Table of Contents
ISRN Mechanical Engineering
Volume 2011, Article ID 321605, 10 pages
http://dx.doi.org/10.5402/2011/321605
Research Article

Non-Fourier Heat Conduction Analysis with Temperature-Dependent Thermal Conductivity

1Department of Chemical Engineering, Persian Gulf University, Bushehr 75168, Iran
2Department of Mechanical Engineering, Persian Gulf University, Bushehr 75168, Iran

Received 27 January 2011; Accepted 10 March 2011

Academic Editor: M. Salvia

Copyright © 2011 H. Rahideh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. Sanderson, C. Ume, and J. Jarzynski, “Hyperbolic heat conduction effects caused by temporally modulated laser pulses,” Ultrasonics, vol. 33, no. 6, pp. 423–427, 1995. View at Publisher · View at Google Scholar · View at Scopus
  2. J. Y. Lin, “The non-Fourier effect on the fin performance under periodic thermal conditions,” Applied Mathematical Modelling, vol. 22, no. 8, pp. 629–640, 1998. View at Publisher · View at Google Scholar · View at Scopus
  3. P. J. Antaki, “Importance of nonFourier heat conduction in solid-phase reactions,” Combustion and Flame, vol. 112, no. 3, pp. 329–341, 1998. View at Publisher · View at Google Scholar · View at Scopus
  4. W. B. Lor and H. S. Chu, “Effect of interface thermal resistance on heat transfer in a composite medium using the thermal wave model,” International Journal of Heat and Mass Transfer, vol. 43, no. 5, pp. 653–663, 2000. View at Publisher · View at Google Scholar · View at Scopus
  5. L. H. Liu, H. P. Tan, and T. W. Tong, “Non-Fourier effects on transient temperature response in semitransparent medium caused by laser pulse,” International Journal of Heat and Mass Transfer, vol. 44, no. 17, pp. 3335–3344, 2001. View at Publisher · View at Google Scholar · View at Scopus
  6. L. Wang, “Solution structure of hyperbolic heat-conduction equation,” International Journal of Heat and Mass Transfer, vol. 43, no. 3, pp. 365–373, 2000. View at Publisher · View at Google Scholar · View at Scopus
  7. R. Cai, C. Gou, and H. Li, “Algebraically explicit analytical solutions of unsteady 3-D nonlinear non-Fourier (hyperbolic) heat conduction,” International Journal of Thermal Sciences, vol. 45, no. 9, pp. 893–896, 2006. View at Publisher · View at Google Scholar · View at Scopus
  8. A. Moosaie, “Non-Fourier heat conduction in a finite medium subjected to arbitrary periodic surface disturbance,” International Communications in Heat and Mass Transfer, vol. 34, no. 8, pp. 996–1002, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. J. S. Loh, I. A. Azid, K. N. Seetharamu, and G. A. Quadir, “Fast transient thermal analysis of Fourier and non-Fourier heat conduction,” International Journal of Heat and Mass Transfer, vol. 50, no. 21-22, pp. 4400–4408, 2007. View at Publisher · View at Google Scholar · View at Scopus
  10. R. Shirmohammadi and A. Moosaie, “Non-Fourier heat conduction in a hollow sphere with periodic surface heat flux,” International Communications in Heat and Mass Transfer, vol. 36, no. 8, pp. 827–833, 2009. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Jadidi, “Non-fourier heat conduction in a long cylindrical media with insulated boundaries and arbitrary initial conditions,” Australian Journal of Basic and Applied Sciences, vol. 3, no. 2, pp. 652–663, 2009. View at Google Scholar · View at Scopus
  12. G. F. Carey and M. Tsai, “Hyperbolic heat transfer with reflection,” Numerical Heat Transfer Part A, vol. 5, no. 3, pp. 309–327, 1982. View at Google Scholar · View at Scopus
  13. D. E. Glass, M. N. Oezisik, D. S. McRae, and B. Vick, “The numerical solution of hyperbolic heat conduction,” Numerical Heat Transfer Part A, vol. 8, no. 4, pp. 497–504, 1985. View at Google Scholar · View at Scopus
  14. K. K. Tamma and S. B. Railkar, “Specially tailored transfinite-element formulations for hyperbolic heat conduction involving non-Fourier effects,” Numerical Heat Transfer, Part B, vol. 15, no. 2, pp. 211–226, 1989. View at Google Scholar · View at Scopus
  15. C. Han-Taw and L. Jae-Yuh, “Numerical analysis for hyperbolic heat conduction,” International Journal of Heat and Mass Transfer, vol. 36, no. 11, pp. 2891–2898, 1993. View at Google Scholar · View at Scopus
  16. C. Han-Taw and L. Jae-Yuh, “Analysis of two-dimensional hyperbolic heat conduction problems,” International Journal of Heat and Mass Transfer, vol. 37, no. 1, pp. 153–164, 1994. View at Google Scholar · View at Scopus
  17. W. K. Yeung and T. T. Lam, “A numerical scheme for non-fourier heat conduction, part I: one-dimensional problem formulation and applications,” Numerical Heat Transfer, Part B, vol. 33, no. 2, pp. 215–233, 1998. View at Google Scholar · View at Scopus
  18. P. T. Hsu and Y. H. Chu, “An inverse non-Fourier heat conduction problem approach for estimating the boundary condition in electronic device,” Applied Mathematical Modelling, vol. 28, no. 7, pp. 639–652, 2004. View at Publisher · View at Google Scholar · View at Scopus
