Film Condensation in Horizontal Triangular Section Microchannels: A Theoretical Model

2004 ◽  
Author(s):  
Huasheng Wang ◽  
John W. Rose
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Shear Stress ◽  
Theoretical Model ◽  
Channel Wall ◽  
Horizontal Tube ◽  
Film Condensation ◽  
General Behaviour ◽  
Condensate Film ◽  
Local Mean

The paper presents a theoretical model to predict film condensation heat transfer from a vapor flowing in a horizontal tube with equilateral triangular section minichannels or microchannels. The model is based on fundamental analysis which assumes laminar condensate flow on the channel walls and takes account of surface tension, vapor shear stress and gravity. The case considered here is where the channel wall temperature is uniform and the vapor is saturated at inlet. Sample numerical results are given for the channel size (side of triangle) of 1.0 mm and for refrigerant R134a. The general behaviour of the condensate flow pattern (spanwise and streamwise profiles of the condensate film), as well as streamwise variation in quality and local mean (over section perimeter) heat-transfer coefficient, are qualitatively in accord with expectations on physical grounds.

A Theory of Film Condensation in Horizontal Noncircular Section Microchannels

2005 ◽  
Vol 127 (10) ◽  
pp. 1096-1105 ◽  
Author(s):  
Hua Sheng Wang ◽  
John W. Rose
Keyword(s):  
Heat Transfer ◽  
Channel Wall ◽  
Interfacial Shear Stress ◽  
Interfacial Shear ◽  
Film Condensation ◽  
Transfer Coefficients ◽  
Condensate Film ◽  
Heat Transfer Coefficients ◽  
Flow Parameters ◽  
Local Mean

The paper presents a theoretical model to predict film condensation heat transfer from a vapor flowing in horizontal square and equilateral triangular section minichannels or microchannels. The model is based on fundamental analysis which assumes laminar condensate flow on the channel walls and takes account of surface tension, interfacial shear stress, and gravity. Results are given for channel sizes (side of square or triangle) in the range of 0.5–5 mm and for refrigerants R134a, R22, and R410A. The cases considered here are where the channel wall temperature is uniform and the vapor is saturated at the inlet. The general behavior of the condensate flow pattern (spanwise and streamwise profiles of the condensate film), as well as streamwise variation of local mean (over section perimeter) heat-transfer coefficient and vapor mass quality, are qualitatively in accord with expectations on physical grounds. The magnitudes of the calculated heat-transfer coefficients are in general agreement with experimental data for similar, but nonidentical, channel geometry and flow parameters.

Numerical Modeling of the Conjugate Heat Transfer Problem for Annular Laminar Film Condensation in Microchannels

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Stefano Nebuloni ◽  
John R. Thome
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Wall Temperature ◽  
Conjugate Heat Transfer ◽  
Channel Wall ◽  
Transfer Problem ◽  
Film Condensation ◽  
Laminar Film Condensation

This paper presents numerical simulations of annular laminar film condensation heat transfer in microchannels of different internal shapes. The model, which is based on a finite volume formulation of the Navier–Stokes and energy equations for the liquid phase only, importantly accounts for the effects of axial and peripheral wall conduction and nonuniform heat flux not included in other models so far in the literature. The contributions of the surface tension, axial shear stresses, and gravitational forces are included. This model has so far been validated versus various benchmark cases and versus experimental data available in literature, predicting microchannel heat transfer data with an average error of 20% or better. It is well known that the thinning of the condensate film induced by surface tension due to gravity forces and shape of the surface, also known as the “Gregorig” effect, has a strong consequence on the local heat transfer coefficient in condensation. Thus, the present model accounts for these effects on the heat transfer and pressure drop for a wide variety of geometrical shapes, sizes, wall materials, and working fluid properties. In this paper, the conjugate heat transfer problem arising from the coupling between the thin film fluid dynamics, the heat transfer in the condensing fluid, and the heat conduction in the channel wall has been studied. In particular, the work has focused on three external channel wall boundary conditions: a uniform wall temperature, a nonuniform wall heat flux, and single-phase convective cooling are presented. As the scale of the problem is reduced, i.e., when moving from mini- to microchannels, the results show that the axial conduction effects can become very important in the prediction of the wall temperature profile and the magnitude of the heat transfer coefficient and its distribution along the channel.

