Analytical study on design analysis of annular fins under dehumidifying conditions with a polynomial relationship between humidity ratio and saturation temperature

The governing equation of wet fins is a function of two dependent variables, namely, temperature and specific humidity. For the solution of this, it is customary to convert a single variable. From the properties of humid air, the relationship between specific humidity of saturated air on the fin surface and the corresponding fin surface temperature varies psychrometrically and hence this process follows along the saturation curve in the psychrometric chart. Using regression analysis, it can be expressed as a function of cubic polynomial in temperature. With adapting this relationship, the governing equation of wet annular fins converts into a high degree of nonlinear equation. An analytical method, namely, differential transformation has been proposed to determine the temperature field in wet fins of rectangular and triangular geometries. The thermal performances are evaluated for a wide range of thermo-psychrometric parameters. The optimization study has also been demonstrated to determine the optimum design variables with the variation of possible design constants. Finally, a comparative study has also been made between the present and published results, and for every case study, superiority of results obtained from the present model is noticed and the degree of supremacy increases with the increase in condensation rate of vapor on fin surfaces.