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Thermophysics and Aeromechanics

, Volume 25, Issue 1, pp 119–132 | Cite as

Annular convective-radiative fins with a step change in thickness, and temperature-dependent thermal conductivity and heat transfer coefficient

  • M. S. M. Barforoush
  • S. Saedodin
Article
  • 19 Downloads

Abstract

This article investigates the thermal performance of convective-radiative annular fins with a step reduction in local cross section (SRC). The thermal conductivity of the fin’s material is assumed to be a linear function of temperature, and heat transfer coefficient is assumed to be a power-law function of surface temperature. Moreover, nonzero convection and radiation sink temperatures are included in the mathematical model of the energy equation. The well-known differential transformation method (DTM) is used to derive the analytical solution. An exact analytical solution for a special case is derived to prove the validity of the obtained results from the DTM. The model provided here is a more realistic representation of SRC annular fins in actual engineering practices. Effects of many parameters such as conduction-convection parameters, conduction-radiation parameter and sink temperature, and also some parameters which deal with step fins such as thickness parameter and dimensionless parameter describing the position of junction in the fin on the temperature distribution of both thin and thick sections of the fin are investigated. It is believed that the obtained results will facilitate the design and performance evaluation of SRC annular fins.

Keywords

SRC annular fins performance analysis convective-radiative heat loss analytical solution 

