目录 前言 第1章绪论 1 1.1引言 1 1.2有限时间热力学的产生、内涵和研究内容 2 1.2.1有限时间热力学的产生与发展 2 1.2.2有限时间热力学的物理内涵 6 1.2.3有限时间热力学的研究内容 7 1.3熵产生最小化理论的产生和物理内涵 9 1.3.1熵产生最小化理论的产生与发展 9 1.3.2熵产生最小化理论的物理内涵 12 1.4*理论的产生、内涵和研究内容 15 1.4.1*理论的产生与发展 15 1.4.2*理论的物理内涵 17 1.4.3*理论的研究内容 18 1.5广义热力学优化理论的产生和研究内容 19 1.5.1广义热力学优化理论的产生与发展 19 1.5.2广义热力学优化理论的研究内容 20 1.6传热过程动态优化现状 24 1.6.1牛顿传热规律下相关研究 24 1.6.2传热规律的影响 26 1.7传质过程动态优化现状 27 1.8电容器充电和电池做功电路动态优化现状 28 1.8.1电容器充电过程相关研究 28 1.8.2原电池放电过程相关研究 29 1.9贸易过程动态优化现状 29 1.10本书的主要工作及章节安排 30 第2章传热过程动态优化 32 2.1引言 32 2.2普适传热规律下传热过程熵产生最小化 32 2.2.1物理模型 32 2.2.2优化方法 34 2.2.3其他传热策略 34 2.2.4特例分析 35 2.2.5数值算例与讨论 37 2.3热漏对传热过程熵产生最小化的影响 40 2.3.1物理模型 40 2.3.2优化方法 42 2.3.3其他传热策略 43 2.3.4特例分析 44 2.3.5数值算例与讨论 50 2.4普适传热规律下传热过程烟耗散最小化 59 2.4.1物理模型 59 2.4.2优化方法 60 2.4.3特例分析 61 2.4.4数值算例与讨论 63 2.5传热过程嫵耗散最小逆优化 70 2.5.1物理模型 70 2.5.2优化方法 71 2.5.3特例分析与讨论 72 2.6热漏对传热过程搬耗散最小化的影响 75 2.6.1物理模型 75 2.6.2优化方法 76 2.6.3特例分析 77 2.6.4数值算例与讨论 80 2.7液-固相变传热过程嫩耗散最小化 91 2.7.1物理模型 91 2.7.2优化方法 93 2.7.3其他传热策略 95 2.7.4数值算例与讨论 98 2.8本章小结 100 第3章传质过程动态优化 102 3.1引言 102 3.2普适传质规律下等温节流过程积耗散最小化 103 3.2.1物理模型 103 3.2.2优化方法 104 3.2.3其他传质策略 105 3.2.4特例分析 106 3.2.5数值算例与讨论 109 3.3普适传质规律下单向等温传质过程积耗散最小化 114 3.3.1物理模型 114 3.3.2优化方法 117 3.3.3其他传质策略 117 3.3.4特例分析 119 3.3.5数值算例与讨论 122 3.4存在质漏的单向等温传质过程熵产生最小化 127 3.4.1物理模型 127 3.4.2优化方法 128 3.4.3特例分析 129 3.4.4数值算例与讨论 131 3.5质漏对单向等温传质过程积耗散最小化的影响 134 3.5.1物理模型 134 3.5.2优化方法 135 3.5.3特例分析 135 3.5.4数值算例与讨论 137 3.6扩散传质规律下等摩尔双向等温传质过程积耗散最小化 141 3.6.1物理模型 141 3.6.2优化方法 142 3.6.3其他传质策略 144 3.6.4数值算例与讨论 145 3.7普适传质规律下等温结晶过程熵产生最小化 147 3.7.1物理模型 147 3.7.2优化方法 148 3.7.3其他传质策略 149 3.7.4特例分析 149 3.7.5数值算例与讨论 152 3.8普适传质规律下等温结晶过程积耗散最小化 154 3.8.1物理模型 154 3.8.2优化方法 155 3.8.3特例分析 155 3.8.4数值算例与讨论 156 3.9本章小结 159 第4章电容器充电和电池做功电路动态优化 160 4.1引言 160 4.2非线性RC电路最优充电过程 162 4.2.1物理模型 162 4.2.2优化方法 163 4.2.3特例分析与讨论 166 4.3存在旁通电阻器的RC电路非线性电容器最优充电过程 173 4.3.1物理模型 173 4.3.2优化方法 173 4.3.3特例分析与讨论 174 4.4存在旁通电阻器的LRC电路非线性电容器最优充电过程 179 4.4.1物理模型 179 4.4.2优化方法 180 4.4.3特例分析与讨论 181 4.5具有内耗散的非线性电容电池最大输出功 186 4.5.1物理模型 186 4.5.2优化方法 187 4.5.3特例分析与讨论 188 4.6复杂反应燃料电池最优电流路径 197 4.6.1物理模型 197 4.6.2优化方法 202 4.6.3数值算例与讨论 207 4.7本章小结 212 第5章贸易过程动态优化 214 5.1引言 214 5.2一类简单贸易过程资本耗散最小化 214 5.2.1物理模型 214 5.2.2优化方法 219 5.2.3其他交易策略 220 5.2.4特例分析 221 5.2.5数值算例与讨论 224 5.3商品流漏对贸易过程资本耗散最小化的影响 229 5.3.1物理模型 229 5.3.2优化方法 230 5.3.3特例分析与讨论 232 5.4本章小结 234 第6章广义流传递过程动态优化 235 6.1引胃 235 6.2广义流传递过程的广义耗散最小化 236 6.2.1物理模型 236 6.2.2优化结果 237 6.2.3应用 239 6.3广义流漏对广义流传递过程广义耗散最小化的影响 245 6.3.1物理模型 245 6.3.2优化结果 246 6.3.3应用 246 6.4本章小结 249 第7章电容器充电电路实验研究 250 7.1实验装置与实验方法 250 7.2实验结果分析 252 7.3本章小结 255 第8章全书总结 256 参考文献 260 附录A最优化理论概述 297 A.1引言 297 A.2静态优化 298 A.2.1无约束函数极值优化 298 A.2.2仅含等式约束函数极值优化 299 A.2.3含不等式约束函数极值优化 300 A.3动态优化 301 A.3.1古典变分法 302 A.3.2极小值原理 307 A.3.3动态规划 310 A.3.4平均最优控制理论 316 A.4本附录小结 318 附录B第6章相关公式推导 319 B.16.2节中定理的证明 319 B.1.1欧拉44格朗日方程方法 319 B.1.2平均最优控制理论方法 321 B.2 6.3节中定理的证明 321 B.2.1欧拉格朗日方程方法 321 B.2.2平均最优控制理论方法 323 附录C主要符号说明 324 Contents Preface Chapter 1 Introduction 1 1.1Introduction 1 1.2The emergence, connotation and research contents of finite time thermodynamics 2 1.2.1The emergence and development of finite time thermodynamics 2 1.2.2The physical connotation of finite time thermodynamics 6 1.2.3The research contents of finite time thermodynamics 7 1.3The emergence and connotation of entropy generation minimization theory 9 1.3.1The emergence and development of entropy generation minimization theory 9 1.3.2The physical connotation of entropy generation minimization theory 12 1.4The emergence, connotation and research contents of entransy theory 15 1.4.1The emergence and development of entransy theory 15 1.4.2The physical connotation of entransy theory 17 1.4.3The research contents of entransy theory 18 1.5The emergence and research contents of generalized thermodynamic optimization