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【答案】应助回帖
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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
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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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