The determination of optimum shapes for fully wet annular fins for maximum efficiency

A fin design problem to determine the optimum shapes of fully wet annular fins adhered to a bare tube based on the desired fin efficiency and fin volume is examined in the present study using an iterative regularization process with the conjugate gradient method (CGM). One of the advantages of applying the CGM in this design problem lies in that the optimal functional form of the fin shape does not need be given before the estimation, the optimal fin shape can be obtained automatically during the iteration process. It is assumed that the surrounding air has an assumed relative humidity of 100% and this will result in the condition of a fully wet annular fin. The results obtained from the numerical experiments using the CGM method are examined to justify the validity of the present inverse design problem. The numerical results show that when the Biot number, conductivity ratio and fin volume are varied, the optimum fin efficiency and the fin shape of the fully annular fin also change. Finally it is concluded that the optimal fin shapes can yield maximum efficiency and this implies that more heat can be dissipated into environment using the present optimal fins.