Optimal Design of Annular Fin Shapes with Temperature-Dependent Properties

Abstract

For many practical engineering applications, the thermal conductivity and heat transfer coefficient of the fin are function of temperatures and this makes the design problem nonlinear and complicated. In this study, the conjugate gradient method is used to design the optimal shape of the annular fins based on the desired fin efficiency and fin volume when the thermal properties are functions of temperature. The functional form of the optimum fin shape is not required before the estimation, and the optimum fin shape can be obtained through an iterative process with the conjugate gradient method. The results of this fin design problem are justified based on the numerical experiments. When the nonlinearity of the Biot numbers for the inner tube () as well as the thermal conductivities of the bare tube () and the annular fin () are varied, the optimum shape and efficiency of the dry annular fin remained almost the same. In addition, noticeable changes occur in the optimum fin efficiency and optimum fin shape as the Biot numbers for ambient air () produced variation. It implies that has the dominant influence on the optimum annular fin shape, rather than the other three thermal parameters.