A Nonlinear Fin Design Problem in Estimating the Optimal Shapes of Longitudinal and Spine Fully Wet Fins

Abstract

In the present nonlinear fully wet fin design problem, the optimum shapes for the longitudinal and spine fins are estimated by using the conjugate gradient method (CGM) based on the desired fin efficiency and fin volume. For many practical engineering applications, thermal conductivity and heat transfer coefficient of fin are a function of temperatures. This makes the design problem nonlinear and complicated. For this reason, the present work is focused on examining these kinds of design problems. The validity of this design algorithm using CGM to solve the nonlinear fin design problems are justified based on the numerical experiments. Results show that when the Biot number, relative humidity, and thermal conductivity are varied, the optimum fin efficiency and optimum fin shape are also subjected to change, and any reasonable designs for fully wet fins can always be obtained.

This work was supported in part through the National Science Council, R. O. C., Grant number, NSC-97-2221-E-262-MY3.