg
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Numerical Solutions ◽  
Horizontal Cylinder ◽  
Film Condensation ◽  
Number Range ◽  
Laminar Film Condensation ◽  
Layer Analysis ◽  
Inertia Forces

A boundary-layer analysis is made for laminar film condensation on a horizontal cylinder. The formulation includes both the inertia forces and energy convection terms, which are neglected in Nusselt’s simple theory. A similarity transformation, valid over most of the cylinder, is found which reduces the partial differential equations of the problem (the conservation laws) to ordinary differential equations. Numerical solutions of the resulting ordinary differential equations are available for the Prandtl number range from 0.003 to 100. Heat-transfer results are presented and discussed.

An Analytical Study of Laminar Film Condensation: Part 2—Single and Multiple Horizontal Tubes

1961 ◽  
Vol 83 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Michael Ming Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Horizontal Tube ◽  
Vertical Tube ◽  
Film Condensation ◽  
Transfer Coefficients ◽  
Inertia Effects ◽  
Horizontal Tubes ◽  
Laminar Film ◽  
Laminar Film Condensation

The boundary-layer equations for laminar film condensation are solved for (a) a single horizontal tube, and (b) a vertical bank of horizontal tubes. For the single-tube case, the inertia effects are included and the vapor is assumed to be stationary outside the vapor boundary layer. Velocity and temperature profiles are obtained for the case μvρv/μρ ≪ 1 and similarity is found to exist exactly near the top stagnation point, and approximately for the most part of the tube. Heat-transfer results computed with these similar profiles are presented and discussed. For the multiple-tube case, the analysis includes the effect of condensation between tubes, which is shown to be partly responsible for the high observed heat-transfer rate for vertical tube banks. The inertia effects are neglected due to the insufficiency of boundary-layer theory in this case. Heat-transfer coefficients are presented and compared with experiments. The theoretical results for both cases are also presented in approximate formulas for ease of application.

Some Reflections On Sparrow's Work On Similarity Solutions for Laminar Film Condensation On a Vertical Plate

2021 ◽  
Author(s):  
Vijay K. Dhir
Keyword(s):  
Heat Transfer ◽  
Vertical Plate ◽  
Generalized Solution ◽  
Similarity Solutions ◽  
Film Condensation ◽  
Gravitational Acceleration ◽  
Curved Surfaces ◽  
Laminar Film ◽  
Laminar Film Condensation ◽  
Variable Gravity

Abstract In this contribution in honor of Late Prof. E. M. Sparrow, we reflect on the pioneering work of Sparrow and Gregg on the development of similarity solutions for laminar film condensation on a vertical plate. Dhir and Lienhard using this work as a basis developed a generalized solution for isothermal curved surfaces on which gravitational acceleration varied along the surface and for variable gravity situations. Subsequently non-isothermal surfaces were also considered. These studies were publisher earlier in the J. Heat Transfer.

Laminar Film Condensation From a Steam-Air Mixture Undergoing Forced Flow Down a Vertical Surface

1971 ◽  
Vol 93 (3) ◽  
pp. 297-304 ◽  
Author(s):  
V. E. Denny ◽  
A. F. Mills ◽  
V. J. Jusionis
Keyword(s):  
Liquid Film ◽  
Numerical Solution ◽  
Finite Difference Methods ◽  
Vertical Surface ◽  
Forced Flow ◽  
Film Condensation ◽  
Two Phase ◽  
Noncondensable Gas ◽  
Laminar Film ◽  
Laminar Film Condensation

An analytical study of the effects of noncondensable gas on laminar film condensation of vapor under going forced flow along a vertical surface is presented. Due to the markedly nonsimilar character of the coupled two-phase-flow problem, the set of parabolic equations governing conservation of momentum, species, and energy in the vapor phase was solved by means of finite-difference methods using a forward marching technique. Interfacial boundary conditions for the numerical solution were extracted from a locally valid Nusselt-type analysis of the liquid-film behavior. Locally variable properties in the liquid were treated by means of the reference-temperature concept, while those in the vapor were treated exactly. Closure of the numerical solution at each step was effected by satisfying overall mass and energy balances on the liquid film. A general computer program for solving the problem has been developed and is applied here to condensation from water-vapor–air mixtures. Heat-transfer results, in the form q/qNu versus x, are reported for vapor velocities in the range 0.1 to 10.0 fps with the mass fraction of air ranging from 0.001 to 0.1. The temperature in the free stream is in the range 100–212 deg F, with overall temperature differences ranging from 5 to 40 deg F. The influence of noncondensable gas is most marked for low vapor velocities and large gas concentrations. The nonsimilar character of the problem is especially evident near x = 0, where the connective behavior of the vapor boundary layer is highly position-dependent.

Condensation of Steam on Finned Surfaces With Addition of a Surfactant

2005 ◽  
Author(s):  
Andrew T. Morrison ◽  
S. M. You
Keyword(s):  
Heat Transfer ◽  
Surface Energy ◽  
Reynolds Numbers ◽  
Film Condensation ◽  
Vapor Flow ◽  
Flow Conditions ◽  
Two Phase ◽  
Enhancement Of Heat Transfer ◽  
Flat Surfaces ◽  
Extended Surfaces

A fundamental knowledge of the parameters affecting film condensation is essential for the design of two phase heat exchangers. The current study examines the effect of extended surfaces and surface energy modifications and their interaction for condensation of steam in quiescent and vapor flow conditions. The enhancement of heat transfer for vertical, flat surfaces and two finned surfaces were compared for Reynolds numbers ranging from approximately 10 to 50. The addition of a nonionic surfactant, alcohol alkoxylate, to the system was evaluated for the same surfaces and vapor field conditions. Vapor flow of 0.25 m/s enhanced the heat transfer approximately 40%, while 0.5 m/s vapor velocity produced almost 100% increase in heat transfer. The addition of surfactant to the system produced small enhancement in heat transfer except in the case of condensate hold-up between the fins. In this case, the addition of surfactant increase the heat transfer an additional 25%, likely because the vapor flow and change of surface energy were sufficient to largely eliminate the hold-up of condensate between the fins.

Analysis of Two-Phase, One-Component Stratified Flow With Condensation

1966 ◽  
Vol 88 (3) ◽  
pp. 265-272 ◽  
Author(s):  
C. E. Rufer ◽  
S. P. Kezios
Keyword(s):  
Horizontal Tube ◽  
Liquid Interface ◽  
Film Condensation ◽  
Bulk Liquid ◽  
Tube Radius ◽  
Two Phase ◽  
Laminar Film Condensation ◽  
Level Data ◽  
Energy And Momentum ◽  
Special Case

A physical model is constructed for the stratified two-phase flow pattern with annular, laminar film condensation superimposed and the equivalent mathematical model is analyzed. Utilizing the principle of conservation of mass, energy, and momentum, an equation is derived which gives the slope of the vapor-bulk liquid interface along the tube. By varying the flow rate, inclination of the tube, tube radius, and film temperature difference, the effect of these variables on the flow level is illustrated in a typical example. A special case of this equation, namely, that describing the vapor-liquid interface when the rate of condensation is zero, is compared with several recent empirical horizontal tube holdup correlations and with flow-level data of Gazley for stratified air-water flow.

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