Entropy generation minimization of a heat and mass exchanger for use in a humidification-dehumidification desalination system

Abstract

The physical mechanisms of entropy generation in a condenser with high fractions of non-condensable gases are examined using control volume, 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. Control volume techniques are first employed, and shown to be ill-suited to understanding why and how balancing a heat and mass exchanger minimizes entropy generation. As a result, a more complex, boundary layer model is introduced; 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 non-condensable gases. Most previous studies of condensation have been restricted to a constant wall temperature, but it is shown here that for high concentrations of non-condensable gases, a varying wall temperature--obtained from balancing the heat and mass exchanger-greatly reduces total entropy generation rate. Further, it is found that the diffusion of the condensing vapor through the vapor-non-condensable 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. Finally, a rigorous, and general definition of balancing for any heat and mass exchanger is discussed.