An Inverse Design Problem of Estimating the Optimal Shape of Annular Fins Adhered to a Bare Tube of an Evaporator

Abstract

The optimum shapes for annular fins adhered to a bare tube are estimated in the present inverse design problem using the conjugate gradient method (CGM), based on the desired fin efficiency and fin volume. The shape of the annular fins adhered to the bare tube must be optimally designed to produce a greater cold-producing effect in the evaporator. One of the advantages of using the present inverse algorithm in this inverse design problem is that it can handle problems with a large number of unknown parameters easily and converge rapidly. The results obtained using the CGM to solve the inverse design problem are justified based on numerical experiments. The study shows that when the Biot number and fin volume are varied, the optimum fin efficiency and optimum fin shape will also change; however, the optimum shape of an annular fin can always be obtained, and its fin efficiency is always better than that of five common annular fins.