Homotopy analysis method for heat radiation equations

International Communications in Heat and Mass Transfer

Volumn 34, Issue 3, 2007, Pages 380-387

  Abbasbandy, S ^a  

^a IMAM KHOMEINI INTERNATIONAL UNIVERSITY   (Iran)

Author keywords

Heat transfer; Homotopy analysis method; Homotopy perturbation method; Perturbation method; Radiation equation

Indexed keywords

HEAT CONVECTION; NONLINEAR EQUATIONS; PERTURBATION TECHNIQUES; RUNGE KUTTA METHODS;

HEAT RADIATION EQUATION; HOMOTOPY ANALYSIS METHOD; HOMOTOPY PERTURBATION METHOD; NONLINEAR CONVECTIVE-RADIATIVE EQUATION;

HEAT RADIATION;

HEAT CONVECTION; HEAT RADIATION; NONLINEAR EQUATIONS; PERTURBATION TECHNIQUES; RUNGE KUTTA METHODS;

EID: 33847658380     PISSN: 07351933     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.icheatmasstransfer.2006.12.001     Document Type: Article

References (19)

1. Abbasbandy S. Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method. Appl. Math. Comput. 172 (2006) 485-490
2. Abbasbandy S. A numerical solution of Blasius equation by Adomian's decomposition method and comparison with homotopy perturbation method. Chaos, Solitons Fractals 31 (2007) 257-260
3. Ayub M., Rasheed A., and Hayat T. Exact flow of a third grade fluid past a porous plate using homotopy analysis method. Int. J. Eng. Sci. 41 (2003) 2091-2103
4. Cole J.D. Perturbation Methods in Applied Mathematics (1968), Blaisdell Publishing Company, Waltham, MA
5. 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
6. Hayat T., and Khan M. Homotopy solutions for a generalized second-grade fluid past a porous plate. Nonlinear Dyn. 42 (2005) 395-405
7. Hayat T., Khan M., and Ayub M. On non-linear flows with slip boundary condition. ZAMP 56 (2005) 1012-1029
8. Karmishin A.V., Zhukov A.I., and Kolosov V.G. Methods of Dynamics Calculation and Testing for Thin-walled Structures (1990), Mashinostroyenie, Moscow
9. S.J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Thesis, Shanghai Jiao Tong University, 1992.
10. Liao S.J. An explicit, totally analytic approximation of Blasius' viscous flow problems. Int. J. Non-Linear Mech. 34 (1999) 759-778
11. Liao S.J. Beyond Perturbation: Introduction to the Homotopy Analysis Method (2003), Chapman and Hall/CRC Press, Boca Raton
12. Liao S.J. On the analytic solution of magnetohydrodynamic flows non-Newtonian fluids over a stretching sheet. J. Fluid Mech. 488 (2003) 189-212
13. Liao S.J. On the homotopy analysis method for nonlinear problems. Appl. Math. Comput. 147 (2004) 499-513
14. 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
15. Liao S.J. Comparison between the homotopy analysis method and homotopy perturbation method. Appl. Math. Comput. 169 (2005) 1186-1194
16. Lyapunov A.M. General Problem on Stability of Motion (English translation) (1992), Taylor and Francis, London
17. Nayfeh A.H. Perturbation Methods (2000), John Wiley and Sons, New York
18. Sajid M., Hayat T., and Asghar S. On the analytic solution of the steady flow of a fourth grade fluid. Phys. Lett., A 355 (2006) 18-26
19. Siddiquia A.M., Mahmoodb R., and Ghorib 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