An analytical study has been made of the condensation of vapor onto falling rivulets of liquid which are constrained in lateral width by vertical non-wetting Teflon stripes on a flat metal heat-transfer surface. Under the condition studied it is shown that finite metal conduction plays a primary role in limiting the overall heat-transfer coefficient because in any system (drops or rivulets) where a triple point of metal, vapor, and liquid exists, the zero water path at the triple point would provide an unlimited conductance of heat were it not for finite metal conductivity or interfacial resistance. In the present paper, the temperature field and heat flow in a liquid rivulet and the underlying metal are computed using finite-difference methods. The metal plate is of constant thickness but the liquid rivulet is bounded by an arc of a circle as dictated by surface tension. The system involves two connected regions of different conductivity and shape, and the entire network is solved by an over-relaxation process taking into account the discontinuity in temperature gradient at the liquid-metal junction. Results are related to the practical application of such a system in desalination processes. The work was supported by the Office of Saline Water, Department of the Interior.

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