Entropy generation in condensation in the presence of high concentrations of noncondensable gases

The physical mechanisms of entropy generation in a condenser with high fractions of noncondensable gases are examined using scaling and boundary layer techniques, with the aim of defining a criterion for minimum entropy generation rate that is useful in engineering analyses. This process is particularly relevant in humidification-dehumidification desalination systems, where minimizing entropy generation per unit water produced is critical to maximizing system performance. The process is modeled by a consideration of the vapor/gas boundary layer alone, as it is the dominant thermal resistance and, consequently, the largest source of entropy production in many practical condensers with high fractions of noncondensable gases. Most previous studies of condensation have been restricted to a constant wall temperature, but it is shown here that for high concentrations of noncondensable gases, a varying wall temperature greatly reduces total entropy generation rate. Further, it is found that the diffusion of the condensing vapor through the vapor/noncondensable mixture boundary layer is the larger and often dominant mechanism of entropy production in such a condenser. As a result, when seeking to design a unit of desired heat transfer and condensation rates for minimum entropy generation, minimizing the variance in the driving force associated with diffusion yields a closer approximation to the minimum overall entropy generation rate than does equipartition of temperature difference.