Numerical Modeling of the Conjugate Heat Transfer Problem for Annular Laminar Film Condensation in Microchannels

2009 ◽  
Author(s):  
Stefano Nebuloni ◽  
John R. Thome
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Heat Flux ◽  
Conjugate Heat Transfer ◽  
Channel Wall ◽  
Transfer Problem ◽  
Film Condensation ◽  
Laminar Film Condensation ◽  
Micro Channels ◽  
Uniform Wall

This paper presents numerical simulations of annular laminar film condensation heat transfer in micro-channels of different internal shapes. The model, which is based on a finite volume formulation of the Navier-Stokes and energy equations for the liquid phase only, importantly accounts for the effects of axial and peripheral wall conduction and non-uniform heat flux not included in other models so far in the literature. The contributions of the surface tension, axial shear stresses and gravitational forces are included. This model has so far been validated versus various benchmark cases and versus experimental data available in literature, predicting microchannel heat transfer data with an average error of 20% or better. It is well-known that the thinning of the condensate film induced by surface tension due to gravity forces and shape of the surface, also known as the ‘Grigorig’ effect, has a strong consequence on the local heat transfer coefficient in condensation. Thus, the present model accounts for these effects on the heat transfer and pressure drop for a wide variety of geometrical shapes, sizes, wall materials and working fluid properties. In this paper, the conjugate heat transfer problem arising from the coupling between the thin film fluid dynamics, the heat transfer in the condensing fluid and the heat conduction in the channel wall has been studied. In particular, the work has focused on three external channel wall boundary conditions: a uniform wall temperature, a non uniform wall heat flux and single-phase convective cooling is presented. As the scale of the problem is reduced, i.e. when moving from mini to micro channels, the results shows that the axial conduction effects can become very important in the prediction of the wall temperature profile and the magnitude of the heat transfer coefficient and its distribution along the channel.

Turbulent Film Condensation on a Nonisothermal Horizontal Tube

2005 ◽  
Vol 21 (4) ◽  
pp. 235-242 ◽  
Author(s):  
Yan-Ting Lin ◽  
Sheng-An Yang
Keyword(s):  
Heat Transfer ◽  
Temperature Variation ◽  
Wall Temperature ◽  
Film Flow ◽  
Horizontal Tube ◽  
Film Condensation ◽  
Condensate Film ◽  
Uniform Wall Temperature ◽  
System Pressure ◽  
Uniform Wall

AbstractA simple model has been developed for the study of turbulent film condensation from downward flowing vapors onto a horizontal circular tube with variable wall temperature. The interfacial shear at the vapor condensate film is evaluated with the help of Colburn analogy. The condensate film flow and local/or mean heat transfer characteristics from a horizontal tube with non-uniform temperature variation under the effect of Froude number, sub-cooling parameter and system pressure parameter has been conducted. Although the non-uniform wall temperature variation has an appreciable influence on the local film flow and heat transfer; however, the dependence of mean heat transfer on the non-uniform wall temperature variation is almost negligible.

Condensation in Microchannels: Detailed Comparisons of Annular Laminar Flow Theory With Measurements

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Hua Sheng Wang ◽  
John W. Rose
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Film Thickness ◽  
Surface Temperature ◽  
Local Heat ◽  
Film Condensation ◽  
Experimental Investigations ◽  
Condensate Film ◽  
Laminar Film Condensation ◽  
Local Quality

A relatively simple theory of annular laminar film condensation in microchannels, based on the Nusselt approximations for the condensate film and a theoretically based approximation for the vapor shear stress, has no empirical input and gives the local heat transfer coefficient and local quality for given vapor mass flux and vapor–surface temperature difference distribution along the channel. As well as streamwise vapor shear stress and gravity, the theory includes transverse (to the flow direction) surface tension-driven motion of the condensate film and gives a differential equation for the local (transverse and streamwise) condensate film thickness. As well as four transverse direction boundary conditions due to condensate surface curvature, a streamwise boundary condition is required as in the Nusselt theory. When the vapor is saturated or superheated at inlet, this is provided by the fact that the film thickness is zero around the channel perimeter at the position of onset on condensation. Most experimental investigations have been conducted with quality less than one at inlet and only approximate comparisons, discussed in earlier papers, can be made. The present paper is devoted to comparisons between theory and measurements in investigations where local heat flux and channel surface temperature were measured and the vapor at inlet was superheated. Measured and calculated heat transfer coefficients and their dependence on distance along the channel and on local quality are in surprisingly good agreement and suggest that the mode of condensation is, in fact, annular and laminar, at least where the quality is high.

