International Scientific Journal


In this letter simple analytical methods called homotopy perturbation method(HPM), variation iteration method(VIM) and perturbation method(PM) are employed to approach temperature distribution of porous fins. also energy balance and Darcy's model used to formulate the heat transfer equation. To study the thermal performance, a type case considered is finite-length fin with insulated tip. The obtained results from variation iteration method (VIM) are compared with other analytical techniques proposed before. These methods are homotopy perturbation method and perturbation method (PM). Also BVP is applied as a numerical method for validation. The obtained results shows that the VIM is more accurate, stable and more appropriate than other techniques. Also it is found that this method is powerful mathematical tools and can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering specially some heat transfer equations.
PAPER REVISED: 2012-04-23
PAPER ACCEPTED: 2012-05-04
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2014, VOLUME 18, ISSUE Issue 2, PAGES [409 - 417]
  1. Kiwan, S., Al-Nmir, M.A., Using porous fins for heat transfer enhancement, ASME J. Heat Transfer, 123 (2001), pp. 790-795s
  2. Nguyen, A., Aziz, A., The heat transfer rates from convecting -radiating fins for different profile shapes, Heat and Mass Transfer, 27 (1992), 2, pp. 67-72
  3. Tadulkar, M., Mishra, A., The effect of combined radiation and convection heat transfer in porous channel bounded by isothermal parallel plates, International Journal of Heat and Mass Transfer, 47 (2004), 5, pp. 1001-1013
  4. Cole, J.D., Perturbation Methods in Applied Mathematics, Blaisdell Waltham, MA, 1968
  5. Nayfeh, A.H., Perturbation Methods, Wiley, New York, USA, 2000
  6. Lyapunov, A.M., General Problem on Stability of Motion, Taylor & Francis, London, UK, 1992
  7. Karmishin, , A.V., Zhukov, A.I., Kolosov, V.G., Methods of Dynamics Calculation and Testing for Thin- Walled Structures, Mashinostroyenie, Moscow, 1990
  8. Adomian, G., Solving Frontier Problems on Physics: The Decomposition Method, Kluwer Academic,Dordrecht, 1994
  9. He, J.H., A coupling method of homotopy technique and perturbation technique for nonlinear problems, Internat. J. Non-Linear Mech. 35 (2000), 1, pp. 37-43
  10. Davood Domiri GANJI, Zaman Ziabkhsh GANJI, and Hosain Domiri GANJI, determination of temperature distribution for annular fins with temperature dependent thermal conductivity by HPM, thermal scince, 15(2011), pp.S111-S115
  11. He, J.H., Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fractals, 26 (2005), pp. 695-700
  12. Esmaeilpour, M., Ganji, D.D., Application of He's homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate, Phys. Lett. A, 372(2007), 1, pp. 33-38
  13. Esmaeilpour, M., Ganji, D.D., Mohseni, E., Application of homotopy perturbation method to micropolar flow in a porous channel, J. Porous Media, 12 (2009), 5, pp. 451-459
  14. SB, Coskun., MT, Atay., Fin efficiency analysis of convective straight fin with temperature dependent thermal conductivity using variational iteration method. Appl Therm Eng, 28 (2008), pp.2345-52
  15. Miansari MO, Ganji DD, Miansar ME. Application of He's variational iteration method to nonlinear heat transfer equations. Phys Lett A, 372 (2008), pp.770-85
  16. Ganji,D.D., Sadighi, A., Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations, J. Comput. Appl. Math, 207(2007), pp. 24-34
  17. Ganji, D.D., Jannatabadi, M., Mohseni, E., Application of He's variational iteration method to nonlinear Jaulent-Miodek equations and comparing it with ADM, J. Comput. Appl. Math, 207(2007), pp.35-45
  18. He, J.H., Variational iteration method - some recent results and new interpretations, Journal of Computational and Applied Mathematics, 207 (2007), 1, pp. 3-17
  19. He, J.H., Wu, X.H., Construction of solitary solution and compaction-like solution by variational iteration method, Chaos Solitons & Fractals, 29 (2006), 1, pp. 108-113
