On the Similarity Solution for Condensation Heat Transfer

2009 ◽  
Vol 131 (11) ◽  
Author(s):  
Gunnar Tamm ◽  
Daisie D. Boettner ◽  
Bret P. Van Poppel ◽  
Michael J. Benson ◽  
A. Özer Arnas
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Film Thickness ◽  
Transfer Coefficient ◽  
Analytical Solutions ◽  
Similarity Solution ◽  
Vertical Plate ◽  
Film Condensation ◽  
Laminar Film Condensation

Analytical solutions for laminar film condensation on a vertical plate are integral to many heat transfer applications, and have therefore been presented in numerous refereed articles and in most heat transfer textbooks. Commonly made assumptions achieve the well known similarity solution for the Nusselt number, heat transfer coefficient, and film thickness. Yet in all of these studies, several critical assumptions are made without justifying their use. Consequently, for a given problem one cannot determine whether these restrictive assumptions are actually satisfied, and thus, how these conditions can be checked for validity of the results. This study provides a detailed solution that clarifies these points.

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.

Flow Regimes for Laminar Film Condensation on a Vertical Plate With an Upward Vapor Flow

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Kentaro Kanatani
Keyword(s):  
Nusselt Number ◽  
Film Thickness ◽  
Average Nusselt Number ◽  
Vertical Plate ◽  
Film Condensation ◽  
Integral Model ◽  
Vapor Flow ◽  
Plate Length ◽  
Laminar Film ◽  
Laminar Film Condensation

Abstract Laminar film condensation on a vertical plate with an upward vapor flow is studied. An approximate integral model of the condensate film and the boundary layer of the vapor is numerically solved, taking into account both gravity and interfacial shear. Here, three types of solution are examined: (i) zero film thickness at the bottom; (ii) zero flowrate with a finite film thickness at the bottom; and (iii) negative flowrates at the bottom. The film thickness and the average Nusselt number are shown as functions of the distance along the plate and the plate length, respectively. The terminal lengths of the solutions of the types (i) and (ii) are calculated against the degree of the subcooling. Moreover, the results are compared with those derived using the approximation method where the shearing stress on the vapor–liquid interface is composed of only the momentum transferred by the suction mass (the Shekriladze–Gomelauri approach). It is found that the average Nusselt number is well described by the Shekriladze–Gomelauri model in the range of the solution type (ii), while the average Nusselt number for the thinnest-film solution of the type (iii) is asymptotically consistent with the Shekriladze–Gomelauri value for long plates.

Film Condensation of Saturated Vapor Over Horizontal Noncircular Tubes With Progressively Increasing Radius of Curvature Drawn in the Direction of Gravity

2004 ◽  
Vol 126 (6) ◽  
pp. 906-914 ◽  
Author(s):  
Arijit Dutta ◽  
S. K. Som ◽  
P. K. Das
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Surface Area ◽  
Circular Tube ◽  
Saturated Vapor ◽  
Film Condensation ◽  
Radius Of Curvature ◽  
Equivalent Diameter

A theoretical study has been made to determine the heat transfer coefficient in film condensation of slowly downward flowing saturated vapor over horizontal noncircular tubes with progressively increasing radius of curvature drawn in the direction of gravity. The noncircular tube profile considered for the present work, is an equiangular spiral described by a curve in polar coordinate as Rp=aemθ (a and m being parametric constants). Nusselt number in case of noncircular tube has been determined on the basis of an equivalent diameter of a circular tube that equals the surface area of the noncircular tube with that of the circular one. It has been recognized that both the local Nusselt number Nuθ and average Nusselt number Nu¯ become a function of m, Ra/Ja1/4 and Nσ=σ/ρ−ρgR2. An enhancement in heat transfer coefficient has been observed in case of a noncircular tube over that of a circular tube of same surface area because of the combined effect of gravity force component and surface tension driven favourable pressure gradient in the direction of flow of the liquid film. The relative weightage of both the components in the enhancement of heat transfer has been reported. An estimation of pressure drop of cooling liquid flowing through the circular and noncircular tubes of same surface area has been made to compare the values against the enhancement in heat transfer rate.

