Convective filmwise condensation on the outer surface of a vertical tube : a theoretical analysis

In this study, laminar filmwise condensation on the outer surface of a vertical tube in the presence of a flowing vapor is theoretically investigated. Analytical solution is obtained for the condensation on an isothermal tube wall when the film thickness is much smaller than the tube radius. The presence of vapor shear stress acting on the liquid-vapor interface was found to enhance the condensation heat transfer by accelerating the condensate film flow. The shearing enhancement factor increases almost linearly with the increase in vapor velocity. In addition, the influence of the vapor shear also increases with the reduction in the tube radius. The combined effect of surface tension and vapor velocity on the condensation heat transfer characteristics of the vertical tube was also investigated. From our investigation, it was determined that the surface tension has negligible effect on the condensation heat transfer performance of mini- and macro-size tubes. However, the influence of the surface tension becomes prominent for condensation on micro-size tubes. The influence of the Kelvin effect was also studied and it was found that the Kelvin effect is insignificant for condensation on micro-size tubes or tubes of larger sizes. A conjugate heat transfer analysis was also performed with cooling water flowing in the internal tube channel and flowing vapor condensation on the outer tube surface. In this analysis, the variation in the tube wall temperature was considered. A good comparison between our theoretical model and experimental results was achieved. The condensation heat transfer coefficient decreases as the cooling water velocity increases. The condensation heat transfer coefficient predicted for countercurrent flow configuration is larger than that for cocurrent flow configuration. The condensation heat transfer coefficients of both cocurrent and countercurrent configurations are larger than those where the tube wall is isothermal. For both cocurrent and countercurrent flow configurations, the thermal resistance lies mainly on conduction through the tube wall and convection of cooling water at the inlet condensing region whereas the dominant thermal resistance gradually shifts to the condensate film as the distance increases from the top of the tube. The tube wall temperature is affected by a combined effect of the thermal resistance distribution and the variation in the overall temperature difference.Ministry of Education (MOE)Nanyang Technological UniversityNational Research Foundation (NRF)This research is supported by the National Research Foundation, Singapore, under its Green Data Centre Research Programme (NRF2015ENC-GDCR01001-010). The second author would like to acknowledge the financial support for his research appointment at the University of Illinois at Urbana-Champaign, USA under the College of Engineering (CoE) International Postdoctoral Fellowship Scholarship (IPS) provided jointly by the Ministry of Education, Singapore and Nanyang Technological University, Singapore