theory 19 1.5.1The emergence and development of generalized thermodynamic optimization theory 19 1.5.2The research contents of generalized thermodynamic optimization theory 20 1.6The dynamic-optimization status of heat transfer processes 24 1.6.1The cases with Newtonian heat transfer law 24 1.6.2Effects of heat transfer laws 26 1.7The dynamic-optimization status of mass transfer processes 27 1.8The dynamic-optimization status of capacitor charging processes and power battery circuits 28 1.8.1Capacitor charging processes 28 1.8.2Primary battery discharging processes 29 1.9The dynamic-optimization status of resource exchange processes 29 1.10The major work and chapters’ arrangement of this book 30 Chapter 2 Dynamic-Optimization of Heat Transfer Processes 32 2.1Introduction 32 2.2Entropy generation minimization of heat transfer processes with a generalized heat transfer law 32 2.2.1Physical model 32 2.2.2Optimization method 34 2.2.3Other heat transfer strategies 34 2.2.4Analyses for special cases 35 2.2.5Numerical examples and discussions 37 2.3Effect of heat leakage on the entropy generation minimization of heat transfer processes 40 2.3.1Physical model 40 2.3.2Optimization method 42 2.3.3Other heat transfer strategies 43 2.3.4Analyses for special cases 44 2.3.5Numerical examples and discussions 50 2.4Thermal entransy dissipation minimization of heat transfer processes with a generalized heat transfer law 59 2.4.1Physical model 59 2.4.2Optimization method 60 2.4.3Analyses for special cases 61 2.4.4Numerical examples and discussions 63 2.5An inverse optimization for minimizing thermal entransy dissipation during heat transfer processes 70 2.5.1Physical model 70 2.5.2Optimization method 71 2.5.3Analyses for special cases and discussions 72 2.6Effect of heat leakage on the thermal entransy dissipation minimization of heat transfer processes 75 2.6.1Physical model 75 2.6.2Optimization method 76 2.6.3Analyses for special cases 77 2.6.4Numerical examples and discussions 80 2.7Thermal entransy dissipation minimization of liquid-solid phase- changeheat transfer processes 91 2.7.1Physical model 91 2.7.2Optimization method 93 2.7.3Other heat transfer strategies 95 2.7.4Numerical examples and discussions 98 2.8Chapter summary 100 Chapter 3 Dynamic-Optimization of Mass Transfer Processes 102 3.1Introduction 102 3.2Mass entransy dissipation minimization of isothermal throttling processes with a generalized mass transfer law 103 3.2.1Physical model 103 3.2.2Optimization method 104 3.2.3Other mass transfer strategies 105 3.2.4Analyses for special cases 106 3.2.5Numerical examples and discussions 109 3.3Mass entransy dissipation minimization of one-way isothermal mass transfer processes with a generalized mass transfer law 114 3.3.1Physical model 114 3.3.2Optimization method 117 3.3.3Other mass transfer strategies 117 3.3.4Analyses for special cases 119 3.3.5Numerical examples and discussions 122 3.4Entropy generation minimization of one-way isothermal mass transfer processes with mass leakage 127 3.4.1Physical model 127 3.4.2Optimization method 128 3.4.3Analyses for special cases 129 3.4.4Numerical examples and discussions 131 3.5Effect of mass leakage on the mass entransy dissipation minimization of one-way isothermal mass transfer processes 134 3.5.1Physical model 134 3.5.2Optimization method 135 3.5.3Analyses for special cases 135 3.5.4Numerical examples and discussions 137 3.6Mass entransy dissipation minimization of equimolar two-way isothermal mass-diffusion process with diffusive mass transfer law 141 3.6.1Physical model 141 3.6.2Optimization method 142 3.6.3Analyses for special cases 144 3.6.4Numerical examples and discussions 145 3.7Entropy generation minimization of isothermal crystallization processes with a generalized mass