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

Volumn 14, Issue 8, 2009, Pages 3327-3338

  Khani, F ^a   Raji, M Ahmadzadeh ^b   Nejad, H Hamedi ^c  

^a Bakhtar Institute of Higher Education Iran   (Iran)

^b RAZI UNIVERSITY   (Iran)

^c SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Fin efficiency; Heat transfer; Homotopy analysis method; Homotopy perturbation method; Thermal conductivity

Indexed keywords

EFFICIENCY; FINS (HEAT EXCHANGE); NONLINEAR ANALYSIS; PERTURBATION TECHNIQUES; THERMAL CONDUCTIVITY;

ANALYSIS METHOD; FIN EFFICIENCY; HEAT TRANSFER CO-EFFICIENTS; HOMOTOPIES; HOMOTOPY ANALYSE METHOD; HOMOTOPY ANALYSIS; HOMOTOPY PERTURBATION METHOD; PERTURBATION METHOD; TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY; THERMAL HEAT;

HEAT TRANSFER COEFFICIENTS;

EID: 60849108033     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.01.012     Document Type: Article

References (26)

1. Aziz A., and Enamul Hug S.M. Perturbation solution for convecting fin with variable thermal conductivity. J Heat Transfer-Trans ASME 97 (1975) 300-301
2. Aziz A., and Benzies J.Y. Application of perturbation techniques to heat-transfer problems with variable thermal properties. Int J Heat Mass Transfer 19 (1976) 271-276
3. Pakdemirli M., and Sahin A.Z. Group classification of fin equation with variable thermal properties. Int J Eng Sci 42 (2004) 1875-1889
4. Bokhari A.H., Kara A.H., and Zaman F.D. A note on a symmetry analysis and exact solutions of a nonlinear fin equation. Appl Math Lett 19 (2006) 1356-1360
5. Kim S., and Huang C.-H. A series solution of the non-linear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient. J Phys D: Appl Phys 40 (2007) 2979-2987
6. Liao SJ, The proposed homotopy analysis technique for the solution of nonlinear problems. PhD thesis, Shanghai Jiao Tong University; 1992.
7. Liao S.J. An explicit, totally analytic approximate solution for Blasius-viscous flow problems. Int J Non-Linear Mech 34 (1999) 759-778
8. Liao S.J. Beyond perturbation: introduction to the homotopy analysis method (2003), Chapman & Hall/CRC Press, Boca Raton (FL)
9. Liao S.J. A general approach to get series solution of non-similarity boundary-layer flows. Commun Nonlinear Sci Numer Simulat 14 (2009) 2144-2159
10. Liao S.J. On the homotopy analysis method for nonlinear problems. Appl Math Comput 147 (2004) 499-513
11. Liao S.J. A new branch of solutions of boundary-layer flows over an impermeable stretched plate. Int J Heat Mass Transfer 48 (2005) 2529-2539
12. Domairry G., and Fazeli M. Homotopy analysis method to determine the fin efficiency of convective straight fins with temperature-dependent thermal conductivity. Commun Nonlinear Sci Numer Simulat 14 (2009) 489-499
13. Inc M. Application of homotopy analysis method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity. Math Comput Simulat (2008) 10.1016/j.matcom.2007.11.009
14. Chowdhury M.S.H., Hashim I., and Abdulaziz O. Comparison of homotopy analysis method and homotopy-perturbation method for purely nonlinear fin-type problems. Commun Nonlinear Sci Numer Simulat 14 (2009) 371-378
15. Tan Y., and Abbasbandy S. Homotopy analysis method for quadratic Riccati differential equation. Commun Nonlinear Sci Numer Simulat 13 3 (2008) 539-546
16. Molabahrami A., and Khani F. The homotopy analysis method to solve the Burgers-Huxley equation. Nonlinear Anal Real World Appl 10 2 (2009) 589-600
17. Khani F., Ahmadzadeh Raji M., and Hamedi-Nezhad S. A series solution of the fin problem with a temperature-dependent 3 thermal conductivity. Commun Nonlinear Sci Numer Simulat 14 (2009) 3007-3017
18. Sajid M., Ahmad I., Hayat T., and Ayub M. Unsteady flow and heat transfer of a second grade fluid over a stretching sheet. Commun Nonlinear Sci Numer Simulat 14 1 (2009) 96-108
19. Abbasbandy S. Soliton solutions for the 5th-order KdV equation with the homotopy analysis method. Nonlinear Dyn 51 (2008) 83-87
20. Song L., and Zhang H.Q. Application of homotopy analysis method to fractional KdV-Burgers-Kuramoto equation. Phys Lett A 367 (2007) 88-94
21. Liao S.J. Notes on the homotopy analysis method: some definitions and theorems. Commun Nonlinear Sci Numer Simulat 14 4 (2009) 983-997
22. Watson L.T. Globally convergent homotopy methods: a tutorial. Appl Math Comput 31 (1989) 369-396
23. Watson L.T. Engineering applications of the Chow-Yorke algorithm. Appl Math Comput 9 (1981) 111-133
24. Liao S.J. Comparison between the homotopy analysis method and homotopy perturbation method. Appl Math Comput 169 (2005) 1186-1194
25. He J.H. Comparison of homotopy perturbation method and homotopy analysis method. Appl Math Comput 156 (2004) 527-539
26. Allan F.M. Derivation of the Adomian decomposition method using the homotopy analysis method. Appl Math Comput 190 (2007) 6-14