火积及其在传热优化中的应用
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摘要
自然界众多的运动都是沿着“用力最小”的途径进行,在物理学上表现为许多物理现象遵循最小作用量原理。本文试图将此原理引入传热学中,传热学目的是研究热量传递的规律及其快慢,本文寻求传热过程中的最小作用量原理,并在其基础上对传热过程进行优化,使热量沿着“用力最小”的途径传递。
首先对非平衡热力学中最低能量耗散原理和最小熵产原理进行了分析,发现它们所要求的热流与温度之间的关系与傅立叶定律不一致。这是因为熵和熵产是描述热功转换的热力学参数,熵产对应的是可用能的损失,所以基于最低能量耗散原理和最小熵产原理来分析和优化热量传递过程是值得讨论的。
对于满足傅立叶定律的传热问题,本文提出了一个新的物理量:火积,用它表征物体(系统)传递热量的总能力。在可逆过程中,火积 是守恒的,不发生热量传递能力的耗散。对于不可逆传热过程,热量从高温流向低温处,会产生火积 耗散,使热量传递能力降低。在火积 这个物理量的基础上,采用加权余量法建立了传热学中的火积 极值原理,包括温度表述的最小火积 原理和热流表述的最小火积 原理。火积 极值原理完整描述了满足傅立叶定律的传热问题,它等效于傅立叶定律、能量守恒方程和边界条件等传热过程所需满足的方程和条件。
针对传热优化过程,根据火积 极值原理提出了火积 耗散极值原理。在给定热流求最小温差时满足温度表述的最小火积 耗散原理,在给定温差求最大热流时满足热流表述的最大火积 耗散原理。采用火积 耗散极值原理对体点问题进行优化的结果优于熵产最小原则,原因在于火积 耗散极值原理的优化目标是提高热量传递的效率,而熵产最小原则的目标是减少可用能的损失。同时,体点问题中导热系数的优化结果证明了导热仿生优化方法中的优化原则:温度梯度均匀性原则。
最后采用加权余量法,对力表述和流表述的最低能量耗散原理进行了补充和修正,建立了完整描述可用能传递过程的变分原理。同时对最低能量耗散原理和最小熵产原理之间的关系进行了分析,结果表明最小熵产原理不是独立的,它只是最低能量耗散原理在特定条件下的一种表现形式。
Many motions in nature take the easiest or minimum paths, which are described in physics by the principles of least action. The subject of heat transfer is to investigate the nature of heat transport phenomena, especially the heat transfer rate. Therefore, the principle of least action in heat transfer is studied and new principles are developed. Based on the principles, the heat transfer process is optimized to maximize the heat transfer rate, so that the heat flux is controlled to flow along the easiest or quickest path for the given conditions.
Firstly, two extremum principles in non-equilibrium thermodynamics, the principle of least dissipation of energy and the principle of minimum entropy production, are analyzed. The linear phenomenological law for heat flux and temperature is found to be different from the Fourier Law because entropy and entropy production are the thermodynamic properties to measure the conversion efficiency of heat to work. The entropy production corresponds to the loss of available energy. Therefore, based on the conception of entropy, principle of least dissipation of energy and the principle of minimum entropy production are unavailable for the analysis or the optimization of the heat transfer rate.
For the heat transfer process following the Fourier Law, a new special word, “entranspy”, is created to define a new physical property, which means the overall capability of heat transport. In reversible process, there is the entranspy conservation, that is, no loss of capability of heat transport. However, in irreversible process where the heat flows from high temperature to low temperature, the entranspy should be dissipated and the heat transport capability should be reduced. Based on the concept of entranspy, the principle of extremum entranspy is developed by the weighted residual method, which includes the principle of minimum entranspy in the temperature representation and the principle of minimum entranspy in the heat flux representation. The principle of extremum entranspy renders the heat transfer process completely, that is, the principle is equivalent to the Fourier Law, energy
conservation equation and the boundary conditions.
According to the principle of extremum entranspy, the principle of extremum entranspy dissipation is presented for heat transfer enhancement. The principle of extremum entranspy dissipation includes two principles, which correspond to the two goals of heat transfer enhancement respectively. When the enhancement aims to minimize the temperature difference for given heat flux, the optimization follows the principle of minimum entranspy dissipation in temperature representation. Alternatively, when the enhancement maximizes the heat flux for given temperature difference, the optimization follows the principle of maximum entranspy dissipation in heat flux representation.
Then, the principle of extremum entranspy dissipation is applied to optimize the volume-to-point problem. Both the theoretical and numerical results show higher heat transfer rate than those obtained by the method of entropy generation minimization. The comparison shows that the principle of extremum entranspy dissipation is to maximize the heat transfer rate, while the entropy generation minimization is to minimize the loss of available energy. At the same time, the result of the principle of extremum entranspy dissipation is characterized by the uniform temperature-gradient, which is exactly the principle to optimize the distribution of high conductivity material in bionic optimization method.