  19. K. C. Liu and H. T. Chen, “Numerical analysis for the hyperbolic heat conduction problem under a pulsed surface disturbance,” Applied Mathematics and Computation, vol. 159, no. 3, pp. 887–901, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. W. Wu and X. Li, “Application of the time discontinuous Galerkin finite element method to heat wave simulation,” International Journal of Heat and Mass Transfer, vol. 49, no. 9-10, pp. 1679–1684, 2006. View at Publisher · View at Google Scholar · View at Scopus
  21. X. Li, D. Yao, and R. W. Lewis, “A discontinuous Galerkin finite element method for dynamic and wave propagation problems in non-linear solids and saturated porous media,” International Journal for Numerical Methods in Engineering, vol. 57, no. 12, pp. 1775–1800, 2003. View at Publisher · View at Google Scholar · View at Scopus
  22. W. Wu and X. Li, “Application of the time discontinuous Galerkin finite element method to heat wave simulation,” International Journal of Heat and Mass Transfer, vol. 49, no. 9-10, pp. 1679–1684, 2006. View at Publisher · View at Google Scholar · View at Scopus
  23. T. M. Chen, “Numerical solution of hyperbolic heat conduction in thin surface layers,” International Journal of Heat and Mass Transfer, vol. 50, no. 21-22, pp. 4424–4429, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. A. P. Reverberi, P. Bagnerini, L. Maga, and A. G. Bruzzone, “On the non-linear Maxwell-Cattaneo equation with non-constant diffusivity: shock and discontinuity waves,” International Journal of Heat and Mass Transfer, vol. 51, no. 21-22, pp. 5327–5332, 2008. View at Publisher · View at Google Scholar · View at Scopus
  25. C. Y. Yang, “Direct and inverse solutions of the two-dimensional hyperbolic heat conduction problems,” Applied Mathematical Modelling, vol. 33, no. 6, pp. 2907–2918, 2009. View at Publisher · View at Google Scholar · View at Scopus
  26. C. A. Dorao, “Simulation of thermal disturbances with finite wave speeds using a high order method,” Journal of Computational and Applied Mathematics, vol. 231, no. 2, pp. 637–647, 2009. View at Publisher · View at Google Scholar · View at Scopus
  27. T. M. Chen, “A hybrid Green's function method for the hyperbolic heat conduction problems,” International Journal of Heat and Mass Transfer, vol. 52, no. 19-20, pp. 4273–4278, 2009. View at Publisher · View at Google Scholar · View at Scopus
  28. T. M. Chen and C. C. Chen, “Numerical solution for the hyperbolic heat conduction problems in the radial-spherical coordinate system using a hybrid Green's function method,” International Journal of Thermal Sciences, 2010. View at Publisher · View at Google Scholar
  29. C. C. Wang, “Direct and inverse solutions with non-Fourier effect on the irregular shape,” International Journal of Heat and Mass Transfer, vol. 53, no. 13-14, pp. 2685–2693, 2010. View at Publisher · View at Google Scholar · View at Scopus
  30. S. Andarwa and H. Basirat Tabrizi, “Non-Fourier effect in the presence of coupled heat and moisture transfer,” International Journal of Heat and Mass Transfer, vol. 53, no. 15-16, pp. 3080–3087, 2010. View at Publisher · View at Google Scholar · View at Scopus
  31. M. H. Hsu, “Differential quadrature method for solving hyperbolic heat conduction problems,” Tamkang Journal of Science and Engineering, vol. 12, no. 3, pp. 331–338, 2009. View at Google Scholar · View at Scopus
  32. P. Malekzadeh and H. Rahideh, “IDQ two-dimensional nonlinear transient heat transfer analysis of variable section annular fins,” Energy Conversion and Management, vol. 48, no. 1, pp. 269–276, 2007. View at Publisher · View at Google Scholar · View at Scopus
  33. P. Malekzadeh, H. Rahideh, and G. Karami, “A differential quadrature element method for nonlinear transient heat transfer analysis of extended surfaces,” Numerical Heat Transfer; Part A, vol. 49, no. 5, pp. 511–523, 2006. View at Publisher · View at Google Scholar · View at Scopus
  34. M. R. G. Haghighi, M. Eghtesad, and P. Malekzadeh, “A coupled differential quadrature and finite element method for 3-D transient heat transfer analysis of functionally graded thick plates,” Numerical Heat Transfer, Part B, vol. 53, no. 4, pp. 358–373, 2008. View at Publisher · View at Google Scholar · View at Scopus
  35. M. R. G. Haghighi, M. Eghtesad, P. Malekzadeh, and D. S. Necsulescu, “Two-dimensional inverse heat transfer analysis of functionally graded materials in estimating time-dependent surface heat flux,” Numerical Heat Transfer; Part A, vol. 54, no. 7, pp. 744–762, 2008. View at Publisher · View at Google Scholar · View at Scopus
  36. P. Malekzadeh, A. R. Fiouz, and H. Razi, “Three-dimensional dynamic analysis of laminated composite plates subjected to moving load,” Composite Structures, vol. 90, no. 2, pp. 105–114, 2009. View at Publisher · View at Google Scholar · View at Scopus