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Heat Conduction in a Cylindrically Anisotropic Tube of a Functionally Graded Material

Published online by Cambridge University Press:  05 May 2011

Jiann-Quo Tarn*
Affiliation:
Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
Yung-Ming Wang*
Affiliation:
Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan 70101, R.O.C.
*
* Professor
** Associate Professor
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Abstract

A state space approach to heat conduction in a cylindrically anisotropic circular tube of functionally graded materials (FGM) is presented. A power-law type of the radial inhomogeneity for the FGM is considered. By means of eigenfunction expansion and matrix algebra, analytic solutions for transient and steady-state heat conduction in the FGM tube under general thermal boundary conditions are derived.

Type
Articles
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2003

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References

REFERENCES

[1]Carslaw, H. S. and Jaeger, J. C., Conduction of Heat in Solids, Clarendon Press, Oxford (1959).Google Scholar
[2]Özisik, M. N., Heat Conduction, Wiley, New York (1993).Google Scholar
[3]Chang, Y. P., Kang, C. S. and Chen, D. J., “The Use of Fundamental Green's Functions for the Solution of Problems of Heat Conduction in Anisotropic Media,” Int. J. Heat Mass Transfer, 16, pp. 19051918 (1973).CrossRefGoogle Scholar
[4]Chang, Y. P. and Tsou, C. H., “Heat Conduction in an Anisotropic Medium Homogeneous in Cylindrical Coordinates, Steady State,” J. Heat Transfer, 99C, pp. 132134 (1977).CrossRefGoogle Scholar
[5]Chang, Y. P. and Tsou, C. H., “Heat Conduction in an Anisotropic Medium Homogeneous in Cylindrical Coordinates, Unsteady State,” J. Heat Transfer, 99C, pp. 4147 (1977).CrossRefGoogle Scholar
[6]Özisik, M. N. and Shouman, S. M., “Transient Heat Conduction in an Anisotropic Medium in Cylindrical Coordinates,” J. Franklin Inst., 309, pp. 457472 (1980).CrossRefGoogle Scholar
[7]Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Body, Mir, Moscow (1981).Google Scholar
[8]Alshits, V. I. and Kirchner, H. O. K., “Cylindrically Anisotropic, Radially Inhomogeneous Elastic Materials,” Proc. R. Soc. Lond, A457, pp. 671693 (2001).CrossRefGoogle Scholar
[9]Horgan, C. O. and Chan, A. M., “Stress Response of Functionally Graded Isotropic Linearly Elastic Rotating Disks,” J. Elastic, 55, pp. 219230 (1999).CrossRefGoogle Scholar
[10]Yang, Y. Y., “Time-dependent Stress Analysis in Functionally Graded Materials,” Int. J. Solids Struct., 37, pp. 75937608 (2000).CrossRefGoogle Scholar
[11]Tarn, J. Q., “Exact Solutions for Functionally Graded Anisotropic Cylinders Subjected to Thermal and Mechanical Loads,” Int. J. Solids Struct., 38, pp. 81898206 (2001).CrossRefGoogle Scholar
[12]Hildebrand, F. B., Advanced Calculus for Applications, 2nd ed., Prentice-Hall, Englewood Cliffs, N.J. (1976).Google Scholar