Research PapersNo Access

Topological stability and patterns of traveling wave for a micro-polar non-Newtonian fluid model

College of Petroleum Engineering, Northeast Petroleum University, Daqing 163318, China

https://doi.org/10.1142/S0217984921502377Cited by:7 (Source: Crossref)

Abstract

A nonlinear micro-polar non-Newtonian fluid model is investigated. By the complete discrimination system for polynomial method, we give the classification of the traveling wave patterns and analysis of topological stability and dynamical behaviors. We also discuss the physical realizations and the conditions of existence of these patterns. As a result, when some of parameters are not intrinsic parameters we show that in general only two stable patterns will be observed.

Keywords:

References

1. S. C. Cowin, The theory of polar fluids, in Advances in Applied Mechanics, ed. C. S. Yih, Vol. 14 (Academic Press, New York, 1974), pp. 279–347. Google Scholar
2. V. K. Stokes, Theories of Fluids with Microstructure: An Introduction (Springer Verlag, New York, 1984). Google Scholar
3. F. Shahzad, M. Sajid, T. Hayat and M. Ayub, Acta Mech. 188 (2007) 93. Web of Science, Google Scholar
4. N. A. Khan, A. Ara and M. Jamil, Int. J. Nonlinear. Sci. Numer. Simul. 10(9) (2009) 1121. Web of Science, Google Scholar
5. F. M. Hady, Int. J. Numer. Methods Heat Fluid Flow 6(6) (1996) 99. Web of Science, Google Scholar
6. F. S. Ibrahem, I. A. Hassanien and A. A. Bakr, J. Appl. Mech. 72(4) (2005) 468. Web of Science, Google Scholar
7. C. Hintze, Z. Naturforsch. A 66(3–4) (2011) 181. Web of Science, Google Scholar
8. S. K. Pandey and M. K. Chaube, Commun. Nonlinear Sci. Numer. Simul. 16(9) (2011) 3591. Web of Science, ADS, Google Scholar
9. H. H. Sherief et al., Eur. J. Mech. B-Fluids 59 (2016) 186. Web of Science, Google Scholar
10. L. Zheng, Z. Chen and S. Zhang, J. Math. Anal. Appl. 468(2) (2018) 865. Web of Science, Google Scholar
11. C.-S. Liu, Commun. Theor. Phys. 44(5) (2005) 799. Web of Science, ADS, Google Scholar
12. C.-S. Liu, Commun. Theor. Phys. 54(6) (2006) 991. ADS, Google Scholar
13. C.-S. Liu, Chin. Phys. Lett. 21(12) (2004) 2369. Web of Science, ADS, Google Scholar
14. C.-S. Liu, Commun. Theor. Phys. 49(2) (2008) 291. Web of Science, ADS, Google Scholar
15. C.-S. Liu, Comput. Phys. Commun. 181(2) (2010) 317. Web of Science, ADS, Google Scholar
16. C.-S. Liu, Acta Phys. Sinica 54(6) (2005) 2505. Web of Science, Google Scholar
17. C.-S. Liu, Acta Phys. Sinica 54(10) (2005) 4506. Web of Science, Google Scholar
18. C.-S. Liu, Found. Phys. 41(5) (2011) 793. Web of Science, ADS, Google Scholar
19. C.-S. Liu, Chaos Soliton Fractals 40(2) (2009) 708. Web of Science, ADS, Google Scholar
20. Y. Liu and X. Wang, Adv. Difference Equations 2019(1) (2019) 134. Web of Science, Google Scholar
21. X. Wang and Y. Liu, Mod. Phys. Lett. B 33(1) (2019) 1850428. Link, Web of Science, ADS, Google Scholar
22. Y. Liu, Appl. Math. Comput. 217(12) (2011) 5866. Web of Science, Google Scholar
23. X. Wang and Y. Liu, Pramana J. Phys. 92 (2019) 31. Web of Science, ADS, Google Scholar
24. Y. Kai et al., Chaos Solitons Fractals 141 (2020) 110314. Web of Science, Google Scholar
25. X. Wang and Y. Liu, Mod. Phys. Lett. B 34(31) (2020) 2050356. Link, Web of Science, ADS, Google Scholar