An analytic solution of the film thickness of laminar film condensation on inclined pipes

The present work investigates an analytical study on the problem of laminar film condensation on a nanosphere. Due to the microscale interaction, the problem is analyzed by taking into account the effects of slip in velocity and jump in temperature. A relation is derived for the liquid film thickness in the form of a nonlinear differential equation which is solved numerically using the fourth order Runge–Kutta method. Finally, the effect of velocity slip and temperature jump on different condensation parameters including the liquid film thickness, velocity and temperature profiles, Nusselt number, and liquid mass flow rate is discussed. It is found that the increase in the velocity slip and temperature jump results in a thinner liquid film and therefore increases the heat transfer coefficient.

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Effect of Vapour Drag on Laminar Film Condensation on a Vertical Rectangular Fin

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/pime_proc_1993_207_099_02 ◽

1993 ◽

Vol 207 (1) ◽

pp. 63-69

Author(s):

H Kazeminejad

Keyword(s):

Heat Transfer ◽

Film Thickness ◽

Transfer Rate ◽

Relative Effect ◽

Film Condensation ◽

Friction Drag ◽

Condensate Film ◽

Fin Efficiency ◽

Laminar Film ◽

Laminar Film Condensation

A simple theory is presented for laminar film condensation of a pure vapour on a vertical rectangular fin which takes account of drag induced on the liquid film by the flow of the condensing vapour. Under these conditions, the governing conjugate differential equations for the fin and condensate flow are solved numerically to determine the fin temperature and condensate film thickness distributions. For the range of parameters investigated, it was found that the reduction in condensate thermal resistance due to vapour shear significantly enhances the heat-transfer rate to the fin and decreases the fin efficiency. The model also provides a clear picture of the relative effect of the gravity force, friction drag and momentum drag on the performance of the fin.

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

Journal of Heat Transfer ◽

10.1115/1.4046307 ◽

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.

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