Shape optimization for the minimum volume of pin fins in simultaneous heat and mass transfer environments

A methodology for determining the optimum pin fin profile is introduced to minimize the fin volume for a constrained heat transfer rate under dehumidifying surface conditions. In this methodology, the mass transfer is evaluated using the polynomial variation of humidity ratio with temperature. A scheme is developed for solving the optimum conditions derived as a function of unknown temperature-dependent parameter and tip temperature under both the fully and partially wet surface conditions. The effect of psychrometric properties of the surrounding air on the optimum wet fin profile has been examined. The analysis presented in this study is pertinent to the dry, fully wet, and partially wet surface conditions. In every case study of optimum wet fins, the excess temperature at the tip vanishes with respect to the surrounding temperature. A non-linear temperature distribution in the optimum wet fin has been identified.