Series solutions of stagnation slip flow and heat transfer by the homotopy analysis method

Science in China, Series G: Physics, Mechanics and Astronomy

Volumn 52, Issue 6, 2009, Pages 893-899

  Cheng, Jun ^a   Liao, Shijun ^b   Mohapatra, R N ^c   Vajravelu, K ^c  

^a SHANGHAI UNIVERSITY   (China)

^b Shanghai Jiao Tong University   (China)

^c UNIVERSITY OF CENTRAL FLORIDA   (United States)

Author keywords

Heat transfer; Homotopy analysis method; Nano fluidics; Navier boundary condition; Stagnation slip flow

Indexed keywords

ANALYTICAL APPROXIMATION; APPROXIMANTS; ASYMPTOTIC APPROXIMATION; CONTINUOUS MAPPINGS; HEAT TRANSFER CHARACTERISTICS; HOMOTOPY; HOMOTOPY ANALYSIS METHOD; HOMOTOPY ANALYSIS METHODS; NAVIER BOUNDARY CONDITION; NUMERICAL RESULTS; PHYSICAL PARAMETERS; SERIES EXPANSION METHODS; SERIES SOLUTIONS; SIMILARITY SOLUTION; SLIP FLOW; SLIP LENGTH; STAGNATION SLIP FLOW; STRONGLY NONLINEAR; THERMAL SLIP;

BOUNDARY CONDITIONS; FLUIDICS; HEAT EXCHANGERS; HEAT TRANSFER;

PERTURBATION TECHNIQUES;

EID: 67649130773     PISSN: 16721799     EISSN: 18622844     Source Type: Journal    
DOI: 10.1007/s11433-009-0117-y     Document Type: Article

References (42)

1. Fisher E G. Extrusion of Plastics. New York: Wiley, 1976
2. Schlichting H. Boundary Layer Theory. New York: McGraw-Hill, 1979
3. Tropea C, Yarin A L, Foss J F. Microfluidics: The no-slip boundary condition. In: Handbook of Experimental Fluid Mechanics, Chaper 19. Berlin Heidelberg: Springer, 2007
4. C. Neto E. Evans E. Bonaccurso 2005 Boundary slip in newtonian liquids: A review of experimental studies Rep Prog Phys 68 2859 2897 (Pubitemid 41435120)
5. Jennissen H P. Boundary-layer exchange by bubble: A novel method for generating transient nanofluidic layers. Phys Fluids, 2005, 17: 100616
6. White F M. Viscous Fluid Flow. 3rd ed. Boston: McGraw-Hill, 2006
7. C. L. M. H. Navier 1823 Mémoire sur les lois du mouvement des fluids Mémoires de l'Académie Royale des Sciences de l'Institut de France 6 389 440
8. Schaaf S, Chambre P. Flow of Rarefied Gass. Princeton: Princeton University Press, 1961
9. N. Kaneta H. Nishikawa K. Kameishi 1990 Observation of wall slip in elastohydrodynamic lubrication ASME: J Tribol 112 447 584
10. Russel W B, Saville D A, Schowalter W R. Colloidal Dispersions. Cambridge: Cambridge University Press, 1989
11. Batchelor G K. An Introduction to Fluid Dynamics. Cambridge: Cambridge University Press, 1967
12. M. von Smolushowski 1898 Ueber Wärmeleitung in verdünnten Gasen Ann Phys Chem 64 101 130
13. C. Y. Wang 2006 Stagnation slip flow and heat transfer on a moving plate Chem Eng Sci 61 7668 7672 (Pubitemid 44648038)
14. M. T. Mathews J. M. Hill 2007 Micro/nano thermal boundary layer equations with slip-creep-jump boundary conditions IMA J Appl Math 72 894 911 (Pubitemid 350186955)
15. N. Ishimura T. K. Ushijima 2004 An elementary approach to the analysis of exact solutions for the Navier-Stokes stagnation flows with slips Arch Math 82 432 441 (Pubitemid 38799721)
16. Nayfeh A H. Perturbation Methods. New York: John Wiley & Sons, 1973
17. Van Dyke M D. Perturbation Methods in Fluid Mechanics. New York: Academic, 1964
18. Von Dyke M D. Perturbation Methods in Fluid Mechanics. Stanford: The Parabolic Press, 1975
19. Nayfeh A H. Introduction to Perturbation Techniques. New York: John Wiley & Sons, 1981
20. Nayfeh A H. Problems in Perturbation. New York: John Wiley & Sons, 1985
21. Murdock J A. Perturbations: Theory and Methods. New York: John Wiley & Sons, 1991
22. Nayfeh A H. Method of Normal Forms. New York: John Wiley & Sons, 1993
23. Nayfeh A H. Perturbation Methods. New York: John Wiley & Sons, 2000
24. Poincaré H. Les methods nouvelles de la mècanique. Paris: Gauthier-Villars, 1892
25. Lyapunov A M. General problem on stability of motion (English translation). London: Taylor & Francis, 1992
26. Karmishin A V, Zhukov A T, Kolosov V G. Methods of dynamics calculation and testing for thin-walled structures (in Russian). Moscow: Mashinostroyenie, 1990
27. Awrejcewicz J, Andrianov I V, Manevitch L I. Asymptotic Approaches in Nonlinear Dynamics. Berlin: Springer-Verlag, 1998
28. G. Adomian 1976 Nonlinear Stochastic Differential Equations J Math Anal Applic 55 441 452
29. G. Adomian R. Rach 1985 On the solution of algebraic equations by the decomposition method Math Anal Appl 105 1 141 166 (Pubitemid 15476665)
30. Y. Cherruault 1988 Convergence of Adomian's method Kyberneters 8 2 31 38
31. G. Adomian 1991 A review of the decomposition method and some recent results for nonlinear equations Comp Math Applic 21 101 127
32. Liao S J. Beyond Perturbation: Introduction to the Homotopy Analysis Method. Boca Raton: Chapman & Hall/CRC Press, 2003
33. Liang S, Jeffrey D J. Comparison of homotopy analysis method and homotopy perturbation method through an evaluation equation. Commun Nonlinear Sci Numer Simul, online, doi: 10.1016/j.cnsns.2009.02.016
34. S. J. Liao E. Magyari 2006 Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones Zeitschrift für angewandte Mathematik und Physik 57 5 777 792 (Pubitemid 44286392)
35. S. J. Liao 2008 Beyond perturbation: The homotopy analysis method and its application Adv Mech 38 1 1 34
36. S. J. Liao Y. Tan 2007 A general approach to obtain series solutions of nonlinear differential equations Stud Appl Math 119 297 355
37. M. Sajid T. Hayat S. Asghar 2007 Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt Nonlinear Dyn 50 27 35 (Pubitemid 47327530)
38. T. Hayat M. Sajid 2007 On analytic solution for thin film flow of a forth grade fluid down a vertical cylinder Phys Lett A 361 316 322 (Pubitemid 44894740)
39. V. Marinca N. Herisanu I. Nemes 2009 A modified homotopy analysis method with application to thin film flow of a fourth grade fluid down a vertical cylinder Central Eur J Phys 14 4 1196 1207
40. Cheng J, Cang J, Liao S J. On the interaction of deep water waves and exponential shear currents. Zeitschrift für angewandte Mathematik und Physik, online, doi: 10.1007/s00033-008-7050-1
41. S. J. Liao 2009 Notes on the homotopy analysis method some definitions and theorems Commun Nonlinear Sci Numer Simul 14 4 983 997
42. M. Van Dyke 1970 Extension of Goldstein's series for the Oseen drag of a sphere J Fluid Mech 44 365 372