Two dominant analytical methods for thermal analysis of convective step fin with variable thermal conductivity

Abstract

Heat transfer in a straight fin with a step change in thickness and variable thermal conductivity which is losing heat by convection to its surroundings is developed via differential transformation method (DTM) and variational iteration method (VIM). In this study, we compare DTM and VIM results, with those of homotopy perturbation method (HPM) and an accurate numerical solution to verify the accuracy of the proposed methods. As an important result, it is depicted that the DTM results are more accurate in comparison with those obtained by VIM and HPM. After these verifications the effects of parameters such as thickness ratio, α, dimensionless fin semi thickness, δ, length ratio, λ, thermal conductivity parameter, β, Biot number, Bi , on the temperature distribution are illustrated and explained.

Keywords

Dates

  • Submission Date2011-09-18
  • Revision Date2012-03-28
  • Acceptance Date2012-03-29

DOI Reference

10.2298/TSCI110918046T

References

  1. A. D. Kraus, A. Aziz, J.R. Welty, Extended Surface Heat Transfer, John Wiley, New York, 2002.
  2. M.H. Sharqawy, S.M. Zubair, Efficiency and optimization of straight fins with combined heat and mass transfer - an analytical solution, Applied Thermal Engineering 28 (2008) 2279-2288.
  3. C.W. Bert, Application of differential transform method to heat conduction in tapered fins, ASME Journal of Heat Transfer 124 (2002) 208-209.
  4. B. Kundu, Performance and optimum design analysis of longitudinal and pin fins with simultaneous heat and mass transfer: unified and comparative investigations, Applied Thermal Engineering 27 (2007) 976-987.
  5. G. Domairry, 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 14 (2009) 489-499.
  6. C. Arslanturk, Correlation equations for optimum design of annular fins with temperature dependent thermal conductivity, Heat and Mass Transfer 45 (4) (2009) 519-525.
  7. D.B. Kulkarni, M.M. Joglekar, Residue minimization technique to analyze the efficiency of convective straight fins having temperature-dependent thermal conductivity, Applied Mathematics and Computation 215 (2009) 2184-2191.
  8. F. Khani, M. Ahmadzadeh Raji, H. Hamedi Nejad, Analytical solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient, Communications in Nonlinear Science and Numerical Simulation 14 (2009) 3327-3338.
  9. A.A. Joneidi, D.D. Ganji, 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 36 (2009) 757-762.
  10. F. Fouladi, E. Hosseinzadeh, A. Barari, G. Domairry, Highly nonlinear temperature-dependent fin analysis by variational iteration method, Heat Transfer Research 41 (2010) 155-165.
  11. F. Khani, 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 15 (2010) 590-601.
  12. Determination of Temperature Distribution for Annular Fins with Temperature Dependent Thermal Conductivity by HPM, Thermal Science 15 (2011) S111-S115.
  13. M. Torabi, H. Yaghoobi, A. Aziz, Analytical Solution for Convective-Radiative Continuously Moving Fin with Temperature Dependent Thermal Conductivity, International Journal of Thermophysics (2012) in Press.
  14. A. Aziz, Optimum design of a rectangular fin with a step change in cross-sectional area. Int Commun Heat Mass Transf 21 (1994) 389-401.
  15. B. Kundu, P.K. Das, Performance analysis and optimization of annular fin with a step change in thickness. J Heat Transf 123 (2001) 601-604.
  16. P. Malekzadeh, H. Rahideh, G. Karami, Optimization of convective-radiative fins by using differential quadrature method, Energy Convers Manag 47 (2006) 1505-1514.
  17. B. Kundu, Analysis of thermal performance and optimization of concentric circular fins under dehumidifying conditions, Int J Heat Mass Transf 52 (2009) 2646-2659.
  18. B. Kundua, S. Wongwises, A decomposition analysis on convecting-radiating rectangular plate fins for variable thermal conductivity and heat transfer coefficient, Journal of the Franklin Institute 349 (2012) 966-984.
  19. C. Arslantürk, Optimization of Straight Fins with a Step Change in Thickness and Variable Thermal Conductivity by Homotopy Perturbation Method, Journal of Thermal Science and Technology 30(2) (2010) 09-19.
  20. A.A. Joneidi, D.D. Ganji, 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 36 (2009) 757-762.
  21. H. Yaghoobi, M. Torabi, The application of differential transformation method to nonlinear equations
Volume 18, Issue 2, Pages431 -442