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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.

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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.

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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.


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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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°®ÓëÓêÏÂ(½ð±Ò+3): 2011-12-07 08:50:26
suchuanqi(½ð±Ò+5, ·­ÒëEPI+1): ¡ïÓаïÖú 2011-12-23 22:07:13
sltmac(½ð±Ò+45): 2011-12-26 12:59:52
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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.
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2Â¥2011-12-06 23:25:54
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