Skip to main content
SpringerLink
Log in

Transient temperature fields in functionally graded materials with different shapes under convective boundary conditions

  • Short Communication
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

This paper presents analyses of the transient temperature fields in an infinite plate, an infinite solid cylinder and a solid sphere made of functionally graded materials (FGMs) under convective boundary conditions. The composition and the thermo-physical properties of the infinite FGM plate, the infinite FGM solid cylinder and the FGM solid sphere are of planar symmetric, axially symmetric and spherically symmetric distributions, respectively. The analytical formulae of the one-dimensional transient temperature fields for the three FGM solids are obtained respectively by using the separation-of-variables method and the variable substitution method. Numerical results reveal that the transient temperature fields of the FGM components exhibit similar shape effect to that of homogeneous components. The present work provides valuable basis for the investigation of the thermal shock resistance of FGMs with various shapes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Obata Y, Noda N (1993) Unsteady thermal stresses in a functionally gradient material plate (Analysis of one-dimensional unsteady heat transfer problem) (in Japanese). Trans Jpn Soc Mech Eng 59A(560):1090–1096

    Google Scholar 

  2. Obata Y, Noda N (1993) Unsteady thermal stresses in a functionally gradient material plate (Influence of heating and cooling conditions on unsteady thermal stresses) (in Japanese). Trans Jpn Soc Mech Eng 59A(560):1097–1103

    Google Scholar 

  3. Araki N, Makino A, Ishiguro T, Mihara J (1992) An analytical solution of temperature response in multilayered materials for transient methods. Int J Thermophys 13(3):515–538

    Article  Google Scholar 

  4. Ishiguro T, Makino A, Araki N, Noda N (1993) Transient temperature response in functionally gradient materials. Int J Thermophys 14(1):101–121

    Article  Google Scholar 

  5. Sugano Y, Sato K, Kimura N, Sumi N (1996) Three-dimensional analysis of transient thermal stresses in a nonhomogeneous plate (in Japanese). Trans Jpn Soc Mech Eng 62A(595):728–736

    Google Scholar 

  6. Sugano Y, Sato K, Sumi N (1997) An analytical solution to transient temperature field in a functionally gradient material plate by piecewise-linear nonhomogeneous approximation method (in Japanese). Trans Jpn Soc Mech Eng 63A(606):378–385

    Google Scholar 

  7. Tanigawa Y, Akai T, Kasai T (1995) One-dimensional transient heat conduction and associated thermal stress problems of a plate with nonhomogeneous material properties (in Japanese). Trans Jpn Soc Mech Eng 61A(583):607–613

    Google Scholar 

  8. Tanigawa Y, Matsumoto M, Akai T (1997) Optimization of material composition to minimize thermal stresses in nonhomogeneous plate subjected to unsteady heat supply. JSME Int J 40A(1):84–93

    Google Scholar 

  9. Tanigawa Y, Oka N, Akai T, Kawamura R (1997) One-dimensional transient thermal stress problem for nonhomogeneous hollow circular cylinder and its optimization of material composition for thermal stress relaxation. JSME Int J 40A(2):117–127

    Google Scholar 

  10. Awaji H, Takenaka H, Honda S, Nishikawa N (1999) Analysis of temperature/stress distributions in a stress-relief-type plate functionally graded material under thermal shock (in Japanese). Trans Jpn Soc Mech Eng 65A(639):2318–2324

    Google Scholar 

  11. Awaji H, Sivakumar R (2001) Temperature and stress distributions in a hollow cylinder of functionally graded material: the case of temperature-independent material properties. J Am Ceram Soc 84(5):1059–1065

    Article  Google Scholar 

  12. Kim KS, Noda N (2002) Green’s function approach to unsteady thermal stresses in an infinite hollow cylinder of functionally graded material. Acta Mech 156(3–4):145–161

    Article  MATH  Google Scholar 

  13. Abd-All AM, Abd-Alla AN, Zeidan NA (1999) Transient thermal stresses in a spherically orthotropic elastic medium with spherical cavity. Appl Math Comp 105(2–3):231–252

    Article  MATH  MathSciNet  Google Scholar 

  14. Wang BL, Mai YW, Zhang XH (2004) Thermal shock resistance of functionally graded materials. Acta Materialia 52(17):4961–4972

    Article  Google Scholar 

  15. Wang BL, Mai YW (2005) Transient one-dimensional heat conduction problems solved by finite element. Int J Mech Sci 47(2):303–317

    Article  Google Scholar 

  16. Zhao J, Ai X, Deng JX, Wang ZX (2004) A model of the thermal shock resistance parameter for functionally gradient ceramics. Mater Sci Eng 382A (1–2):23–29

    Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (50105011 and 50575126) and the Foundation for the Author of National Excellent Doctoral Dissertation of P. R. China (200231) as well as the Natural Science Foundation of Shandong Province (Y2004F14).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Shandong University, 73 Jingshi Road, Jinan, 250061, People’s Republic of China

    J. Zhao, X. Ai & Y. Z. Li

Authors
  1. J. Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. X. Ai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Y. Z. Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Zhao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhao, J., Ai, X. & Li, Y.Z. Transient temperature fields in functionally graded materials with different shapes under convective boundary conditions. Heat Mass Transfer 43, 1227–1232 (2007). https://doi.org/10.1007/s00231-006-0135-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-006-0135-5

Keywords

Search

Navigation