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

  • 鍾 昀龍

Student thesis: Doctoral Thesis


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
Date of Award2016 Aug 30
Original languageEnglish
SupervisorCheng-Hung Huang (Supervisor)

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