Some nonlinear heat transfer equations solved by three approximate methods

International Communications in Heat and Mass Transfer

Volumn 34, Issue 8, 2007, Pages 1003-1016

  Ganji, D D ^a   Hosseini, M J ^a   Shayegh, J ^a  

^a UNIVERSITY OF MAZANDARAN   (Iran)

Author keywords

Homotopy perturbation method; Nonlinear heat transfer; Perturbation method; Variational iteration method

Indexed keywords

APPROXIMATION THEORY; FINS (HEAT EXCHANGE); FREEZING; ITERATIVE METHODS; PERTURBATION TECHNIQUES; TEMPERATURE DISTRIBUTION; VARIATIONAL TECHNIQUES;

HOMOTOPY PERTURBATION METHOD; VARIATIONAL ITERATION METHOD;

HEAT TRANSFER;

APPROXIMATION THEORY; FINS (HEAT EXCHANGE); FREEZING; HEAT TRANSFER; ITERATIVE METHODS; PERTURBATION TECHNIQUES; TEMPERATURE DISTRIBUTION; VARIATIONAL TECHNIQUES;

EID: 34547842881     PISSN: 07351933     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.icheatmasstransfer.2007.05.010     Document Type: Article

References (30)

1. Abdou M.A., and Soliman A.A. Variational iteration method for solving Burger's and coupled Burger's equations. J. Comput. Appl. Math. 181 (2005) 245-251
2. Abulwafa E.M., Abdou M.A., and Mahmoud A.A. The solution of nonlinear coagulation problem with mass. Chaos, Solitons Fractals 29 (2006) 313-330
3. Aziz A., and Na T.Y. Perturbation Method in Heat Transfer (1984), Hemisphere Publishing corporation, Washington, DC
4. Bildik N., and 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) 65-70
5. Tari H., Ganji D.D., and Babazadeh H. The application of He's variational iteration method to nonlinear equations arising in heat transfer. Phys. Lett., A, 363 3 (2007) 213-217
6. Ganji D.D., and Rajabi A. Assessment of homotopy-perturbation and perturbation methods in heat radiation equations. Int. Commun. Heat Mass Transf. 33 (2006) 391-400
7. Ganji D.D. The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer. Phys. Lett., A 355 (2006) 337-341
8. He J.H. Variational iteration method a kind of non-linear analytical technique: some examples. Int. J. Non-linear Mech. 34 (1999) 699-708
9. He J.H. Homotopy perturbation technique. Com. Methods Appl. Mech. Eng. 178 (1999) 257-262
10. He J.H. Variational iteration method for autonomous ordinary differential systems. Appl. Math. Comput. 114 (2000) 115-123
11. He J.H. A coupling method of a homotopy technique and a perturbation technique for non-linear problems. Int. J. Non-linear Mech. 35 (2000) 37-43
12. He J.H. Homotopy perturbation method: a new nonlinear analytical technique. Appl. Math. Comput. 135 (2003) 73-79
13. Rajabi A., Ganji D.D., and Taherian H. Application of homotopy perturbation method in nonlinear heat conduction and convection equations. Phys. Lett., A 360 (2006) 570-573
14. He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons Fractals 26 (2005) 695-700
15. He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. Int. J. Nonlinear Sci. Numer. Simul. 6 (2005) 207-208
16. He J.H. Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 20 (2006) 1141-1199
17. J.H. He, Non-perturbative methods for strongly nonlinear problems, Dissertation, de-Verlag im Internet GmbH, Berlin, 2006.
18. He J.H., and Wu X.H. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos, Solitons Fractals, 29 (2006) 108-113
19. Odibat Z.M., and Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. Int. J. Nonlinear Sci. Numer. Simul. 7 (2006) 27-34
20. Siddiqui A.M., Mahmood R., and Ghori Q.K. Homotopy perturbation method for thin film flow of a fourth grade fluid down a vertical cylinder. Phys. Lett. A 352 (2006) 404-410
21. Siddiqui A.M., Mahmood R., and Ghori Q.K. Thin film flow of a third grade fluid on amoving belt by He's homotopy perturbation method. Int. J. Nonlinear Sci. Numer. Simul. 7 (2006) 7-14
22. Mobedi M., and Sunden B. Natural convection heat transfer from a thermal heat source located in a vertical plate fin. Int. Commun. Int. J. Heat Mass Transf 33-8 (2006) 943-950
23. Nayfeh A.H. Perturbation Methods (1973), Wiely, Newyork
24. Rahman M.M., and Siikonen T. An improved simple method on a collocated grid. Numer. Heat Transf., Part B Fundam. (2000) 177-201
25. Scheerlinck N., Verboven P., De Stigter J.D., Baerdemaeker J., Van Impe J.F., and Nicolai B.V. Stochastic finite-element analysis of coupled heat and mass transfer problems with random field parameters. Numer. Heat Transf., Part B Fundam. (2000) 309-330
26. Aude P., Beghein C., Depecher P., and Inard C. Perturbation of the input data of models used for the prediction of turbulent air flow in an enclosure. Numer. Heat Transf., Part B Fundam (1998) 139-164
27. Kuznetsov A.V., and Vafai K. Comparison between the two-and three-phase models for analysis of porosity formation in aluminum-rich castings. Numer. Heat Transf., Part B Fundam. (1996) 859-867
28. Wilson R.V., and Demuren A.O. Two-dimensional spatially developing mixing layers. Numer. Heat Transf., Part B Fundam. (1996) 485-509
29. Fillo J., and Geer J. Hybrid perturbation-Galerkin technique for nonlinear heat conduction problems II: partial differential equations. Numer. Heat Transf., Part B Fundam. (1996) 75-89
30. Fillo J., and Geer J. Hybrid perturbation-Galerkin technique for nonlinear heat conduction problems I: Steady problem. Numer. Heat Transf., Part B Fumdam. (1996) 61-73