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摘要：从导热微分方程出发推导出了一般情况下平均温度随时间的变化规律，它是对能量守恒定律的反映。由初边值条件的积分形式给出了第二类边界条件下平均温度的表达式，并推出边界热流一定时的平均温度与时间呈线性关系，绝热边界条件下的平均温度不随时间变化。 Abstract. The variation of average temperature with time in general case is derived by the differential equation of heat conduction, it is the reflection of the conservation of energy principle. The average temperature was expressed by the integral form of initial and boundary conditions under the second boundary condition. The average temperature has linear relationship with time when the boundary heat flux is constant and it does not change with time under the adiabatic boundary condition. 引言 在工程实际中，往往需要知道生产设备或所加工材料所处的温度状态，以便对生产加工过程进行控制。但是，非稳态导热问题的解析求解是非常复杂的，尤其是形状不规则物体的高维导热问题。这时在生产要求许可的情况下，我们可以分析物体平均温度随时间的变化规律。顾祥红针对无限长圆柱体和圆球物体，提出了非稳态导热的平均温度集总参数分析法。由于平均温度只与时间有关，而与空间坐标无关，这样我们便可把三维导热问题转化成只含时间变量的零维导热问题来处理，这时平均温度满足一个常微分方程。平均温度的变化规律可由初边值条件的积分来表达。 Introduction In engineering practice, we usually need to know the temperature state of production equipments and processing materials. But it is usually very difficult by analytic method to solve unsteady heat conduction problems, especially multidimensional heat conduction problems of irregular shape objects . In this case, we could research on the variation of average temperature by the premise of meet the production requirement. Xianghong Gu proposed the average temperature lumped parameter analysis method aiming at infinite plate, infinite cylinder and global objects. The average temperature is only related to time variable, and it is not relevant to space coordinates. So three dimensional heat conduction system can be transformed into a lumped parameter system. The average temperature meets an ordinary differential equation. The variation of average temperature can be expressed by the integral form of initial and boundary conditions. 结论 （1）推导出了一般情况下平均温度随时间的变化规律，平均温度的变化规律与吸热量相关，这是对能量守恒定律的反映。 （2）由初边值条件的积分形式给出了第二类边界条件下平均温度的表达式，并推出边界热流一定时的平均温度与时间呈线性关系，绝热边界条件下的平均温度不随时间变化。 conclusion (1) The variation of average temperature with time in general case is derived, it is related to the absorbed heat. It is the reflection of the conservation of energy principle. (2) The average temperature was expressed by the integral form of initial and boundary conditions under the second boundary condition. The average temperature has linear relationship with time when the boundary heat flux is constant and it does not change with time under the adiabatic boundary condition. 本文从信息熵与导热系统两个方面对正态分布与狄拉克 函数的性质及其相互关系进行了分析。计算得到狄拉克 函数所对应的信息熵为负无穷大，并对这一结果的物理含义做了解释。与控制理论相类比，定义了导热系统的传递函数，并用系统的观点分析了正态分布与 狄拉克函数在导热系统中的联系。 In this paper, the properties and relationship of the normal distribution and Dirac function are analyzed from two aspects of information entropy and heat conduction system. The information entropy corresponding to Dirac function is negative infinity, and the physical meaning of this result is given. Transfer function of heat conduction system is defined by analogy with control theory, and the relationship of normal distribution and Dirac function in heat conduction system is analyzed from system viewpoint. |
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爱与雨下(金币+3): 2011-12-07 08:50:26
suchuanqi(金币+5, 翻译EPI+1): ★有帮助 2011-12-23 22:07:13
sltmac(金币+45): 2011-12-26 12:59:52
爱与雨下(金币+3): 2011-12-07 08:50:26
suchuanqi(金币+5, 翻译EPI+1): ★有帮助 2011-12-23 22:07:13
sltmac(金币+45): 2011-12-26 12:59:52
个人认为，全文翻译都比较流畅，仅作了小范围润色，请你自己再次对比斟酌。内容仅供参考。 Abstract. The variation of average temperature with time in general could be derived by the differential equations of heat conduction, it is the reflection of the conservation of energy principle. The expresion of average temperature under the second boundary condition could be obtained by the integral form of initial and boundary conditions.Meanwhile, the average temperature has a linear relationship with the time when the boundary heat flux is constant which means it won't change with time under the adiabatic boundary conditions. Introduction In engineering practice, it is neccessary to know the temperature state of production equipments and processing materials. However, it is usually very difficult to solve problems under unsteady heat conduction by analytical methods, especially for multidimensional heat conduction problems of irregular shape objects. In this case,the dependance of average temperature on the time could be analyzed following the production requirements. It was proposed by Xianghong Gu that the average temperature lumped parameter analysis method could be used for infinite plate, infinite cylinder and global objects. The average temperature is only depandant on time and independant on space coordinates, a three dimensional heat conduction system could thereby be transformed into a lumped parameter system. Then the average temperature meets an ordinary differential equation. The variation of average temperature could be expressed by the integral form of initial and boundary conditions. Conclusions (1) The variation of average temperature with time in general case is derived, it is related to the heat absorbsion . It is the reflection of the principle of energy conservation. (2) The average temperature under the second boundary condition was expressed by the integral form of initial and boundary conditions. The average temperature has linear relationship with time when the boundary heat flux is constant which means it won't change with time under the adiabatic boundary conditions. In this paper, the properties and relationship of the normal distribution and Dirac function were analyzed from two aspects of information entropy and heat conduction system. The information entropy corresponding to Dirac function was negative infinity, and the physical meaning of this result was given. Transfer function of heat conduction system was defined by analogy with control theory, and the relationship of normal distribution and Dirac function in heat conduction system was also analyzed from system viewpoint. |
2楼2011-12-06 23:25:54