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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 68, 2015 - Issue 6
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Original Articles

Precise Time-Domain Expanding BEM for Solving Non-Fourier Heat Conduction Problems

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Pages 511-532 | Received 18 Apr 2015, Accepted 30 May 2015, Published online: 01 Oct 2015

REFERENCES

  • M. Wang, N. Yang, and Z. Y. Guo, Non-Fourier Heat Conductions in Nanomaterials, J. Appl. Phys., vol. 110, 064310, 2011.
  • J. Shiomi and S. Maruyama, Non-Fourier Heat Conduction in a Single-Walled Carbon Nanotube: Classical Molecular Dynamics Simulations, Phys. Rev. B, vol. 73, 205420, 2006.
  • D. W. Tang and N. Araki, Non-Fourier Heat Conduction in a Finite Medium under Periodic Surface Thermal Disturbance, Int. J. Heat Mass Transfer, vol. 39, pp. 1585–1590, 1996.
  • Q. M. Fan and W. Q. Lu, A New Numerical Method to Simulate the Non-Fourier Heat Conduction in a Single-Phase Medium, Int. J. Heat Mass Transfer, vol. 45, pp. 2815–2821, 2002.
  • F. Xu, K. A. Seffen, and T. J. Lu, Non-Fourier Analysis of Skin Biothermomechanics, Int. J. Heat Mass Transfer, vol. 51, pp. 2237–2259, 2008.
  • S. C. Mishra and H. Sahai, Analysis of Non-Fourier Conduction and Radiation in a Cylindrical Medium Using Lattice Boltzmann Method and Finite Volume Method, Int. J. Heat Mass Transfer, vol. 61, pp. 41–55, 2013.
  • R. Palma, J. L. Pérez-Aparicio, and R. L. Taylor, Non-linear Finite Element Formulation Applied to Thermoelectric Materials under Hyperbolic Heat Conduction Model, Comput. Meth. Appl. M., vol. 213, pp. 93–103, 2012.
  • V. Vishwakarma, A. K. Das, and P. K. Das, Analysis of Non-Fourier Heat Conduction Using Smoothed Particle Hydrodynamics, Appl. Thermal Eng., vol. 31, pp. 2963–2970, 2011.
  • S. Liao, General Boundary Element Method for Non-linear Heat Transfer Problems Governed by Hyperbolic Heat Conduction Equation, Comput. Mech., vol. 20, pp. 397–406, 1997.
  • E. Majchrzak and L. Turchan, The General Boundary Element Method for 3D Dual-Phase Lag Model of Bioheat Transfer, Eng. Anal. Bound. Elem., vol. 50, pp. 76–82, 2015.
  • D. Nardini and C. A. Brebbia, A New Approach to Free Vibration Analysis Using Boundary Elements, Appl. Math. Model., vol. 7, pp. 157–162, 1983.
  • S. Gümgüm and M. Tezer-Sezgin, DRBEM Solution of the Natural Convective Flow of Micropolar Fluids, Numer. Heat Transfer A, vol. 57, pp. 777–798, 2010.
  • N. Alsoy-Akgün and D. Lesnic, A Numerical Solution for an Inverse Natural Magneto-Convection Problem, Numer. Heat Transfer B, 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 Transfer A, vol. 61, pp. 633–650, 2013.
  • M. A. Fahmy, A Three-Dimensional Generalized Magneto-Thermo-Viscoelastic Problem of a Rotating Functionally Graded Anisotropic Solid with and without Energy Dissipation, Numer. Heat Transfer A, vol. 63, pp. 713–733, 2013.
  • P. W. Partridge, C. A. Brebbia, and L. C. Wrobel, The Dual Reciprocity Boundary Element Method, Computational Mechanics Publication, Southampton, UK, 1992.
  • 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.
  • E. L. Albuquerque, P. Sollero, and W. Portilho de Paiva, The BEM and the RIM in the Dynamic Analysis of Symmetric Laminate Composite Plates, Brazil. Soc. Mech. Sci. Engi., 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. Fract. Mech., 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 Fow Problems, Eng. Anal. Bound. Elem., vol. 37, pp. 293–300, 2013.
  • 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 X. W. Gao, Radial Integration BEM for One-Phase Solidification Problems, Eng. Anal. Bound. Elem., vol. 39, pp. 36–43, 2014.
  • H. T. Yang, A Precise Algorithm in the Time Domain to Solve the Problem of Heat Transfer, Numer. Heat Transfer B, vol. 35, pp. 243–249, 1999.
  • H. T. Yang and Z. Han, Solving Non-linear Viscoelastic Problems via a Self-adaptive Precise Algorithm in Time Domain, Int. J. Solids Struct., vol. 54, pp. 5483–5498, 2004.
  • Y. Ren and H. T. Yang, Equivalent Analysis of Orthogonal Viscoelastic Jointed Rock via an Adaptive Algorithm in Time Domain, Finite Elem. Anal. Des., vol. 46, pp. 875–888, 2010.
  • H. T. Yang and Y. Liu, A Combined Approach of EFGM and Precise Algorithm in Time Domain Solving Viscoelasticity Problem, Int. J. Solids Struct., vol. 40, pp. 701–714, 2003.
  • B. Yu, W. A. Yao, and X. W. Gao, A Combined Approach of RIBEM and Precise Time Integration Algorithm for Solving Transient Heat Conduction Problems, Numer. Heat Transfer B, vol. 65, pp. 155–173, 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 Transfer B, vol. 66, pp. 422–445, 2014.
  • C. Cattaneo, A Form of Heat Conduction Equation which Eliminates the Paradox of Instantaneous Propagation, Compte Rendus, vol. 247, pp. 431–33, 1958.
  • P. Vernotte, Some Possible Complications in the Phenomena of Thermal Conduction, Compte Rendus, vol. 252, pp. 2190–2191, 1961.
  • E. A. Divo and A. J. Kassab, Boundary Element Methods for Heat Conduction: With Applications in Non-homogeneous Media, WIT Press, Southampton, UK, 2003.
  • S. R. Karur and P. A. Ramachandran, Augmented Thin Plate Spline Approximation in DRM, Bound. Elem. Commun., vol. 6, pp. 55–58, 1995.
  • M. Lewandowska, Hyperbolic Heat Conduction in the Semi-infinite Body with a Time-Dependent Laser Heat Source, Heat Mass Transfer, vol. 37, pp. 333–342, 2001.

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