Open AccessA Hamiltonian-based analytical approach for three-dimensional heat conduction of cylinders with specific mixed boundary conditions
Author(s) -
Dalun Rong,
Zhenhuan Zhou,
Xu Wang,
H Y Li,
Jiabin Sun,
Xinsheng Xü
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/531/1/012003
Subject(s) - symplectic geometry , mathematics , separation of variables , thermal conduction , boundary value problem , heat flux , mathematical analysis , hamiltonian (control theory) , partial differential equation , symplectic integrator , thermodynamics , physics , symplectic manifold , heat transfer , mathematical optimization
A novel analytical symplectic method is introduced to investigate the three-dimensional steady-state heat conduction of cylinders with specific mixed boundary conditions (partial temperature and partial heat flux density). By defining the temperature and heat flux density as the mutually dual variables, the Hamiltonian form of governing equations are established. The original problem is reduced into a symplectic eigenproblem which can be solved by the method of separation of variables and a symplectic sub-system. Exact analytical solution is obtained and expressed in terms of symplectic eigensolutions. Comparison studies demonstrate the accuracy of the proposed method. Some new results are given also.