Radial integration boundary element method for heat conduction problems with convective heat transfer boundary

References

• E. A. Divo and A. J. Kassab, Boundary Element Methods for Heat Conduction: With Applications in Non-Homogeneous Media. Southampton: WIT Press, 2003.
   Google Scholar
• J. Sladek, V. Sladek, and S. N. Atluri, “Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties,” Comput. Mech., vol. 24, pp. 456–462, 2000.
   Web of Science ®Google Scholar
• A. Sutradhar and G. H. Paulino, “The simple boundary element method for transient heat conduction in functionally graded materials,” Comput. Methods Appl. Mech. Eng., vol. 193, pp. 4511–4539, 2004.
   Web of Science ®Google Scholar
• N. Simoes, A. Tadeu, J. Antonio, and W. Mansur, “Transient heat conduction under nonzero initial conditions: a solution using the boundary element method in the frequency domain,” Eng. Anal. Boundary Elem., vol. 36, pp. 562–567, 2012.
   Web of Science ®Google Scholar
• J. Sladek, V. Sladek, and C. H. Zhang, “Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method,” Comput. Mater. Sci., vol. 28, pp. 494–504, 2003.
   Web of Science ®Google Scholar
• 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 Transfer B, vol. 45, pp. 472–493, 2014.
   Google Scholar
• B. Yu, H. L. Zhou, J. Yan, and Z. Meng, “A differential transformation boundary element method for solving transient heat conduction problems in functionally graded materials,” Numer. Heat Transfer A, vol. 70, no. 3, pp. 293–309, 2016.
   Web of Science ®Google Scholar
• 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 Transfer B, vol. 66, no. 5, pp. 422–445, 2014.
   Web of Science ®Google Scholar
• S. Z. Feng, X. Y. Cui, and A. M. Li, “Fast and efficient analysis of transient nonlinear heat conduction problems using combined approximations method,” Int. J. Heat Mass Transfer, vol. 97, pp. 638–644, 2016.
   Web of Science ®Google Scholar
• D. Nardini and C. A. Brebbia, “A new approach for free vibration analysis using boundary elements,” in Boundary Element Methods in Engineering, C. A. Brebbia, Ed. Berlin: Springer, 1982, pp. 312–326.
   Google Scholar
• P. W. Partridge, C. A. Brebbia, and L. C. Wrobel, The Dual Reciprocity Boundary Element Method. Southampton: Computational Mechanics Publications, 1992.
   Google Scholar
• X. W. Gao, “The radial integration method for evaluation of domain integrals with boundary-only discretization,” Eng. Anal. Boundary Elem., vol. 26, pp. 905–916, 2002.
   Web of Science ®Google Scholar
• X. W. Gao, “A boundary element method without internal cells for two-dimensional and three-dimensional elastoplastic problems,” J. Appl. Mech. ASME, vol. 69, pp. 154–160, 2002.
   Web of Science ®Google Scholar
• X. W. Gao, “Boundary element analysis in thermoelasticity with and without internal cells,” Int. J. Numer. Methods Eng., vol. 57, pp. 975–990, 2003.
   Web of Science ®Google Scholar
• X. W. Gao, C. H. Zhang, and L. Guo, “Boundary only element solutions of 2D and 3D nonlinear and nonhomogeneous elastic problems,” Eng. Anal. Boundary Elem., vol. 31, pp. 974–982, 2007.
   Web of Science ®Google Scholar
• K. Yang, J. Wang, J. M. Du, H. F. Peng, and X. W. Gao, “Radial integration boundary element method for nonlinear heat conduction problems with temperature-dependent conductivity,” Int. J. Heat. Mass Transfer, vol. 104, pp. 1145–1151, 2017.
   Web of Science ®Google Scholar
• K. Yang, H. F. Peng, J. Wang, C. H. Xing, and X. W. Gao, “Radial integration BEM for solving transient nonlinear heat conduction with temperature-dependent conductivity,” Int. J. Heat Mass Transfer, vol. 108, pp. 1551–1559, 2017.
   Web of Science ®Google Scholar
• X. W. Gao, “A boundary element method without internal cells for two-dimensional and three-dimensional elastoplastic problems,” J. Appl. Mech. ASME, vol. 69, pp. 154–160, 2002.
   Web of Science ®Google Scholar
• H. F. Peng, M. Cui, and X. W. Gao, “A boundary element method without internal cells for solving viscous flow problems,” Eng. Anal. Boundary Elem., vol. 37, pp. 293–300, 2013.
   Web of Science ®Google Scholar
• X. W. Gao, “A meshless BEM for isotropic heat conduction problems with heat generation and spatially varying conductivity,” Int. J. Numer. Methods Eng., vol. 66, pp. 1411–1431, 2006.
   Web of Science ®Google Scholar
• J. Wang, X. W. Gao, and C. H. Zhang, “Crack analysis of 3D functionally graded materials by a BEM,” Key Eng. Mater., vol. 385–387, pp. 881–884, 2008.
   Google Scholar
• H. F. Peng, K. Yang, and X. W. Gao, “Element nodal computation-based radial integration BEM for non-homogeneous problems,” Acta Mech. Sin., vol. 29, pp. 429–436, 2013.
   Web of Science ®Google Scholar
• C. H. Zhang, M. Cui, J. Wang, and X. W. Gao, “3D crack analysis in functionally graded material,” Eng. Fract. Mech., vol. 26, pp. 119–132, 2012.
   Google Scholar
• X. W. Gao and K. Yang, “Interface integral BEM for solving multi-medium elasticity problems,” Comput. Methods Appl. Mech. Eng., vol. 198, pp. 1429–1436, 2009.
   Web of Science ®Google Scholar
• X. W. Gao and J. Wang, “Interface integral BEM for solving multi-medium heat conduction problems,” Eng. Anal. Boundary Elem., vol. 33, pp. 539–546, 2009.
   Web of Science ®Google Scholar
• K. Yang, W. Z. Feng, J. Li, and X. W. Gao, “New analytical expressions in radial integration BEM for stress computation with several kinds of variable coefficients,” Comput. Methods Appl. Mech. Eng., vol. 289, pp. 44–59, 2015.
   Web of Science ®Google Scholar
• K. Yang and X. W. Gao, “Radial integration BEM for transient heat conduction problems,” Eng. Anal. Boundary Elem., vol. 34, pp. 557–563, 2010.
   Web of Science ®Google Scholar
• X. W. Gao and H. F. Peng, “A boundary-domain integral equation method for solving convective heat transfer problems,” Int. J. Heat Mass Transfer, vol. 63, pp. 183–190, 2013.
   Web of Science ®Google Scholar
• K. Yang, W. Z. Feng, and X. W. Gao, “A new approach for computing hyper-singular interface stresses in IIBEM for solving multi-medium elasticity problems,” Comput. Methods Appl. Mech. Eng., vol. 287, pp. 54–68, 2015.
   Web of Science ®Google Scholar
• K. Yang, H. F. Peng, M. Cui, and X. W. Gao, “New analytical expressions in radial integration BEM for solving heat conduction problems with variable coefficients,” Eng. Anal. Boundary Elem., vol. 50, pp. 224–230, 2015.
   Web of Science ®Google Scholar
• K. Yang and X. W. Gao, “Using analytical expressions in radial integration BEM for variable coefficient heat conduction problems,” Eng. Anal. Boundary Elem., vol. 35, pp. 1085–1089, 2011.
   Web of Science ®Google Scholar