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References

  1. 1.
    A.D. Kraus, A. Aziz, and J. Welty, Extended surface heat transfer, John Wiley & Sons, Inc., New York, 2001.Google Scholar
  2. 2.
    P. Razelos, A critical review of extended surface heat transfer, Heat Transf. Engng, 2003, Vol. 24, P. 11–28.ADSCrossRefGoogle Scholar
  3. 3.
    M. Torabi and Q.B. Zhang, Analytical solution for evaluating the thermal performance and efficiency of convective–radiative straight fins with various profiles and considering all non-linearities, Energy Convers. Manag., 2013, Vol. 66, P. 199–210.CrossRefGoogle Scholar
  4. 4.
    T.L. Bergman, A.S. Lavine, F.P. Incropera, and D.P. DeWitt, Introduction to Heat Transfer, 6th ed., John Wiley and Sons, Inc., N.Y., 2011.Google Scholar
  5. 5.
    B. Kundu and S. Wongwises, A decomposition analysis on convecting–radiating rectangular plate fins for variable thermal conductivity and heat transfer coefficient, J. Franklin Inst., 2012, Vol. 349, P. 349–966.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    M. Torabi and A. Aziz, Thermal performance and efficiency of convective–radiative T-shaped fins with temperature dependent thermal conductivity, heat transfer coefficient and surface emissivity, Int. Commun. Heat Mass Transf., 2012, Vol. 39, P. 39–1018.Google Scholar
  7. 7.
    S. Sadri, M.R. Raveshi, and S. Amiri, Efficiency analysis of straight fin with variable heat transfer coefficient and thermal conductivity, J. Mech. Sci. Technol., 2012, Vol. 26, P. 26–1283.CrossRefGoogle Scholar
  8. 8.
    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., 2009, Vol. 14, P. 14–3327.zbMATHGoogle Scholar
  9. 9.
    F. Khani and A. Aziz, Thermal analysis of a longitudinal trapezoidal fin with temperature-dependent thermal conductivity and heat transfer coefficient, Commun. Nonlinear Sci. Numer. Simul., 2010, Vol. 15, P. 15–590.CrossRefGoogle Scholar
  10. 10.
    A. Aziz and M. Torabi, Convective-radiative fins with simultaneous variation of thermal conductivity, heat transfer coefficient, and surface emissivity with temperature, Heat Transf.–Asian Res., 2012, Vol. 41, P. 41–99.Google Scholar
  11. 11.
    A. Aziz and T. Fang, Thermal analysis of an annular fin with (a) simultaneously imposed base temperature and base heat flux and (b) fixed base and tip temperatures, Energy Convers. Manag., 2011, Vol. 52, P. 52–2467.Google Scholar
  12. 12.
    R. Hassanzadeh and H. Pekel, Heat transfer enhancement in annular fins using functionally graded material, Heat Transf.–Asian Res., 2013, Vol. 42, P. 42–603.Google Scholar
  13. 13.
    H.-S. Peng and C.-L. Chen, Hybrid differential transformation and finite difference method to annular fin with temperature-dependent thermal conductivity, Int. J. Heat Mass Transf., 2011, Vol. 54, P. 54–2427.zbMATHGoogle Scholar
  14. 14.
    A. Aziz, M. Torabi, and K. Zhang, Convective–radiative radial fins with convective base heating and convective–radiative tip cooling: Homogeneous and functionally graded materials, Energy Convers. Manag., 2013, Vol. 74, P. 74–366.CrossRefGoogle Scholar
  15. 15.
    M. Hatami and D.D. Ganji, Thermal performance of circular convective–radiative porous fins with different section shapes and materials, Energy Convers. Manag., 2013, Vol. 76, P. 76–185.CrossRefGoogle Scholar
  16. 16.
    A. Aziz, Optimum design of a rectangular fin with a step change in cross-sectional area, Int. Commun. Heat Mass Transf., 1994, Vol. 21, P. 21–389.CrossRefGoogle Scholar
  17. 17.
    B. Kundu and A. Aziz, Performance of a convectively heated rectangular fin with a step change in cross-sectional area and losing heat by simultaneous convection and radiation (step fins under radiation environment), J. Heat Transfer, 2010, Vol. 132, P. 132–104502-104502-6.CrossRefGoogle Scholar
  18. 18.
    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 Transf., 2010, Vol. 47, P. 47–131.Google Scholar
  19. 19.
    B. Kundu and P.K. Das, Performance analysis and optimization of annular fin with a step change in thickness, J. Heat Transfer, 2001, Vol. 123, P. 123–601.CrossRefGoogle Scholar
  20. 20.
    B. Kundu, K.-S. Lee, and A. Campo, Exact and approximate analytic methods to calculate maximum heat flow in annular fin arrays with a rectangular step profile, Int. J. Thermophys., 2012, Vol. 33, P. 33–1314.CrossRefGoogle Scholar
  21. 21.
    R. Chiba, Application of differential transform method to thermoelastic problem for annular disks of variable thickness with temperature-dependent parameters, Int. J. Thermophys., 2012, Vol. 33, P. 33–363.CrossRefGoogle Scholar
  22. 22.
    J.K. Zhou, Differential Transform and Its Applications for Electrical Circuits, Huarjung University Press, Wuhan, 1986.Google Scholar
  23. 23.
    P.L. Ndlovu and R.J. Moitsheki, Application of the two-dimensional differential transform method to heat conduction problem for heat transfer in longitudinal rectangular and convex parabolic fins, Commun. Nonlinear Sci. Numer. Simul., 2013, Vol. 18, P. 18–2689.MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    M. Torabi, A. Aziz, and K. Zhang, A comparative study of longitudinal fins of rectangular, trapezoidal and concave parabolic profiles with multiple nonlinearities, Energy, 2013, Vol. 51, P. 51–243.Google Scholar
  25. 25.
    M. Torabi and H. Yaghoobi, Accurate solution for convective–radiative fin with variable thermal conductivity and nonlinear boundary condition by DTM, Arab. J. Sci. Eng., 2013, Vol. 38, P. 38–3575.CrossRefGoogle Scholar
  26. 26.
    Yaghoobi H., Torabi M. The application of differential transformation method to nonlinear equations arising in heat transfer, Int. Commun. Heat Mass Transf., 2011, Vol. 38, P. 38–815.CrossRefGoogle Scholar
  27. 27.
    M. Torabi, H. Yaghoobi, and M.R. Kiani, Thermal analysis of the convective-radiative fin with a step change in thickness and temperature dependent thermal conductivity, J. Theor. Appl. Mech., 2013, Vol. 51, P. 51–593.Google Scholar
  28. 28.
    M. Torabi and H. Yaghoobi, Analytical approaches for thermal analysis of radiative fin with a step change in thickness and variable thermal conductivity, Heat Transf. - Asian Res., 2012, Vol. 41, Iss. 4, P. 354–370.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.University of SemnanSemnanIran

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