Open Access

ARTICLE

Heat Conduction Analysis of Nonhomogeneous Functionally Graded Three-Layer Media

Chien-Ching Ma^1,2, Yi-Tzu Chen²

1 Corresponding author. Tel.: +886-2-23659996; fax: + 886-2-23631755. E-mail address: ccma@ntu.edu.tw
2 Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.

Computers, Materials & Continua 2013, 36(2), 177-201. https://doi.org/10.3970/cmc.2013.036.177

Abstract

Functionally graded material (FGM) is a particulate composite with continuously changing its thermal and mechanical properties in order to raise the bonding strength in the discrete composite made from different phases of material constituents. Furthermore, FGM is a potent tool to create an intermediate layer in metal–ceramic composites to avoid the properties discontinuities and reduce, thereby, the residual stresses. For the nonhomogeneous problem, the mathematical derivation is much complicated than the homogeneous case since the material properties vary with coordinate. To analyze the problem, the Fourier transform is applied and the general solution in transform domain is obtained. The inverse Fourier transform is performed to get the results in physical domain for temperature and heat fluxes. Numerical results for the full-field distributions of temperature and heat fluxes with different functionally graded parameters are presented. The continuous characteristics of the temperature and heat flux along the interface are emphasized and some interesting phenomena are presented in this study. The results show that all the fields (temperature and heat fluxes) are continuous at the interface if the conductivities are continuous at the interface. Moreover, the first derivatives of temperature and heat flux qy are continuous at the interface.

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