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.

scholarly journals Experimental Estimation of Temporal and Spatial Resolution of Coefficient of Heat Transfer in a Channel Using Inverse Heat Transfer Method

2019 ◽  
Author(s):  
Majid Karami ◽  
Somayeh Davoodabadi Farahani ◽  
Farshad Kowsary ◽  
Amir Mosavi
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Spatial Resolution ◽  
Time History ◽  
Inverse Technique ◽  
Inverse Heat Transfer ◽  
Temporal And Spatial ◽  
Transfer Method

In this research, a novel method to investigation the transient heat transfer coefficient in a channel is suggested experimentally, in which the water flow, itself, is considered both just liquid phase and liquid-vapor phase. The experiments were designed to predict the temporal and spatial resolution of Nusselt number. The inverse technique method is non-intrusive, in which time history of temperature is measured, using some thermocouples within the wall to provide input data for the inverse algorithm. The conjugate gradient method is used mostly as an inverse method. The temporal and spatial changes of heat flux, Nusselt number, vapor quality, convection number, and boiling number have all been estimated, showing that the estimated local Nusselt numbers of flow for without and with phase change are close to those predicted from the correlations of Churchill and Ozoe (1973) and Kandlikar (1990), respectively. This study suggests that the extended inverse technique can be successfully utilized to calculate the local time-dependent heat transfer coefficient of boiling flow.

Effect of Open Micro-Channels on External Condensation Heat Transfer

2016 ◽  
Author(s):  
Brandon Hulet ◽  
Andres Martinez ◽  
Melanie Derby ◽  
Amy Rachel Betz
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Film Thickness ◽  
Transfer Coefficient ◽  
Heat Fluxes ◽  
Condensation Heat Transfer ◽  
Dropwise Condensation ◽  
Micro Channels ◽  
Lower Heat ◽  
The Heat Transfer Coefficient

This research experimentally investigates the heat transfer performance of open-micro channels under filmwise condensation conditions. Filmwise condensation is an important factor in the design of steam condensers used in thermoelectric power generation, desalination, and other industrial applications. Filmwise condensation averages five times lower heat transfer coefficients than those present in dropwise condensation, and filmwise condensation is the dominant condensation regime in the steam condensers due to a lack of a durable dropwise condensation surface. Film thickness is also of concern because it is directly proportional to the condenser’s overall thermal resistance. This research focuses on optimizing the channel size to inhibit the creation of a water film and/or to reduce its overall thickness in order to maximize the heat transfer coefficient of the surface. Condensation heat transfer was measured in three square channels and a plane surface as a control. The sizes of the square fins were 0.25 mm; 0.5 mm; and 1 mm, and tests were done at a constant pressure of 6.2 kPa. At lower heat fluxes, the 0.25mm fins perform better, whereas at larger heat fluxes a smooth surface offers better performance. At lower heat fluxes, droplets are swept away by gravity before the channels are flooded. Whereas, at higher heat fluxes, the channels are flooded increasing the total film thickness, thereby reducing the heat transfer coefficient.

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.

Convective Heat Transfer Coefficient and Pressure Drop of Al2O3-Water Nanofluid in a Single-Phase Microchannel for Cooling of High Heat Output Devices

2008 ◽  
Author(s):  
Guillermo E. Valencia ◽  
Miguel A. Ramos ◽  
Antono J. Bula
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Pressure Drop ◽  
Transfer Coefficient ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Convective Heat Transfer Coefficient ◽  
Heat Output ◽  
Flux Boundary Condition

The paper describes an experimental procedure performed to obtain the convective heat transfer coefficient of Al2O3 nanofluid working as cooling fluid under turbulent regimen through arrays of aluminum microchannel heat sink having a diameter of 1.2 mm. Experimental Nusselt number correlation as a function of the volume fractions, Reynolds, Peclet and Prandtl numbers for a constant heat flux boundary condition is presented. The correlation for Nusselt number has a good agreement with experimental data and can be used to predict heat transfer coefficient for this specific nanofluid, water/Al2O3. Furthermore, the pressure drop is also analyzed considering the different nanoparticles concentration.

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