The exact variational formulation of the extended unsteady heat conduction equation with finite propagation speed （the 2nd sound speed） of hyperbolic type is derived herein via a systematic and natural way. Moreover...The exact variational formulation of the extended unsteady heat conduction equation with finite propagation speed （the 2nd sound speed） of hyperbolic type is derived herein via a systematic and natural way. Moreover, the boundary- and the physically acceptable initial-value conditions are accommodated in the variational principle by a novel method suggested just recently. In this way a perfect justification of the variational theory of transient heat conduction and a rigorous theoretical basis for the finite element analysis of heat conduction are provided.展开更多
应用顺序函数法(sequential function specificationmethod,SFSM)研究利用未来时刻的温度测量信息反演非稳态导热系统表面热流问题。分析表面热流反演过程中未来时间步的优化问题,依据残差原理建立最优未来时间步的估算方法,并讨论了温...应用顺序函数法(sequential function specificationmethod,SFSM)研究利用未来时刻的温度测量信息反演非稳态导热系统表面热流问题。分析表面热流反演过程中未来时间步的优化问题,依据残差原理建立最优未来时间步的估算方法,并讨论了温度测量误差和测点位置对未来时间步的优化结果及表面热流反演结果的影响。数值试验结果表明,采用该文方法能够在综合考虑温度测量误差水平和温度测点位置等相关因素的基础上,恰当地选择未来时间步数,从而有效地改善表面热流的反演效果。展开更多
基金The support of the National Natural Science Foundation of China （Grant No. 50136030） the Shanghai Leading Acad. Discipline Project （No. Y0103） is gratefully appreciated.
文摘The exact variational formulation of the extended unsteady heat conduction equation with finite propagation speed （the 2nd sound speed） of hyperbolic type is derived herein via a systematic and natural way. Moreover, the boundary- and the physically acceptable initial-value conditions are accommodated in the variational principle by a novel method suggested just recently. In this way a perfect justification of the variational theory of transient heat conduction and a rigorous theoretical basis for the finite element analysis of heat conduction are provided.
文摘应用顺序函数法(sequential function specificationmethod,SFSM)研究利用未来时刻的温度测量信息反演非稳态导热系统表面热流问题。分析表面热流反演过程中未来时间步的优化问题,依据残差原理建立最优未来时间步的估算方法,并讨论了温度测量误差和测点位置对未来时间步的优化结果及表面热流反演结果的影响。数值试验结果表明,采用该文方法能够在综合考虑温度测量误差水平和温度测点位置等相关因素的基础上,恰当地选择未来时间步数,从而有效地改善表面热流的反演效果。
