Prediction of a Semi-Exact Analytic Solution of a Convective Porous Fin with Variable Cross Section by Different Methods


  • Majid SHAHBABAEI Department of Mechanical Engineering, Shirgah Branch, Azad University, Shirgah
  • Davood Domayri GANJI Department of Mechanical Engineering, Babol University of Technology, Babol
  • Iman RAHIMIPETROUDI Young Researchers Club, Sari Branch, Islamic Azad University, Sari


Porous fin, variable cross section, Collocation Method, Homotopy Perturbation Method, Variation Iteration Method


In the present study, the problem of nonlinear equations arising in a convective porous fin with a variable cross section is investigated using a Collocation Method (CM). The obtained results from this method are compared with the Homotopy Perturbation Method (HPM), Variation Iteration Method (VIM), and those from a numerical solution, namely the Boundary Value Problem method (BVP), to verify the accuracy of the proposed method. It is found that the CM can achieve suitable results in predicting the solutions of such problems.



Download data is not yet available.


Metrics Loading ...


DD Ganji, H Kachapi and H Seyed. Analytical and numerical method in engineering and applied science. Prog. Nonlinear Sci. 2011; 3, 1-579.

JH He. Homotopy perturbation technique. Comp. Meth. App. Mech. Eng. 1999; 178, 257-62.

JH He. Homotopy perturbation method for bifurcation of nonlinear problems. Int. J. Nonlinear Sci. Numer. Simulat. 2005; 6, 207-8.

JH He. Application of homotopy perturbation method to nonlinear wave equations. Chaos Soliton. Fract. 2005; 26, 695-700.

M Esmaeilpour and DD Ganji. Application of He's homotopy perturbation method to boundary layer flow and convection heat transfer over a flat plate. Phys. Lett. A 2007; 372, 33-8.

JH He. A note on the homotopy perturbation method. Therm. Sci. 2010; 14, 565-8.

DD Ganji and A Rajabi. Assessment of homotopy-perturbation and perturbation methods in heat radiation equations. Int. Comm. Heat Mass Tran. 2006; 33, 391-400.

DD Ganji, ZZ Ganji and HD Ganji. Determination of temperature distribution for annular fin with temperature dependent thermal conductivity by HPM. Therm. Sci. 2011; 15, 111-5.

DD Ganji and A Sadighi. Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations. J. Comput. Appl. Math. 2007; 207, 24-34.

DD Ganji and EM Languri. Mathematical Methods in Nonlinear Heat Transfer. Xlibris Corporation, USA, 2010.

SJ Liao. 1992, The proposed homotopy analysis technique for the solution of nonlinear problems. Ph. D. Dissertation, Shanghai Jiao Tong University, China.

SJ Liao and KF Cheung . Homotopy analysis of nonlinear progressive waves in deep water. J. Eng. Math. 2003; 45, 103-16.

SJ Liao. On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 2004; 47, 499-513.

DD Ganji, M Jannatabadi and E Mohseni. Application of He’s variational iteration method to nonlinear Jaulent-Miodek equations and comparing it with ADM. J. Comput. Appl. Math. 2007; 207, 35-45.

JH He. Variational iteration method-some recent results and new interpretations. J. Comput. Appl. Math. 2007; 207, 3-17.

JH He and XH Wu. Construction of solitary solution and compaction-like solution by variational iteration method. Chaos Soliton. Fract. 2006; 29, 108-13.

DD Ganji, Y Rostamiyan, IR Petroudi and MK Nejad. Analytical investigation of nonlinear model arising in heat transfer through the porous fin. Therm. Sci. 2014; 18, 409-17.

DD Ganji, H Tari and MB Jooybari. Variational iteration method and homotopy perturbation method for nonlinear evolution equations. Comput. Math. Appl. 2007; 54, 1018-27.

JH He. Variational iteration method-a kind of nonlinear analytical technique: Some examples. Int. J. Nonlinear Mech. 1999; 34, 699-708.

DD Ganji and SHH Kachapi. Analysis of nonlinear Equations in fluids. Prog. Nonlinear Sci. 2011; 3, 1-294.

J Singh, D Kumar and A Kılıçman. Homotopy perturbation method for fractional gas dynamics equation using sumudu transform. Abstr. Appl. Anal. 2013; 2013, Article ID

J Sushila, J Singh and YS Shishodia. An efficient analytical approach for MHD viscous flow over a stretching sheet via homotopy perturbation sumudu transform method. Ain Shams Eng. J. 2013; 4, 549-55.

J Singh, D Kumar and S Kumar. New treatment of fractional Fornberg-Whitham equation via Laplace transform. Ain Shams Eng. J. 2013; 4, 557-62.

J Singh, D Kumar and S Kumar. A reliable algorithm for solving discontinued problems arising in nanotechnology. Sci. Iran. 2013; 3, 1059-62.

A Aziz. Heat Conduction with Maple. R.T. Edwards, Philadelphia, 2006.

A Rasekh, DD Ganji, B Haghighi and S Tavakoli. Thermal performance assessment of a convective porous fin with variable cross section by means of OHAM. Int. J. Nonlinear Dynam. Eng. Sci. 2011; 3, 181-91.




How to Cite

SHAHBABAEI, M., GANJI, D. D., & RAHIMIPETROUDI, I. (2014). Prediction of a Semi-Exact Analytic Solution of a Convective Porous Fin with Variable Cross Section by Different Methods. Walailak Journal of Science and Technology (WJST), 12(10), 909–921. Retrieved from