Optimal Shape of Non-Linear Partially Wet Annular Fins for Maximum Efficiency

Cheng-Hung Huang,Yun-Lung Chung

doi:10.3390/en14040844

Abstract

Heat exchangers with annular finned-tube type and partially wetted condition are utilized widely in engineering systems, such as air-conditioning systems and refrigeration systems. In addition, the physical properties of fin materials should be considered as functions of temperature in reality and thus become a non-linear problem. Based on the above two conditions, an optimal partially wet annular fin design problem, with temperature-dependent thermal properties of the fin, to yield optimal fin efficiency was investigated in the present work, which has not been examined previously and it is the novelty of this study. An iterative regularization algorithm using the conjugate gradient method (CGM) is considered as the optimization tool based on the desired fin efficiency under a fixed fin volume constraint. The partially wet annular fin condition can result if the relative humidity of surrounding air is between 80 and 90%. Finally, the optimal fin shape, with the highest computed efficiency among examined fins under identical operational conditions, can be obtained. It is found that when the Biot numbers for ambient air (Bia) and relative humidity (φ) increased, the optimum computed fin efficiency and interfacial radius between wet and dry fin domains (rwd) will be increased, and the estimated optimum fin shape also changed. However, the shape of optimal fin remained approximately unchanged when the Biot numbers for the inner tube (Bii), the thermal conductivities of the tube (kw) and fin (kf) varied. It reveals that Bii, kw and kf have an insignificant influence on the optimal shape of the annular fin in a partially wet condition.

Highlights

Depending on the dew point of the surrounding air, fin base temperature, and boundary temperature, the fin surface conditions can be classified as dry, partially wet, or fully wet
The aim of this study was to estimate the optimal shapes for partially wet annular fins under the condition that kw, kf, Biot numbers for the inner tube (Bii), and Biot numbers for ambient air (Bia) of the fin are functions of temperature
In the present fin design problem, an iterative algorithm of conjugate gradient method (CGM) is utilized, and the minimization process is based on Φ and V

Summary

Introduction

Depending on the dew point of the surrounding air, fin base temperature, and boundary temperature, the fin surface conditions can be classified as dry, partially wet, or fully wet. For the case of condensers, the fin surface temperature is generally below the dew point temperature; as a result, heat and mass transfer occur simultaneously, and the fin surface is partially wetted. The physical properties of fin and tube materials are considered functions of temperature, in reality, the investigation of non-linear design problem becomes important. An optimal partially wet annular fin design problem with temperature-dependent physical properties of fin materials is investigated in this study and the fin efficiency can be improved. Charters and Theerakulpisut [1] examined the efficiency equations for constant-thickness annular fins. They have derived a simplified relationship to compute the fin efficiency of a specified annular fin. Kern and Kraus [7] reported the investigation of the optimum design of wetted fin surfaces

Objectives

Results

Conclusion