An analysis of simultaneous condensation inside and evaporation outside a horizontal conduit has been performed for various shapes of conduits. The study is aimed at improving the performance of horizontal evaporator-condenser water desalination units by establishing the most promising shape. Comparison of various shapes indicates that vertically oriented elongated elliptical conduits yield the highest overall heat transfer coefficients. The effects of intermittent removal of the condensate film by internal horizontal films decreases as the vertical to horizontal axis ratio increases. Effect of non-condensables are included in the analysis.