Publication Cover
Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 70, 2016 - Issue 3
289
Views
18
CrossRef citations to date
0
Altmetric
Original Articles

A differential transformation boundary element method for solving transient heat conduction problems in functionally graded materials

, , &
Pages 293-309 | Received 01 Oct 2015, Accepted 09 Feb 2016, Published online: 13 Jul 2016

References

  • Y. Miyamoto, W. A. Kaysser, B. H. Rabin, A. Kawasaki, and R. G. Ford, Functionally Graded Materials: Design, Processing and Applications, Springer Science & Business Media, New York, NY, 2013.
  • O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, McGraw-Hill Book Co, London, England, 1977.
  • M. N. Özişik, Finite Difference Methods in Heat Transfer, CRC Press, FL, USA, 1994.
  • H. K. Versteeg and W. Malalasekera, The Finite Volume Method: An Introduction to Computational Fluid Dynamics, Pearson Education Limited, Edinburgh Gate, 2007.
  • S. N. Atluri, The Meshless Method (MLPG) for Domain & BIE Discretizations, Forsyth: Tech Science Press, Forsyth, 2004.
  • L. C. Wrobel and C. A. Brebbia, Boundary Element Methods in Heat Transfer, Computational Mechanics Publications, Boston, 2012.
  • A. M. Zhang and Y. L. Liu, Improved three-dimensional bubble dynamics model based on boundary element method, J. Comput. Phys., Vol. 294, pp. 208–223, 2015.
  • B. T. Jin and W. Chen, Boundary knot method based on geodesic distance for anisotropic problems, J. Comput. Phys., Vol. 215, pp. 614–629, 2006.
  • H. Han, D. B. Ingham, and Y. Yuan, The boundary element method for the solution of the backward heat conduction equation, J. Comput. Phys., Vol. 116, pp. 292–299, 1995.
  • X. Y. Qin, J. M. Zhang, L. P. Liu, and G. Y. Li, Steady-state heat conduction analysis of solids with small open-ended tubular holes by BEM, Int. J. Heat Mass Tran., Vol. 55, pp. 6846–6853, 2012.
  • W. A. Yao, B. Yu, X. W. Gao, and Q. Gao, A precise integration boundary element method for solving transient heat conduction problems, Int. J. Heat Mass Tran., Vol. 78, pp. 883–891, 2014.
  • B. Yu, H. L. Zhou, H. L. Chen, and Y. Tong, Precise time-domain expanding dual reciprocity boundary element method for solving transient heat conduction problems, Int. J. Heat Mass Tran., Vol. 91, pp. 110–118, 2015.
  • F. J. Wang, W. Chen, and Y. Gu, Boundary element analysis of inverse heat conduction problems in 2D thin-walled structures, Int. J. Heat Mass Tran., Vol. 91, pp. 1001–1009, 2015.
  • J. Sladek, V. Sladek, and C. Zhang, Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method, Com. Mater. Sci., Vol. 28, pp. 494–504, 2003.
  • P. W. Partridge, C. A. Brebbia, and L. C. Wrobel, The Dual Reciprocity Boundary Element Method, Computational Mechanics Publication, Southampton, 1992.
  • S. N. Ghadiali, D. Halpern, and D. P. Gaver, A dual-reciprocity boundary element method for evaluating bulk convective transport of surfactant in free-surface flows, J. Comput. Phys., Vol. 171, pp. 534–559, 2001.
  • X. W. Gao, The radial integration method for evaluation of domain integrals with boundary-only discretization, Eng. Anal. Bound. Elem., Vol. 26, pp. 905–916, 2002.
  • X. W. Gao, A boundary element method without internal cells for two-dimensional and three-dimensional elastoplastic problems, J. Appl. Mech., Vol. 69, pp. 154–160, 2002.
  • S. Gümgüm and M. Tezer-Sezgin, DRBEM solution of the natural convective flow of micropolar fluids, Numer. Heat Tr. A-Appl., Vol. 57, pp. 777–798, 2010.
  • N. Alsoy-Akgün and D. Lesnic, A numerical solution for an inverse natural magneto-convection problem, Numer. Heat Tr. B-Fund., Vol. 63, pp. 115–138, 2013.
  • M. A. Fahmy, Transient magneto-thermo-elastic stresses in an anisotropic viscoelastic solid with and without a moving heat source, Numer. Heat Tr. A-Appl., Vol. 61, pp. 633–650, 2013.
