1Department Geotechnical Engineering, Nanjing Hydraulic Research Institute, China
2Key Laboratory of Failure Mechanism and Safety Control Techniques of Earth-Rock Dams, Ministry of Water Resource, China
*Corresponding author: Zhongzhi Fu, Key Laboratory of Failure Mechanism and Safety Control Techniques of Earth-Rock Dams, Ministry of Water Resource, China
Submission: May 30, 2018; Published: August 28, 2018
ISSN 2639-0574Volume2 Issue2
A heat transfer problem was taken as an example to provide the analytical solutions of a one-dimensional conduction problem with two different kinds of boundary conditions. The theoretical solutions were obtained by using the method of separation of variables for solving partial differential equations. Temperature distribution in two simple cases were studied using the analytical solutions and were compared with corresponding numerical results. Reliability of the analytical results were shown by their excellent agreement with those numerical ones. The solutions presented in this note can be used for the verification of new numerical algorithms.
Keywords: Heat transfer; Conduction problem; Analytical solution; Boundary condition