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Research Papers: Evaporation, Boiling, and Condensation

# Using Generalized Dimensional Analysis to Obtain Reduced Effective Model Equations for Condensation in Slender Tubes With Rotational Symmetry

[+] Author and Article Information
Andrea Dziubek

Assistant Professor
Department of Engineering,
Science, and Mathematics,
SUNY Institute of Technology,
Utica, NY 13502
e-mail: dziubea@sunyit.edu

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received February 12, 2012; final manuscript received December 27, 2012; published online April 9, 2013. Assoc. Editor: Louis C. Chow.

J. Heat Transfer 135(5), 051501 (Apr 09, 2013) (11 pages) Paper No: HT-12-1053; doi: 10.1115/1.4023350 History: Received February 12, 2012; Revised December 27, 2012

## Abstract

In this paper, we study the continuum physics model equations for condensation (two phase flow problems) in vertical tubes with small diameter and obtain reduced model equations. We found that generalization of dimensional analysis to multiple spatial dimensions is an excellent tool for that purpose, so that a review of this method is also part of the paper. We obtain the nondimensional numbers of the problem and derive reduced bulk and interface equations. The problem is characterized by three length scales, tube radius R, tube length L, and initial film thickness H. For small ratio $ɛ=H/L$, we derive a single ordinary differential equation for the condensate film thickness as function of axial position with tube radius as parameter, which agrees well with commonly used (parametric) models from literature. Our model is based on the physical dimensions of the problem which gives a greater geometrical flexibility and a wider range of applicability. We also discuss the effect of surface tension and the limit of the model.

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## Figures

Fig. 1

Vertical tube with condensate and vapor

Fig. 2

Wavy condensate film

Fig. 3

Water: Nusselt (84), ODE without (83), and with (82) surface tension

Fig. 4

Water: Nusselt (84), ODE without (83), and with (82) surface tension for d = 60 mm and d = 7 mm

Fig. 5

R134a: Nusselt (84), ODE without (83), and with (82) surface tension

Fig. 6

Local Nusselt number of Water and R134a

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