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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 69, 2016 - Issue 1
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Original Articles

Predication of nonlinear heat transfer in a convective-radiative fin with temperature-dependent properties by the collocation spectral method

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Pages 68-83 | Received 16 Apr 2015, Accepted 22 Jun 2015, Published online: 30 Nov 2015

References

  • A. D. Kraus, A. Aziz, and J. Welty, Extended Surface Heat Transfer, John Wiley, New York, 2002.
  • R. W. Powell, C. Y. Ho, and P. E. Liley, Thermal Conductivity of Selected Materials, U.S. Government Printing Office, Washington, DC, 1966.
  • F. Khani, M. A. Raji, and H. H. Nejad, Analytical Solutions and Efficiency of the Nonlinear Fin Problem with Temperature-Dependent Thermal Conductivity and Heat Transfer Coefficient, Commun. Nonlinear Sci. Numer. Simul., vol. 14, pp. 3327–3338, 2009.
  • A. Aziz, Perturbation Solution for Convective Fin with Internal Heat Generation and Temperature Dependent Thermal Conductivity, Int. J. Heat Mass Transfer, vol. 20, pp. 1253–1255, 1977.
  • A. Razani and G. Ahmadi, On Optimization of Circular Fins with Heat Generation, J. Franklin Inst., vol. 303, pp. 211–218, 1977.
  • A. Aziz and M. N. Bouaziz, A Least Squares Method for a Longitudinal Fin with Temperature Dependent Internal Heat Generation and Thermal Conductivity, Energy Convers. Manage., vol. 52, pp. 2876–2882, 2011.
  • S. E. Ghasemi, M. Hatami, and D. D. Ganjj, Thermal Analysis of Convection Fin with Temperature-Dependent Thermal Conductivity and Heat Generation, Case Stud. Thermal Eng., vol. 4, pp. 1–8, 2014.
  • B. Kundu and K. S. Lee, A Non-Fourier Analysis for Transmitting Heat in Fins with Internal Heat Generation, Int. J. Heat Mass Transfer, vol. 64, pp. 1153–1162, 2013.
  • M. F. Modest, Radiative Heat Transfer, 3rd ed., Academic Press, New York, 2013.
  • Y. A. Cengel and A. J. Ghajar, Heat and Mass Transfer: Fundamentals and Applications, 5th ed., McGraw-Hill Science, London, 2014.
  • M. Torabi and A. Aziz, Thermal Performance and Efficiency of Convective-Radiative T-Shaped Fins with Temperature Thermal Conductivity, Heat Transfer Coefficient and Surface Emissivity, Int. Commun. Heat Mass Transfer, vol. 30, pp. 1018–1029, 2012.
  • C. Arslanturk, Performance Analysis and Optimization of Radiating Fins with a Step Change in Thickness and Variable Thermal Conductivity by Homotopy Perturbation Method, Heat Mass Transfer, vol. 47, pp. 131–138, 2011.
  • M. Torabi, A. Aziz, and K. L. Zhang, A Comparative Study of Longitudinal Fins of Rectangular, Trapezoidal and Concave Parabolic Profiles with Multiple Nonlinearities, Energy, vol. 51, pp. 243–256, 2013.
  • S. Saedodin and M. S. M. Barforoush, Comprehensive Analytical Study for Convective-Radiative Continuously Moving Plates with Multiple Non-linearities, Energy Convers. Manage., vol. 8, pp. 160–168, 2014.
  • J. S. Hesthaven and E. M. Ronquist, Spectral and High Order Methods for Partial Differential Equations, Springer-Verlag, Heidelberg, 2010.
  • J. Shen, T. Tang, and L. L. Wang, Spectral Methods: Algorithms, Analysis and Applications, Springer-Verlag, London, 2011.
  • A. Karageorghis and T. N. Phillips, Chebyshev Spectral Collocation Methods for Laminar Flow through a Channel Contraction, J. Comput. Phys., vol. 84, pp. 114–133, 1989.
  • B. W. Li, Y. R. Zhao, Y. Yu, and Z. D. Qian, Three-Dimensional Transient Navier–Stokes Solvers in Cylindrical Coordinate System Based on a Spectral Collocation Method Using Explicit Treatment of the Pressure, Int. J. Numer. Meth. Fluids, vol. 66, pp. 284–298, 2011.
  • M. Najafi, K. Hejranfar, and V. Esfahanian, Application of a Shock-Fitted Spectral Collocation Method for Computing Transient High-Speed Inviscid Flows over a Blunt Nose, J. Comput. Phys., vol. 257, pp. 954–980, 2014.
  • F. H. Zeng, H. P. Ma, and D. Liang, Energy-Conserved Splitting Spectral Methods for Two Dimensional Maxwell’s Equations, J. Comput. Appl. Math., vol. 265, pp. 301–321, 2014.
  • Y. Yu, B. W. Li, and A. Thess, The Effect of a Uniform Magnetic Field on Vortex Breakdown in a Cylinder with Rotating Upper Lid, Comput. Fluids, vol. 88, pp. 510–523, 2013.
  • X. H. Luo, B. W. Li, J. K. Zhang, and Z. M. Hu, Simulation of Thermal Radiation Effects on MHD Free Convection in a Square Cavity Using Chebyshev Collocation Spectral Method, Numer. Heat Transfer A, vol. 66, pp. 792–815, 2014.
  • O. Turk and M. Tezer-Sezgin, Chebyshev Spectral Collocation Method for Unsteady MHD Flow and Heat Transfer of a Dusty Fluid between Parallel Plates, Numer. Heat Transfer A, vol. 64, pp. 597–610, 2013.
  • N. Li, B. Meng, X. Feng, and D. Gui. The Spectral Collocation Method for the Stochastic Allen-Cahn Equation via Generalized Polynomial Chaos, Numer. Heat Transfer B, vol. 68, pp. 11–29, 2015.
  • J. Ma, Y. S. Sun, and B. W. Li, Analysis of Radiative Transfer in a One-Dimensional Nonlinear Anisotropic Scattering Medium with Space-Dependent Scattering Coefficient Using the Spectral Collocation Method, Int. J. Heat Mass Transfer, vol. 67, pp. 569–574, 2013.
  • Y. S. Sun, J. Ma, and B. W. Li, Chebyshev Collocation Spectral Method for Three-Dimensional Transient Coupled Radiative-Conductive Heat Transfer, ASME J. Heat Transfer, vol. 134, 092701, 2012.
  • G. U. Li, J. Ma, and B. W. Li, Collocation Spectral Method for the Transient Conduction Radiation Heat Transfer with Variable Thermal Conductivity in Two-Dimensional Rectangular Enclosure, ASME J. Heat Transfer, vol. 137, 032701, 2015.
  • Y. S. Sun, J. Ma, and B. W. Li, Spectral Collocation Method for Convective-Radiative Transfer of a Moving Rod with Variable Thermal Conductivity, Int. J. Thermal Sci., vol. 90, pp. 187–196, 2015.
  • D. D. Ganji, and A. S. Dogonchi, Analytical Investigation of Convective Heat Transfer of a Longitudinal Fin with Temperature-Dependent Thermal Conductivity, Heat Transfer Coefficient and Heat Generation, Int. J. Phys. Sci., vol. 9, pp. 466–474, 2014.

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