  20. Odibat, Z.M., Momani, S., Application of variational iteration method to nonlinear differential equations of fractional order, International Journal of Nonlinear Sciences and Numerical Simulation, 7 (2006), 1, pp. 27-34
  21. Xu, Lan., Variational principles for coupled nonlinear Schrِ dinger equations, Physics Letters A, 359 (2006), pp. 627-629
  22. Momani, S., Abuasad, S., Application of He's variational iteration method to Helmholtz equation, Chaos Solitons & Fractals, 27 (2006), 5, pp. 1119-1123
  23. Ganji, D.D., Jamshidi, N., Ganji, Z.Z., HPM and VIM methods for finding the exact solutions of the nonlinear dispersive equations and seventh-order Sawada- Kotera equation, International Journal of Modern Physics B, 23 (2009), 1, pp. 39-52
  24. Ganji, D.D., Afrouzi, G.A., Talarposhti,R.A., Application of He's variational iteration method for solving the reaction-diffusion equation with ecological parameters, Computers and Mathematics with Applications, 54 (2007), pp. 1010- 1017
  25. Ganji, D.D., Tari, Hafez., Bakhshi Jooybari, M., Variational iteration method and homotopy perturbation method for nonlinear evolution equations, Computers and Mathematics with Applications, 54 (2007), pp.1018- 1027
  26. Rafei, M., Ganji, D.D., Daniali, H., Pashaei, H., The variational iteration method for nonlinear oscillators with discontinuities, Journal of Sound and Vibration, 305 (2007), pp. 614-620
  27. Ganji, D.D., Afrouzi, G.A., Talarposhti, R.A., Application of variational iteration method and homotopy-perturbation method for nonlinear heat diffusion and heat transfer equations, Physics Letters A, 368 (2007), pp.450-457
  28. He, J.H., Variational iteration method—a kind of nonlinear analytical technique: Some examples, International Journal of Non-linear Mechanics, 34 (1999), 4, pp. 699-708
  29. He, J.H., Approximate analytical solution for seepage with fractional derivatives in porous media, Computational Methods in Applied Mechanics and Engineering, 167 (1998), pp. 57-68
  30. GANJI, D. D., SAJJADI, H., new analytical solution for natural convection of darcian fluid in porous media prescribed surface heat flux, thermal scince, 15( 2011), pp. S221-S227
  31. Esmaeilpour M, Ganji D.D.,solution of the Jeffery-Hamel flow problem by optimal homotopy asymptotic method, computers and mathematics with applications, 59 (2010), pp.3405-3411
  32. Herisanu N, Marinca V, Explicit analytical approximation to large-amplitude non-linear oscillations of a uniform cantilever beam carrying an intermediate lumped mass and rotary inertia, Meccanica, 45 (2010), pp. 847-855
  33. Marinca, V., Herisanu, N, Nonlinear dynamic analysis of an electrical machine rotor-bearing system by the optimal homotopy perturbation method, computers and mathematics with applications, 61 (2011), pp. 2019-2024
  34. Bildik ,N., Konuralp, A., The use of variational iteration method, differential transform method and adomian decomposition method for solving different types of nonlinear partial differential equations, Int. J. Nonlinear Sci.Numer. Simul, 7 (2006), pp. 65-70
  35. Tari, Hafez., Ganji, D.D., Babazadeh, H., The application of He's variational iteration method to nonlinear equations arising in heat transfer, Phys. Lett, A, 363 (2007), 3, pp. 213-217
  36. Inokuti, M., General use of the Lagrange multiplier in non-linear mathematical physics, in: S. Nemat- Nasser (Ed.), Variational Method in the Mechanics of Solids, Pergamon, Oxford, (1978), pp.156-162
  37. He, J.H., Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbo machinery aerodynamics, Int J Turbo Jet Engines, 14(1997), (1),pp. 23-8
  38. Finlayson, B.A., The Method of Weighted Residuals and Variational Principles, Academic Press, New York, USA, 1972
  39. He, J.H., Variational iteration method a kind of non-linear analytical technique: some examples, Int. J. Non-linear Mech, 34 (1999), pp. 699-708.

© 2023 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence