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Theoretical analysis of heat conduction problems of nonhomogeneous functionally graded materials for a layer sandwiched between two half-planes

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Abstract

Functionally graded materials are the materials whose material properties are smoothly varying along one axis, and they are used as buffer layers to connect two dissimilar materials. By choosing proper functionally graded parameters, the material properties at the interface can be identical to prevent the interfacial fracture problem. This study analyzes the heat conduction problem of nonhomogeneous functionally graded materials for a layer sandwiched between two half-planes. From the Fourier transform method, the full-field solutions of temperature and heat flux are obtained in explicit forms. Numerical calculations based on the analytical solutions are performed and are discussed in detail. The continuous characteristics of the temperature and heat flux along the interface are emphasized, and some interesting phenomena are presented in this study. It is noted that the temperature and heat flux fields along the interface for nonhomogeneous functionally graded materials are continuous if the conductivities are identical at the interface. Furthermore, the temperature and heat flux q y have the identical contour slopes across the interface.

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  1. Department of Mechanical Engineering, National Taiwan University, Taipei, 10617, Taiwan, ROC

    Chien-Ching Ma & Yi-Tzu Chen

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  1. Chien-Ching Ma
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  2. Yi-Tzu Chen
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Correspondence to Chien-Ching Ma.

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Ma, CC., Chen, YT. Theoretical analysis of heat conduction problems of nonhomogeneous functionally graded materials for a layer sandwiched between two half-planes. Acta Mech 221, 223–237 (2011). https://doi.org/10.1007/s00707-011-0498-7

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  • DOI: https://doi.org/10.1007/s00707-011-0498-7

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