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.

Laminar Film Condensation on a Porous Vertical Wall With Uniform Suction Velocity

1964 ◽  
Vol 86 (4) ◽  
pp. 481-489 ◽  
Author(s):  
K. C. Jain ◽  
S. G. Bankoff
Keyword(s):  
Heat Capacity ◽  
Vertical Wall ◽  
Power Series Expansion ◽  
Porous Wall ◽  
Film Condensation ◽  
Suction Velocity ◽  
Laminar Film ◽  
Laminar Film Condensation ◽  
Constant Suction ◽  
Prandtl Numbers

A perturbation method developed by Chen for laminar film condensation on a vertical, constant-temperature wall, taking into account condensate subcooling and vapor drag, is refined and extended to the case where some of the condensate is sucked off at constant velocity through a porous wall. The refinement consists of a single, rather than a double, power-series expansion in the heat capacity and the acceleration parameters. The extension consists of an exact solution of the Nusselt problem with constant suction velocity, followed by a perturbation procedure to take into account the heat capacity and acceleration effects. The results show that substantial increases in heat transfer can be effected in this manner, especially at high Prandtl numbers.

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.

A Boundary-Layer Treatment of Laminar-Film Condensation

1959 ◽  
Vol 81 (1) ◽  
pp. 13-18 ◽  
Author(s):  
E. M. Sparrow ◽  
J. L. Gregg
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Prandtl Number ◽  
Vertical Plate ◽  
Film Condensation ◽  
Laminar Film ◽  
Laminar Film Condensation ◽  
Prandtl Numbers ◽  
Mathematical Techniques

The problem of laminar-film condensation on a vertical plate is attacked using the mathematical techniques of boundary-layer theory. Starting with the boundary-layer (partial differential) equations, a similarity transformation is found which reduces them to ordinary differential equations. Energy-convection and fluid-acceleration terms are fully accounted for. Solutions are obtained for values of the parameter cpΔT/hfg between 0 and 2 for Prandtl numbers between 1 and 100. These solutions take their place in the boundary-layer family along with those of Blasius, Pohlhausen, Schmidt and Beckmann, and so on. Heat-transfer results are presented. It is found that the Prandtl-number effect, which arises from retention of the acceleration terms, is very small for Prandtl numbers greater than 1.0. Low Prandtl number (0.003–0.03) heat-transfer results are given in Appendix 2, and a greater effect of the acceleration terms is displayed.

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.

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.

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