Finally, the weighted residual method is also applied to modify and complete the principle of least dissipation of energy to represent the transport process of available energy. Then the relation between the principle of least dissipation of energy and the principle of minimum entropy production is analyzed. The result shows that the minimum entropy production is not an independent principle but a reformulation of the principle of least dissipation of energy for special cases.
首先对非平衡热力学中最低能量耗散原理和最小熵产原理进行了分析,发现它们所要求的热流与温度之间的关系与傅立叶定律不一致。这是因为熵和熵产是描述热功转换的热力学参数,熵产对应的是可用能的损失,所以基于最低能量耗散原理和最小熵产原理来分析和优化热量传递过程是值得讨论的。
对于满足傅立叶定律的传热问题,本文提出了一个新的物理量:火积,用它表征物体(系统)传递热量的总能力。在可逆过程中,火积 是守恒的,不发生热量传递能力的耗散。对于不可逆传热过程,热量从高温流向低温处,会产生火积 耗散,使热量传递能力降低。在火积 这个物理量的基础上,采用加权余量法建立了传热学中的火积 极值原理,包括温度表述的最小火积 原理和热流表述的最小火积 原理。火积 极值原理完整描述了满足傅立叶定律的传热问题,它等效于傅立叶定律、能量守恒方程和边界条件等传热过程所需满足的方程和条件。
针对传热优化过程,根据火积 极值原理提出了火积 耗散极值原理。在给定热流求最小温差时满足温度表述的最小火积 耗散原理,在给定温差求最大热流时满足热流表述的最大火积 耗散原理。采用火积 耗散极值原理对体点问题进行优化的结果优于熵产最小原则,原因在于火积 耗散极值原理的优化目标是提高热量传递的效率,而熵产最小原则的目标是减少可用能的损失。同时,体点问题中导热系数的优化结果证明了导热仿生优化方法中的优化原则:温度梯度均匀性原则。
最后采用加权余量法,对力表述和流表述的最低能量耗散原理进行了补充和修正,建立了完整描述可用能传递过程的变分原理。同时对最低能量耗散原理和最小熵产原理之间的关系进行了分析,结果表明最小熵产原理不是独立的,它只是最低能量耗散原理在特定条件下的一种表现形式。
Many motions in nature take the easiest or minimum paths, which are described in physics by the principles of least action. The subject of heat transfer is to investigate the nature of heat transport phenomena, especially the heat transfer rate. Therefore, the principle of least action in heat transfer is studied and new principles are developed. Based on the principles, the heat transfer process is optimized to maximize the heat transfer rate, so that the heat flux is controlled to flow along the easiest or quickest path for the given conditions.
Firstly, two extremum principles in non-equilibrium thermodynamics, the principle of least dissipation of energy and the principle of minimum entropy production, are analyzed. The linear phenomenological law for heat flux and temperature is found to be different from the Fourier Law because entropy and entropy production are the thermodynamic properties to measure the conversion efficiency of heat to work. The entropy production corresponds to the loss of available energy. Therefore, based on the conception of entropy, principle of least dissipation of energy and the principle of minimum entropy production are unavailable for the analysis or the optimization of the heat transfer rate.
For the heat transfer process following the Fourier Law, a new special word, “entranspy”, is created to define a new physical property, which means the overall capability of heat transport. In reversible process, there is the entranspy conservation, that is, no loss of capability of heat transport. However, in irreversible process where the heat flows from high temperature to low temperature, the entranspy should be dissipated and the heat transport capability should be reduced. Based on the concept of entranspy, the principle of extremum entranspy is developed by the weighted residual method, which includes the principle of minimum entranspy in the temperature representation and the principle of minimum entranspy in the heat flux representation. The principle of extremum entranspy renders the heat transfer process completely, that is, the principle is equivalent to the Fourier Law, energy
conservation equation and the boundary conditions.
According to the principle of extremum entranspy, the principle of extremum entranspy dissipation is presented for heat transfer enhancement. The principle of extremum entranspy dissipation includes two principles, which correspond to the two goals of heat transfer enhancement respectively. When the enhancement aims to minimize the temperature difference for given heat flux, the optimization follows the principle of minimum entranspy dissipation in temperature representation. Alternatively, when the enhancement maximizes the heat flux for given temperature difference, the optimization follows the principle of maximum entranspy dissipation in heat flux representation.
Then, the principle of extremum entranspy dissipation is applied to optimize the volume-to-point problem. Both the theoretical and numerical results show higher heat transfer rate than those obtained by the method of entropy generation minimization. The comparison shows that the principle of extremum entranspy dissipation is to maximize the heat transfer rate, while the entropy generation minimization is to minimize the loss of available energy. At the same time, the result of the principle of extremum entranspy dissipation is characterized by the uniform temperature-gradient, which is exactly the principle to optimize the distribution of high conductivity material in bionic optimization method.
Finally, the weighted residual method is also applied to modify and complete the principle of least dissipation of energy to represent the transport process of available energy. Then the relation between the principle of least dissipation of energy and the principle of minimum entropy production is analyzed. The result shows that the minimum entropy production is not an independent principle but a reformulation of the principle of least dissipation of energy for special cases.
引文
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