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论文类型：期刊论文

发表时间：2017-01-01

发表刊物：JOURNAL OF THERMAL SCIENCE AND TECHNOLOGY

收录刊物：SCIE、EI

卷号：12

期号：2

页面范围：1-11

ISSN号：1880-5566

关键字：Hamiltonian system; Symplectic method; Heat conduction; Mixed boundary value problem; Laplace transform

摘要：A novel Hamiltonian-based method is introduced to the two-dimensional (2-D) transient heat conduction in a rectangular domain with partial temperature and partial heat flux density on one boundary. This boundary condition is very difficult to deal with in the classical Lagrangian solving system. Because of this, a total unknown vector consisting of both temperature and heat flux density is regarded as the primary unknown so that the problem is converted to the Hamiltonian form. By using the Laplace transform and method of separation of variables, the total unknown vector is solved and expressed in terms of symplectic eigensolutions in the complex frequency domain (s-domain). The undetermined coefficients of the symplectic series are obtained according to a generalized adjoint symplectic orthogonality. In this manner, analytical expressions for the rectangular domain with specific mixed boundary conditions are achieved in the s-domain. Highly accurate numerical results in the time domain (t-domain) are then obtained by using inverse Laplace transform. Numerical examples are given to demonstrate the efficiency and accuracy of the proposed method.