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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 273052, 14 pages
http://dx.doi.org/10.1155/2013/273052
Research Article

Analytical Solutions for Steady Heat Transfer in Longitudinal Fins with Temperature-Dependent Properties

Center for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Johannesburg 2050, South Africa

Received 30 January 2013; Accepted 24 April 2013

Academic Editor: Ireneusz Zbicinski

Copyright © 2013 Partner L. Ndlovu and Raseelo J. Moitsheki. 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. A. D. Kraus, A. Aziz, and J. Welty, Extended Surface Heat Transfer, Wiley, New York, NY, USA, 2001.
  2. R. J. Moitsheki, T. Hayat, and M. Y. Malik, “Some exact solutions of the fin problem with a power law temperature-dependent thermal conductivity,” Nonlinear Analysis. Real World Applications, vol. 11, no. 5, pp. 3287–3294, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  3. R. J. Moitsheki, “Steady one-dimensional heat flow in a longitudinal triangular and parabolic fin,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 10, pp. 3971–3980, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. R. J. Moitsheki, “Steady heat transfer through a radial fin with rectangular and hyperbolic profiles,” Nonlinear Analysis. Real World Applications, vol. 12, no. 2, pp. 867–874, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Mo. Miansari, D. D. Ganji, and Me. Miansari, “Application of He's variational iteration method to nonlinear heat transfer equations,” Physics Letters A, vol. 372, no. 6, pp. 779–785, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. C. H. Chiu and C. K. Chen, “A decomposition method for solving the convective longitudinal fins with variable thermal conductivity,” International Journal of Heat and Mass Transfer, vol. 45, no. 10, pp. 2067–2075, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. A. Rajabi, “Homotopy perturbation method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity,” Physics Letters A, vol. 364, no. 1, pp. 33–37, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. G. Domairry and M. Fazeli, “Homotopy analysis method to determine the fin efficiency of convective straight fins with temperature-dependent thermal conductivity,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 2, pp. 489–499, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Campo and R. J. Spaulding, “Coupling of the methods of successive approximations and undetermined coefficients for the prediction of the thermal behaviour of uniform circumferential fins,” Heat and Mass Transfer, vol. 34, no. 6, pp. 461–468, 1999. View at Scopus
  10. A. Campo and F. Rodrfguez, “Approximate analytic temperature solution for uniform annular fins by adapting the power series method,” International Communications in Heat and Mass Transfer, vol. 25, no. 6, pp. 809–818, 1998. View at Scopus
  11. R. Chiba, “Application of differential transform method to thermoelastic problem for annular disks of variable thickness with temperature-dependent parameters,” International Journal of Thermophysics, vol. 33, pp. 363–380, 2012.
  12. S. Sadri, M. R. Raveshi, and S. Amiri, “Efficiency analysis of straight fin with variable heat transfer coefficient and thermal conductivity,” Journal of Mechanical Science and Technology, vol. 26, no. 4, pp. 1283–1290, 2012.
  13. M. Torabi, H. Yaghoori, and A. Aziz, “Analytical solution for convective-radiative continously moving fin with temperature dependent thermal conductivity,” International Journal of Thermophysics, vol. 33, pp. 924–941, 2012.
  14. M. Torabi and H. Yaghoobi, “Two dominant analytical methods for thermal analysis of convective step fin with variable thermal conductivity,” Thermal Science. In press. View at Publisher · View at Google Scholar
  15. A. Moradi, “Analytical solutions for fin with temperature dependant heat transfer coefficient,” International Journal of Engineering and Applied Sciences, vol. 3, no. 2, pp. 1–12, 2011.
  16. A. Moradi and H. Ahmadikia, “Analytical solution for different profiles of fin with temperature-dependent thermal conductivity,” Mathematical Problems in Engineering, vol. 2010, Article ID 568263, 15 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. H. Yaghoobi and M. Torabi, “The application of differential transformation method to nonlinear equations arising in heat transfer,” International Communications in Heat and Mass Transfer, vol. 38, no. 6, pp. 815–820, 2011. View at Publisher · View at Google Scholar · View at Scopus
  18. S. Ghafoori, M. Motevalli, M. G. Nejad, F. Shakeri, D. D. Ganji, and M. Jalaal, “Efficiency of differential transformation method for nonlinear oscillation: Comparison with HPM and VIM,” Current Applied Physics, vol. 11, no. 4, pp. 965–971, 2011. View at Publisher · View at Google Scholar · View at Scopus
  19. A. A. Joneidi, D. D. Ganji, and M. Babaelahi, “Differential transformation method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity,” International Communications in Heat and Mass Transfer, vol. 36, no. 7, pp. 757–762, 2009. View at Publisher · View at Google Scholar · View at Scopus
  20. J. K. Zhou, Differential Transform Method and Its Applications for Electric circuIts, Huazhong University Press, Wuhan, China, 1986.
  21. S. Mukherjee, “Reply to comment on ‘solutions of the duffing-van der pol oscillator equation by the differential transform method’,” Physica Scripta, vol. 84, Article ID 037003, 2 pages, 2011.
  22. C. Bervillier, “Status of the differential transformation method,” Applied Mathematics and Computation, vol. 218, no. 20, pp. 10158–10170, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. A. Arikoglu and I. Ozkol, “Solution of fractional differential equations by using differential transform method,” Chaos, Solitons and Fractals, vol. 34, no. 5, pp. 1473–1481, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. Z. Odibat, S. Momani, and V. S. Erturk, “Generalized differential transform method: application to differential equations of fractional order,” Applied Mathematics and Computation, vol. 197, no. 2, pp. 467–477, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. C. W. Bert, “Application of differential transform method to heat conduction in tapered fins,” Journal of Heat Transfer, vol. 124, no. 1, pp. 208–209, 2002. View at Publisher · View at Google Scholar · View at Scopus
  26. F. Khani and A. Aziz, “Thermal analysis of a longitudinal trapezoidal fin with temperature-dependent thermal conductivity and heat transfer coefficient,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 3, pp. 590–601, 2010. View at Publisher · View at Google Scholar · View at Scopus
  27. H. C. Ünal, “An anlytical study of boiling heat transfer from a fin,” International Journal of Heat and Mass Transfer, vol. 31, no. 7, pp. 1483–1496, 1988.
  28. M. H. Chang, “A decomposition solution for fins with temperature dependent surface heat flux,” International Journal of Heat and Mass Transfer, vol. 48, no. 9, pp. 1819–1824, 2005. View at Publisher · View at Google Scholar · View at Scopus
  29. A. Jezowski, B. A. Danilchenko, M. Boćkowski et al., “Thermal conductivity of GaN crystals in 4.2–300 K range,” Solid State Communications, vol. 128, no. 2-3, pp. 69–73, 2003. View at Publisher · View at Google Scholar · View at Scopus
  30. S. Vitanov, V. Palankovski, S. Maroldt, and R. Quay, “High-temperature modeling of AlGaN/GaN HEMTs,” Solid-State Electronics, vol. 54, no. 10, pp. 1105–1112, 2010. View at Publisher · View at Google Scholar · View at Scopus