transfer law 147 3.7.1Physical model 147 3.7.2Optimization method 148 3.7.3Other mass transfer strategies 149 3.7.4Analyses for special cases 149 3.7.5Numerical examples and discussions 152 3.8Mass entransy dissipation minimization of isothermal crystallization processes with the generalized mass transfer law 154 3.8.1Physical model 154 3.8.2Optimization method 155 3.8.3Analyses for special cases 155 3.8.4Numerical examples and discussions 156 3.9Chapter summary 159 Chapter 4 Dynamic-Optimization of Capacitor Charging Processes and Power Battery Circuits 160 4.1Introduction 160 4.2Optimal capacitor charging processes in nonlinear RC circuits 162 4.2.1Physical model 162 4.2.2Optimization method 163 4.2.3Analyses for special cases and discussions 166 4.3Optimal capacitor charging process of a nonlinear capacitor in RC circuit with bypass resistor 173 4.3.1Physical model 173 4.3.2Optimization method 173 4.3.3Analyses for special cases and discussions 174 4.4Optimal capacitor charging process of a nonlinear capacitor in LRC circuit with bypass resistor 179 4.4.1Physical model 179 4.4.2Optimization method 180 4.4.3Analyses for special cases and discussions 181 4.5Maximum work output of a battery with nonlinear equivalent capacitance and internal dissipation 186 4.5.1Physical model 186 4.5.2Optimization method 187 4.5.3Analyses for special cases and discussions 188 4.6Optimal current paths of fuel cells with a class of complex chemical reactions 197 4.6.1Physical model 197 4.6.2Optimization method 202 4.6.3Numerical examples and discussions 207 4.7Chapter summary 212 Chapter 5 Dynamic-Optimization of Resource Exchange Processes 214 5.1Introduction 214 5.2Capital dissipation minimization of a common of resource exchange processes 214 5.2.1Physical model 214 5.2.2Optimization method 219 5.2.3Other exchange strategies 220 5.2.4Analyses for special cases 221 5.2.5Numerical examples and discussione 224 5.3 Effect of commodity flow leakage on the capital dissipation minimization of resource exchange processes 229 5.3.1Physical model 229 5.3.2Optimization method 230 5.3.3Analyses for special cases and discussione 232 5.4Chapter summary 234 Chapter 6 Dynamic-Optimization of Generalized Flow Transfer Processes 235 6.1Introduction 235 6.2Generalized dissipation minimization of generalized flow transfer processes 236 6.2.1Physical model 236 6.2.2Optimization results 237 6.2.3Applications 239 6.3Effect of generalized flow leakage on the generalized dissipation minimization of generalized flow transfer processes 245 6.3.1Physical model 245 6.3.2Optimization results 246 6.3.3Applications 246 6.4Chapter summary 249 Chapter 7 Experimental Research onthe Capacitor Charging Circuit 250 7.1Experimental setup and experiment method 250 7.2Analysis for experiment results 252 7.3Chapter summary 255 Chapter 8 Book summary 256 References 260 Appendix A An Overview of Optimization Theory 297 A. 1Introduction 297 A.2Static optimization 298 A.2.1Function extremum optimization with no constraint 298 A.2.2Function extremum optimization with equality constraints 299 A.2.3Function extremum optimization with inequality constraints 300 A.3Dynamic optimization 301 A.3.1Classical variational method 302 A.3.2 The minimum extreme principle 307 A.3.3Dynamic programming 310 A.3.4Average optimal control theory 316 A.4Appendix A summary 318 Appendix B The Derivations for the Related Formulas in Chapter 6 319 B.1The proof of theorem in Section 6.2 319 B.1.1The method of Euler-Lagrange equation 319 B. 1.2The method of average optimal control theory 321 B.2The proof of theorem in Section 6.3 321 B.2.1The method of Euler-Lagrange equation 321 B.2.2The method of average optimal control theory 323 Appendix C Nomenclature 324
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