Laminar Film Condensation on a Porous Horizontal Tube With Uniform Suction Velocity

1965 ◽  
Vol 87 (1) ◽  
pp. 95-102 ◽  
Author(s):  
N. A. Frankel ◽  
S. G. Bankoff
Keyword(s):  
Heat Transfer ◽  
Perturbation Technique ◽  
Porous Plate ◽  
Horizontal Tube ◽  
Film Condensation ◽  
Suction Velocity ◽  
Uniform Suction ◽  
Laminar Film Condensation ◽  
Wide Range ◽  
Perturbation Parameters

The analysis of Bankoff and Jain [10] of film condensation on a vertical porous plate with uniform suction velocity is extended to the case of a horizontal porous tube. Integral momentum and energy balances are written for the system, including the effects of interface drag and condensate heat capacity, and the dimensionless equations are solved using a perturbation technique. All dependent variables are expressed in a double power series in the two perturbation parameters, ξ = kΔt/μλ (acceleration parameter) and α (dimensionless suction velocity), and the resulting equations are solved up to the second order perturbation. An asymptotic solution valid for high values of α is derived, and this solution together with the perturbation solution describes the system for a wide range of α. The case of heat transfer in a zero gravity field is treated, and the Nusselt number is found to be directly proportional to the suction velocity. Based on the results it is concluded that significant increases in heat transfer are possible with the use of suction.

Effect of Uniform Suction on Laminar Film Condensation on a Porous Vertical Wall

1970 ◽  
Vol 92 (2) ◽  
pp. 252-256 ◽  
Author(s):  
Ji Wu Yang
Keyword(s):  
Heat Transfer ◽  
Vertical Wall ◽  
Power Series Expansion ◽  
Porous Wall ◽  
Film Condensation ◽  
Condensation Rate ◽  
Suction Velocity ◽  
Uniform Suction ◽  
Laminar Film Condensation ◽  
Prandtl Numbers

The problem of film condensation on a porous wall has been solved by a boundary layer treatment. A dimensionless suction velocity parameter β, which is proportional to the uniform suction velocity vw and 1/4th the power of longitudinal coordinate (x1/4), is defined to characterize the process. The results are restricted to small values of β, as the solutions are given by power series expansion in β. The effects of uniform suction on heat transfer, condensation rate, film thickness, and velocity and temperature profiles are demonstrated through various examples. In general, uniform suction causes a substantial increase of heat transfer and condensation rate, especially at low subcooling and at high Prandtl numbers. The problem involves three governing parameters: subcooling, Prandtl number, and suction velocity. Comparison with the previous work of Jain and Bankoff is 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.

Mixed-Convection Laminar Film Condensation on an Inclined Elliptical Tube

2000 ◽  
Vol 123 (2) ◽  
pp. 294-300 ◽  
Author(s):  
M. Mosaad
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Circular Tube ◽  
Film Condensation ◽  
Equivalent Diameter ◽  
Laminar Film ◽  
Laminar Film Condensation ◽  
Wide Range ◽  
Convection Dominated ◽  
The Heat Transfer Coefficient

The present theoretical study concerns with mixed-convection laminar film condensation outside an inclined elliptical tube with isothermal surface. The assumptions used are as in the classical Nusselt-Rohsenow theory, however, with considering the interfacial vapor shear by extending a circular-tube shear model developed in a previous study. An equivalent diameter, based on equal surface area, is introduced in the analysis to enable comparison with circular tubes. For zero ellipticity, the approach simplifies to the circular tube model developed in our previous work. A numerical solution has been obtained for a wide range of the independent parameters. The results indicate that the heat transfer performance of the inclined elliptical tube enhances with the increase of tube ellipticity compared to an inclined circular tube of equivalent diameter. For forced-convection-dominated film condensation, the rate of this enhancement in the heat transfer coefficient is found smaller than that for pure-free-convection film.

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.

Superheated laminar film condensation on a nonisothermal horizontal tube

10.2514/3.931 ◽  
1997 ◽  
Vol 11 ◽  
pp. 526-532
Author(s):  
V. R. Murthy ◽  
Yu-An Lin ◽  
Steven W. O' ◽  
Hara Har ◽  
Sheng-An Yang
Keyword(s):  
Horizontal Tube ◽  
Film Condensation ◽  
Laminar Film ◽  
Laminar Film Condensation

Heat and Mass Transfer in an Incompressible Turbulent Boundary Layer

1972 ◽  
Vol 94 (1) ◽  
pp. 23-28 ◽  
Author(s):  
E. Brundrett ◽  
W. B. Nicoll ◽  
A. B. Strong
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Porous Plate ◽  
Mixing Length ◽  
Two Dimensional ◽  
Transfer Data ◽  
Incompressible Turbulent Boundary Layer ◽  
Wide Range ◽  
Incompressible Boundary

The van Driest damped mixing length has been extended to account for the effects of mass transfer through a porous plate into a turbulent, two-dimensional incompressible boundary layer. The present mixing length is continuous from the wall through to the inner-law region of the flow, and although empirical, has been shown to predict wall shear stress and heat transfer data for a wide range of blowing rates.

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.

scholarly journals Effect of endoscope on the peristaltic transport of a couple stress fluid with heat transfer: Application to biomedicine

2019 ◽  
Vol 8 (1) ◽  
pp. 619-629 ◽  
Author(s):  
K. Ramesh ◽  
M. Devakar
Keyword(s):  
Heat Transfer ◽  
Couple Stress ◽  
Medical Engineering ◽  
Horizontal Tube ◽  
Vertical Tube ◽  
Long Wavelength ◽  
Flow Parameters ◽  
Wide Range ◽  
Cylindrical Coordinate ◽  
Frictional Forces

Abstract In this investigation, we have studied the problem of peristaltic flow with heat transfer through the gap between coaxial inclined tubes where the inner tube is rigid and the outer tube has sinusoidal wave travelling down its wall. The problem has been formulated in cylindrical coordinate system. The equations governing the flow have been simplified under the long wavelength and low Reynolds number assumptions. The exact solution is obtained for the temperature profile. The perturbation solutions for the velocity and pressure gradient are obtained for small couple stress parameter. Pressure difference per wavelength and frictional forces on the tube walls have been computed numerically. Results are demonstrated for various flow parameters. The better pumping results occur in vertical tube, while less pumping is seen in horizontal tube. The size of trapped bolus is small in triangular wave as compared to other waves. The present study has a wide range of applications in bio-medical engineering like the transport phenomenon in peristaltic micro pumps.

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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