Condensation of a Vapor Flowing Inside a Horizontal Rectangular Duct

1995 ◽  
Vol 117 (2) ◽  
pp. 418-424 ◽  
Author(s):  
Q. Lu ◽  
N. V. Suryanarayana
Keyword(s):  
Heat Transfer ◽  
Shear Stress ◽  
Heat Transfer Coefficient ◽  
Film Thickness ◽  
Transfer Coefficient ◽  
Interfacial Shear Stress ◽  
Interfacial Shear ◽  
Rectangular Duct ◽  
Interfacial Waves ◽  
Condensate Film

Condensation of a vapor flow inside a horizontal rectangular duct, using the bottom plate as the only condensing surface, was experimentally investigated. The experimental measurements included condensate film thickness and heat transfer coefficients with R-113 and FC-72. The condensate film thickness, measured with an ultrasonic transducer, was used to obtain the local heat transfer coefficient. The heat transfer coefficient increased with increasing inlet vapor velocity. The rate of increase was enhanced noticeably after the appearance of interfacial waves. Within the limited range of the experimental variables, a correlation between St and RegL was developed by a linear regression analysis. However, because of the effect of the interfacial waves, instead of a single correlation for the entire range of RegL, two separate equations (one for the wave-free regime and another for the regime with waves) were found. Analytical predictions of heat transfer rates in the annular condensation regime require the proper modeling of the interfacial shear stress. A properly validated interfacial shear stress model with condensation is not yet available. The measurement of condensate film thickness at several axial locations opens the door for determining the local interfacial stress and, hence, a model for the interfacial shear stress.

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.

Film Condensation of Refrigerant-113 and Ethanediol on a Horizontal Tube—Effect of Vapor Velocity

1984 ◽  
Vol 106 (3) ◽  
pp. 524-530 ◽  
Author(s):  
W. C. Lee ◽  
S. Rahbar ◽  
J. W. Rose
Keyword(s):  
Heat Transfer ◽  
Ethylene Glycol ◽  
Horizontal Tube ◽  
Low Pressure ◽  
Film Condensation ◽  
Vapor Velocity

Heat transfer measurements are reported for condensation of refrigerant-113 and ethanediol (ethylene glycol) on a single horizontal tube with vertical downflow. For refrigerant-113, vapor velocities up to around 6 m/s were obtained, while for ethanediol, velocities in excess of 100 m/s were obtained at low pressure. The results are compared with those of earlier investigators and with theory.

Experimental Study of Film Condensation From Steam-Air Mixtures Flowing Downward Over a Horizontal Tube

1974 ◽  
Vol 96 (1) ◽  
pp. 83-88 ◽  
Author(s):  
J. W. Rauscher ◽  
A. F. Mills ◽  
V. E. Denny
Keyword(s):  
Heat Transfer ◽  
Experimental Study ◽  
Theoretical Analysis ◽  
Mass Fraction ◽  
Horizontal Tube ◽  
Forced Flow ◽  
Film Condensation ◽  
Air Mass ◽  
Average Value ◽  
Pure Steam

Experiments have been performed to study the effects of air on filmwise condensation from steam-air mixtures undergoing forced flow over a 3/4 in. OD horizontal tube. Local condensation rates at the stagnation point are reported for saturation temperatures of 100–150 deg F, bulk to wall temperature differences of 3–30 deg F, bulk air mass fraction 0–7 percent and oncoming vapor velocity 1–6 ft/sec. For pure steam the average value of q/qNu, where qNu is the Nusselt result, was 0.98 ± 0.10, which compares favorably with the value of 1.04 predicted by a theory which accounts for vapor drag. For steam-air mixtures the reduction in heat transfer was found to be in excellent agreement with the theoretical analysis of Denny and South; the average discrepancy in q/qNu was −2.7 percent, while the maximum was 7.1 percent.

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