Transient 3D heat conduction in functionally graded materials by the method of fundamental solutions

• Published in: Engineering analysis with boundary elements Vol. 45; pp. 62 - 67
• Main Authors: Li, Ming, Chen, C.S., Chu, C.C., Young, D.L.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2014
• Subjects: Diffusion equation; Finite element method; Functionally graded materials; Method of fundamental solutions; Specific heat; Thermal conductivity; Finite element method; Specific heat; Thermal conductivity; Diffusion equation; Functionally graded materials; Method of fundamental solutions
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/j.enganabound.2014.01.019

In this paper, the three-dimensional transient heat conduction problems in functionally graded materials (FGMs) have been solved using the method of fundamental solutions (MFS). To be more specific, we consider the FGMs with thermal conductivity and specific heat vary exponentially in z-direction. In the numerical simulation, we coupled the fundamental solution of diffusion equation with the method of time–space unification which provides a simple and direct approach for solving time-dependent problems. The parameter transformation technique is also utilized to obtain the fundamental solutions which contain the thermal conductivity and the specific heat conditions. The MFS is very attractive in handling problems with irregular domain due to the simplicity of the method. The numerical results are in good agreement comparing with analytical solution and results obtained from the finite element method.