  • X. W. Gao, Evaluation of regular and singular domain integral with boundary-only discretization-theory and Fortran code, J. Comput. Appl. Math., Vol. 175, pp. 265–290, 2005.
  • K. Yang and X. W. Gao, Radial integration BEM for transient heat conduction problems, Eng. Anal. Bound. Elem., Vol. 34, pp. 557–563, 2010.
  • K. Yang, X. W. Gao, and Y. F. Liu, Using analytical expressions in radial integration BEM for variable coefficient heat conduction problems, Eng. Anal. Bound. Elem., Vol. 35, pp. 1085–1089, 2011.
  • E. L. Albuquerque, P. Sollero, and W. P. de Paiva, The BEM and the RIM in the dynamic analysis of symmetric laminate composite plates, Braz. Soc. Mech. Sci. Eng., pp. 41–50, 2007.
  • X. W. Gao, C. Zhang, and L. Guo, Boundary-only element solutions of 2D, and 3D nonlinear, and nonhomogeneous elastic problems, Eng. Anal. Bound. Elem., Vol. 31, pp. 974–982, 2007.
  • C. Zhang, M. Cui, J. Wang, X. W. Gao, J. Sladek, and V. Sladek, 3D crack analysis in functionally graded materials, Eng. Anal. Bound. Elem., Vol. 78, pp. 585–604, 2011.
  • H. F. Peng, M. Cui, and X. W. Gao, A boundary element method without internal cells for solving viscous flow problems, Eng. Anal. Bound. Elem., Vol. 37, pp. 293–300, 2013.
  • B. Yu, W. A. Yao, X. W. Gao, and S. Zhang, Radial integration BEM for one-phase solidification problems, Eng. Anal. Bound. Elem., Vol. 39, pp. 36–43, 2014.
  • M. A. Al-Jawary and L. C. Wrobel, Radial integration boundary integral and integro-differential equation methods for two-dimensional heat conduction problems with variable coefficients, Eng. Anal. Bound. Elem., Vol. 36, pp. 685–695, 2012.
  • B. Yu, W. A. Yao, and Q. Gao, A precise integration boundary-element method for solving transient heat conduction problems with variable thermal conductivity, Numer. Heat Tr. B-Fund., Vol. 65, pp. 472–493, 2014.
  • B. Yu and W. A. Yao, A precise time-domain expanding boundary-element method for solving three-dimensional transient heat conduction problems with variable thermal conductivity, Numer. Heat Tr. B-Fund., Vol. 66, pp. 422–445, 2014.
  • J. K. Zhou, Differential Transform and its Applications for Electrical Circuits, Huazhong Science & Technology University Press, Wuhan, 1988.
  • A. Kurnaza and G. Oturanç, The differential transform approximation for the system of ordinary differential equations, Int. J. Comput. Math., Vol. 82, pp. 709–719, 2005.
  • A. Arikoglu and I. Ozkol, Vibration analysis of composite sandwich beams with viscoelastic core by using differential transform method, Compos. Struct., Vol. 92, pp. 3031–3039, 2010.
  • H. Yaghoobi and M. Torabi, The application of differential transformation method to nonlinear equations arising in heat transform, Int. Commun. Heat Mass., Vol. 38, pp. 815–820, 2011.
  • H. Chu and C. Lo, Application of the hybrid differential transform-finite difference method to nonlinear transient heat conduction problems, Numer. Heat Tr. A-Appl., Vol. 53, pp. 295–307, 2008.
  • C. Y. Lo and B. Y. Chen, Application of hybrid differential transform/control-volume method to hyperbolic heat conduction problems, Numer. Heat Tr. B-Fund., Vol. 55, pp. 219–231, 2009.
  • H. S. Peng and C. L. Chen, Hybrid differential transformation and finite difference method to annular fin with temperature-dependent thermal conductivity. Int. J. Heat Mass Tran., Vol. 54, pp. 2427–2433, 2011.
  • S. Rajasekaran, Static, stability and free vibration analysis of arches using a new differential transformation-based arch element, Int. J. Mech. Sci., Vol. 77, pp. 82–97, 2013.
  • S. R. Karur and P. A. Ramachandran, Augmented thin plate spline approximation in DRM, Bound. Elem. Commun., Vol. 6, pp. 55–58, 1995.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.