A series solution of the fin problem with a temperature-dependent thermal conductivity

Communications in Nonlinear Science and Numerical Simulation

Volumn 14, Issue 7, 2009, Pages 3007-3017

  Khani, F ^a   Ahmadzadeh Raji, M ^b   Hamedi Nezhad, S ^c  

^a ILAM UNIVERSITY   (Iran)

^b RAZI UNIVERSITY   (Iran)

^c Bakhtar Institute of Higher Education Iran   (Iran)

Author keywords

Fin; Homotopy analysis method; Homotopy perturbation method; Thermal conductivity

Indexed keywords

APPROXIMATION ALGORITHMS; FINS (HEAT EXCHANGE); PERTURBATION TECHNIQUES;

ADOMIAN DECOMPOSITION METHOD; ANALYSIS METHOD; FIN; HOMOTOPIES; HOMOTOPY ANALYSE METHOD; HOMOTOPY ANALYSIS; HOMOTOPY PERTURBATION METHOD; PERTURBATION METHOD; SERIES SOLUTIONS; TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY;

THERMAL CONDUCTIVITY;

EID: 59849100822     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2008.11.004     Document Type: Article

References (25)

1. Kern D.Q., and Kraus D.A. Extended surface heat transfer (1972), McGraw-Hill, New York
2. 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
3. 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
4. Chang Y.M., Wang T.-S., and Chen C.-K. Optimal linearization and variational embedding solutions for convective fins with variable thermal conductivity. Lett Heat Mass Transfer 9 (1982) 99-106
5. Yu L.-T., and Chen C.-K. Application of Taylor transformation to optimize rectangular fins with variable thermal parameters. Appl Math Modell 22 (1998) 11-21
6. Yu L.-T., and Chen C.-K. Optimization of circular fins with variable thermal parameters. J Franklin Inst 336 (1999) 77-95
7. Chiu C.-H., and Chen C.-K. A decomposition method for solving the convective longitudinal fins with variable thermal conductivity. Int J Heat Mass Transfer 45 (2002) 2067-2075
8. Pakdemirli M., and Sahin A.Z. Group classification of fin equation with variable thermal properties. Int J Eng Sci 42 (2004) 1875-1889
9. Kim S., and Huang C.-H. A series solution of the fin problem with a temperature-dependent thermal conductivity. J Phys D: Appl Phys 39 (2006) 4894-4901
10. Liao SJ. The proposed homotopy analysis technique for the solution of nonlinear problems, PhD thesis. Shanghai Jiao Tong University, 1992.
11. Liao S.J. An explicit, totally analytic approximate solution for Blasius viscous flow problems. Int J Non-Linear Mech 34 (1999) 759-778
12. Liao S.J. Beyond perturbation: introduction to the homotopy analysis method (2003), Chapman & Hall/CRC Press, Boca Raton
13. Liao S.J. A general approach to get series solution of non-similarity boundary-layer flows. Commun Nonlinear Sci Numer Simulat 14 5 (2009) 2144-2159
14. Liao S.J. On the homotopy analysis method for nonlinear problems. Appl Math Comput 147 (2004) 499-513
15. 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
16. Tan Y., and Abbasbandy S. Homotopy analysis method for quadratic Riccati differential equation. Commun Nonlinear Sci Numer Simulat 13 3 (2008) 539-546
17. Molabahrami A., and Khani F. The homotopy analysis method to solve the Burgers-Huxley equation. Nonlinear Analysis Real World Applications. 10 12 (2009) 589-600
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 KdVBurgersKuramoto 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