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

• Main Authors: Yun-LungChung, 鍾昀龍
• Other Authors: Cheng-Hung Huang
• Format: Others
• Language: en_US
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/283296

博士 === 國立成功大學 === 系統及船舶機電工程學系 === 104 === This dissertation is intended to find an optimum shape and fin efficiency of annular fin adhere to the bare tube of evaporator for the air conditioner when considering the thermal properties of fin are either constant or temperature-dependent. It uses the conjugate gradient method (CGM) of inverse heat conduction problem to design an optimum annular fin based on the desired fin efficiency and fin volume. The amount of vapor in the ambient air influences fin shape a lot, as a result, it needs to consider the specific humidity when the optimum annular fin shape is designed. There are three types of annular fin surfaces including dry, fully wet and partially wet, respectively. In order to find the temperature distribution on bare tube and the fin, the finite difference method is utilized. Based on the temperature difference between the fin and the surrounding air, the heat flux and the efficiency of annular fin can be calculated in the dry, fully wet and partially wet conditions. This dissertation consists six chapters. Chapter 1 is the preface as stated above. Chapter 2 shows the computational procedure of the inverse problem in determining the linear optimal annular fin shapes by using the conjugate gradient method under dry, fully wet and partially wet conditions. It clearly illustrates the direct problem, sensitivity problem, adjoint problem and gradient equation and leads to an objection function and fin efficiency equation. On the above process of numerical computation, the thermal conductivities kf and kw and Biot numbers Bii, Bio and Bia are considered constants. Chapter 3 introduces the computation procedure to estimate nonlinear dry, fully wet and partially wet optimum annular fin shapes by assuming the thermal conductivities kf and kw, Biot numbers Bii and Bia are temperature-dependent. The CGM is utilized to solve the present nonlinear inverse design problem. Chapter 4 illustrates the numerical results for the optimal shapes and fin efficiency for linear annular fin under the dry, fully wet and partially wet conditions based on the desired fin volume and fin efficiency by using different Biot numbers Bii and Bia, fin volume V, conductivity ratio G and relative humidity. The technique of optimal fin design problem can indeed obtain the maximum fin efficiency when compared with five common annular fins. Annular finned-tube heat exchangers are widely used in applications of air-conditioning and refrigeration systems. Besides, the thermal parameters of the fin are also function of temperatures in many practical engineering applications. Based on the above stated two conditions a nonlinear optimum annular fin design problem is considered in Chapter 5. The conjugate gradient method (CGM) is utilized as the optimization algorithm based on the desired fin efficiency and fin volume. The numerical experiments show that the optimum annular fin has the highest fin efficiency among six annular fins with the same operating fin conditions. When the Biot numbers for ambient air (Bia) varied, the optimum fin efficiency and optimum fin shape of the nonlinear annular fin also changed. However, when the Biot numbers for the inner tube (Bii), the thermal conductivities of the bare tube (kw) and the annular fin (kf) varied, the optimum fin shape remained almost the same. This implies that Bii, kw and kf have a limited influence on the optimum annular fin shape. Based on the above studies it can be concluded that the conjugate gradient method (CGM) with iterative regularization process is applied successfully to the fin design problem to estimate the optimum shape of annular fins with constant and temperature-dependent thermal parameters.