Analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation

Communications in Nonlinear Science and Numerical Simulation

Volumn 16, Issue 4, 2011, Pages 1874-1889

  Rashidi, M M ^a   Mohimanian pour, S A ^a   Abbasbandy, S ^b  

^a BU ALI SINA UNIVERSITY   (Iran)

^b ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

Convergence; Homotopy analysis method; Micropolar fluid; Porous medium

Indexed keywords

HEAT TRANSFER; NONLINEAR EQUATIONS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; RUNGE KUTTA METHODS;

ANALYSIS METHOD; ANALYTIC APPROXIMATE SOLUTION; ANALYTIC SOLUTION; CONVERGENCE; HOMOTOPY ANALYSE METHOD; HOMOTOPY ANALYSIS; MICRO-POLAR FLUIDS; NONLINEAR ORDINARY DIFFERENTIAL EQUATION; POROUS MEDIUM; SERIES SOLUTIONS;

POROUS MATERIALS;

EID: 78049374319     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.08.016     Document Type: Article

References (28)

1. Nayfeh AH. Introduction to perturbation techniques 1979, Wiley.
2. Rand RH., Armbruster D. Perturbation methods, bifurcation theory and computer algebraic 1987, Springer.
3. Lyapunov A.M. General problem on stability of motion (English translation) 1992, Taylor and Francis, London, Original work published 1892.
4. Karmishin A.V., Zhukov A.I., Kolosov V.G. Methods of dynamics calculation and testing for thin-walled structures 1990, Mashinostroyenie, Moscow, in Russian.
5. Adomian G. Solving frontier problems of physics: the decomposition method 1994, Kluwer Academic Publishers., Boston and London.
6. Liao SJ. The proposed homotopy analysis technique for the solution of nonlinear problems. Ph.D. Thesis. Shanghai Jiao Tong University; 1992.
7. Liao S.J. Beyond perturbation: introduction to the homotopy analysis method 2003, Chapman and Hall/CRC Press, Boca Raton.
8. Liao S.J. An explicit, totally analytic approximation of Blasius viscous flow problems. Int J NonLinear Mech 1999, 34:759-778.
9. Liao S.J. On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. J Fluid Mech 2003, 488:189-212.
10. Liao S.J. On the homotopy analysis method for nonlinear problems. Appl Math Comput 2004, 147:499-513.
11. Liao S.J. Comparison between the homotopy analysis method and homotopy perturbation method. Appl Math Comput 2005, 169:1186-1194.
12. Sajid M., Hayat T., Asghar S. Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt. Nonlinear Dyn 2007, 50:27-35.
13. Allan F.M. Derivation of the Adomian decomposition method using the homotopy analysis method. Appl Math Comput 2007, 190:6-14.
14. Abbasbandy S. The application of homotopy analysis method to nonlinear equations arising in heat transfer. Phys Lett A 2006, 360:109-113.
15. Abbasbandy S. Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method. Chem Eng J 2008, 136(2-3):144-150.
16. Allan F.M. Construction of analytic solution to chaotic dynamical systems using the homotopy analysis method. Chaos, Solitons Fractals 2009, 39(4):744-1752.
17. Allan F.M., Syam M.I. On the analytic solution of non-homogeneous Blasius problem. J Comput Appl Math 2005, 182:362-371.
18. Hayat T., Javed T. On analytic solution for generalized three-dimensional MHD flow over a porous stretching sheet. Phys Lett A 2007, 370:243-250.
19. Sajid M., Siddiqui A.M., Hayat T. Wire coating analysis using MHD Oldroyd 8-constant fluid. Int J Eng Sci 2007, 45:381-392.
20. Hayat T., Sajid M. Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet. Int J Heat Mass Transfer 2007, 50:75-84.
21. Hayat T., Ahmed Naveed, Sajid M., Asghar S. On the MHD flow of a second grade fluid in a porous channel. Comput Math Appl 2007, 54:407-414.
22. Hayat T., Sajid M., Ayub M. A note on series solution for generalized Couette flow. Commun Nonlinear Sci Numer Simul 2007, 12:481-1487.
23. Ran X.J., Zhu Q.Y., Li Y. An explicit series solution of the squeezing flow between two infinite plates by means of the homotopy analysis method. Commun Nonlinear Sci Numer Simul 2009, 14(1):119-132.
24. Rashidi M.M., Dinarvand S. Purely analytic approximate solutions for steady three-dimensional problem of condensation film on inclined rotating disk by homotopy analysis method. Nonlinear Anal: Real World Appl 2009, 10(4):2346-2356.
25. Rashidi M.M., Domairry G., Dinarvand S. Approximate solutions for the Burger and regularized long wave equations by means of the homotopy analysis method. Commun Nonlinear Sci Numer Simul 2009, 14(3):708-717.
26. Ziabakhsh Z., Domairry G. Solution of the laminar viscous flow in a semi-porous channel in the presence of a uniform magnetic field by using the homotopy analysis method. Commun Nonlinear Sci Numer Simul 2009, 14(4):1284-1294.
27. Abo-Eldahab E.M., Ghonaim A.F. Radiation effect on heat transfer of a micropolar fluid through a porous medium. Appl Math Comput 2005, 169:500-510.
28. Liao S.J. An optimal homotopy-analysis approach for strongly nonlinear differential equations. Commun Nonlinear Sci Numer Simul 2010, 15:2003-2016.