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	Volume 1, Issue 3 Pg 233 - 342 (October 2007)
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JP Journal of Heat and Mass Transfer

JP Journal of Heat and Mass Transfer
Volume 1, Issue 3, Pages 285 - 296 (October 2007)

A MODIFIED HOMOTOPY-PERTURBATION METHOD FOR PURELY NONLINEAR FIN-TYPE PROBLEMS M. S. H. Chowdhury (Malaysia) and I. Hashim (Malaysia) Received August 13, 2007 References:
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S. H. Chowdhury, I. Hashim and O. Abdulaziz, Application of homotopy-perturbation method to nonlinear population dynamics models, Phys. Lett. A doi:10.1016/j.physleta.2007.04.007. [8] M. S. H. Chowdhury, I. Hashim and S. Momani, The multistage homotopy-perturbation method: A powerful scheme for handling the Lorenz system, Chaos, Solitons & Fractals (accepted). [9] D. D. Ganji, The application of He’s homotopy perturbation method to nonlinear equations arising in heat transfer, Phys. Lett. A 355 (2006), 337-341. [10] D. D. Ganji and A. Rajabi, Assessment of homotopy-perturbation and perturbation methods in heat radiation equations, Int. Comm. Heat Mass Transfer 33 (2006), 391-400. [11] T. S. Gill, A. Singh, H. Kaur, N. S. Saini and P. Bala, Ion-acoustic solitons in weakly relativistic plasma containing electron-positron and ion, Phys. Lett. A 361(4-5) (2007), 364-367. [12] K. W. Haley and J. W. Westwater, Boiling heat transfer from single fins, Proceedings of the 3rd International Heat Transfer Conference, Chicago, 1966. [13] J. H. He, Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput. Methods Appl. Mech. Engrg. 167(1-2) (1998), 57-68. [14] J. H. He, Homotopy perturbation technique, Comput. Methods Appl. Mech. Engrg. 178(3/4) (1999), 257-262. [15] J. H. He, A coupling method of homotopy technique and perturbation technique for nonlinear problems, Inter. J. Non-Linear Mech. 35(1) (2000), 37-43. [16] J. H. He, Homotopy perturbation method: a new nonlinear analytical technique, Appl. Math. Comput. 135 (2003), 73-79. [17] J. H. He, Comparison of homotopy perturbation method and homotopy analysis method, Appl. Math. Comput. 156 (2004), 527-539. [18] J. H. He, Non-perturbative Methods for Strongly Nonlinear Problems, Die Deutsche Bibliothek, Germany, 2006. [19] Q. D. Kern and D. A. Kraus, Extended Surface Heat Transfer, McGraw-Hill, New York, 1972. [20] F. S. Lai and Y. Y. Hsu, Temperature distribution in a fin partially cooled by nucleate boiling, AIChE J. 13 (1967), 817-821. [21] D. Lesnic and P. J. Heggs, A decomposition method for power-law fin-types problems, Int. Comm. Heat Mass Transfer 31(5) (2004), 673-682. [22] S. P. Liaw and R. H. Yeh, Fins with temperature dependent surface heat flux–I: Single heat transfer mode, Int. J. Heat Mass Transfer 37 (1994), 1509-1515. [23] S. P. Liaw and R. H. Yeh, Fins with temperature dependent surface heat flux–II: Multi-boiling heat transfer, Int. J. Heat Mass Transfer 37 (1994), 1517-1524. [24] G. L. Liu, Weighted residual decomposition method in nonlinear applied mathematics, Proceedings of the 6th Congress of Modern Mathematical and Mechanics, Suzhou, China, 1995. [25] S. T. Mohyud-Din and M. A. Noor, Homotopy perturbation method for solving fourth-order boundary value problems, Math. Prob. Engrg. doi:10.1155/2007/98602. [26] S. Momani and Z. Odibat, Homotopy perturbation method for nonlinear partial differential equations of fractional order, Phys. Lett. A doi:10.1016/j.physleta.2007.01.046. [27] M. A. Noor and S. T. Mohyud-Din, An efficient algorithm for solving fifth-order boundary value problems, Math. Comput. Model 45(7-8) (2007), 954-964. [28] Z. Odibat and S. Momani, Modified homotopy perturbation method: Application to quadratic riccati differential equation of fractional order, Chaos, Solitons & Fractals doi:10.1016/j.chaos.2006.06.041. [29] Turgut Ozis and Ahmet Y1ld1r1m, A note on He’s homotopy perturbation method for van der Pol oscillator with very strong nonlinearity, Chaos, Solitons & Fractals doi:10.1016/j.chaos.2006.04.013. [30] A. Rajabi, Homotopy perturbation method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity, Phys. Lett. A doi:10.1016/j.physleta.2006.11.062. [31] A. Rajabi, D. D. Ganji and H. Taherian, Application of homotopy perturbation method in nonlinear heat conduction and convection equations, Phys. Lett. A 360 (2007), 570-573. [32] F. Shakeri and M. Dehghan, Inverse problem of diffusion equation by He’s homotopy perturbation method, Phys. Scr. 75(4) (2007), 551-556. [33] A. M. Siddiqui, R. Mahmood and Q. K. Ghori, Thin film flow of a third grade fluid on a moving belt by He’s homotopy perturbation method, Int. J. Nonlinear Sci. Numer. Simul. 7(1) (2006), 7-14. [34] A. M. Siddiqui, R. Mahmood and Q. K. Ghori, Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder, Phys. Lett. A 352 (2006), 404-410. [35] H. C. Unal, Determination of the temperature distribution in an extended surface with a non-uniform heat transfer coefficient, Int. J. Heat Mass Transfer 28 (1986), 2279-2284. [36] H. C. Unal, A simple method of dimensioning straight fins for nucleate pool boiling, Int. J. Heat Mass Transfer 29 (1987), 640-644. [37] H. C. 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Keywords and phrases: homotopy-perturbation method, nonlinear DEs, fins.

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