Solving the Navier Stokes Flow Equations of Micro-Polar Fluids by Adomian Decomposition Method

Adanhounmè, Villevo; de Paule Codo, François; Adomou, Alain

doi:10.18052/www.scipress.com/BMSA.2.30

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Solving the Navier Stokes Flow Equations of Micro-Polar Fluids by Adomian Decomposition Method

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Abstract:

In this paper we investigate the Navier Stokes flow equations of micro-polar fluids by peristaltic pumping through the cylindrical tube. Taking into account the slip boundary conditions at the wall and using the suitable change of variables, we transform these equations into the ordinary differential equations for which we apply the Adomian decomposition method. Doing so we obtain the stream function, the axial velocity, the micro-polar vector and the pressure.

Info:

Periodical:

Bulletin of Mathematical Sciences and Applications (Volume 2)

Pages:

30-37

DOI:

https://doi.org/10.18052/www.scipress.com/BMSA.2.30

Citation:

V. Adanhounmè et al., "Solving the Navier Stokes Flow Equations of Micro-Polar Fluids by Adomian Decomposition Method", Bulletin of Mathematical Sciences and Applications, Vol. 2, pp. 30-37, 2012

Online since:

November 2012

Authors:

Villevo Adanhounmè, François de Paule Codo, Alain Adomou

Keywords:

Change of Variable, Micro-Polar Fluid, Navier Stokes Flow, Slip Boundary Conditions

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Open Access

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Creative Commons Attribution 4.0 International License

References:

[1] C. Eringen, Theory of micro-polar fluids, Journal of Mathematics and Mechanics, 16, pp.1-16. (1966).

[2] D. Srinivacharya, M. Mishra and A.R. Rao, Peristaltic pumping of a micro-polar fluid in a tube,. Acta Mechanica, 161, pp.165-178, (2003).

[3] T. Hayat, N. Ali and Z. Abbas, Peristaltic flow of micro-polar fluid in a channel with different wave forms, Physics letters A, 370, pp.331-344, (2007).

DOI: https://doi.org/10.1016/j.physleta.2007.05.099

[4] W. Kwang, H. Chu and J. Fang, Peristaltic transport in a slip flow, European Physical Journal B, 16, pp.543-547, (2000).

[5] D. Tripathi, M.K. Chaube and P.K. Gupta, Stokes flow of micro-polar fluids by peristaltic pumping through tube with slip boundary condition, Appl. Math. Mech. -Engl. Ed., vol. 32, n0. 12, pp.1587-1598, (2011).

DOI: https://doi.org/10.1007/s10483-011-1525-6

[6] D. Tripathi, P.K. Gupta and S. Das, Influence of slip condition on peristaltic transport of a viscoelastic fluid with fractional Burgers' model, Thermal Science , vol. 15, n0. 2, pp.501-515, (2011).

DOI: https://doi.org/10.2298/tsci1102501t

[7] S.K. Pandey and D. Tripathi, Peristaltic transport of a casson fluid in a finite channel: application to flows of concentrated fluids in oesophagus, International Journal of Biomathematics, 3, pp.473-491. (2000).

DOI: https://doi.org/10.1142/s1793524510001100

[8] D. Tripathi, Numerical and analytical simulation of peristaltic flows of generalized Oldroyd-B fluids, " International Journal for Numerical Methods in Fluids, DOI 10. 1002/. d. 2466.

DOI: https://doi.org/10.1002/fld.2466

[9] D. Tripathi, Numerical study on peristaltic flow of generalized Burgers' fluids in uniform tubes in presence of an endoscope, International Journal for Numerical Methods in Biomedical Engineering, vol. 27, n0. 11, pp.1812-1828, (2011).

DOI: https://doi.org/10.1002/cnm.1442

[10] D. Tripathi, Peristaltic transport of fractional Maxwell fluids in uniform tubes: application of an endoscope, Computers and Mathematics with Applications, vol. 62, n0. 3, pp.1116-1126, (2011).

DOI: https://doi.org/10.1016/j.camwa.2011.03.038

[11] D. Tripathi, S.K. Pandey and S. Das, Peristaltic flow of viscoelastic fluid with fractional Maxwell model through a channel, Applied Mathematics and Computation, 215, pp.3645-3654, (2010).

DOI: https://doi.org/10.1016/j.amc.2009.11.002

[12] A. N. Shapiro, M.K. Jaferin and S.L. Weinberg, Peristaltic pumping with long wavelengths at low Reynolds number, Journal of Fluid Mechanics, 37, pp.799-825, (1969).

DOI: https://doi.org/10.1017/s0022112069000899

[13] G. Adomian, A review of the decomposition method and some recent results for nonlinear equations, Comput. Math. Applic, vol. 21, n0. 5 pp.101-127, (1991).

[14] G. Adomian, A review of the decomposition method and some recent results for nonlinear equations, Math. Comp. Modelling, vol. 13, n0. 7, pp.17-43, (1990).

[15] Y. Cherruault, Convergence of Adomian's method, Kybernetes, vol. 18, n0. 2, p.3138, (1989).

[16] J. Jin and M. Liu, A new modification of Adomian decomposition method for solving a kind of evolution equations, Appl. Math. Comput., 169, p.953962, (2005).

[17] E. Babolian and J. Biazar, Solution of nonlinear equations by modified Adomian decomposition method, Appl. Math. Comput., 132, pp.167-172, (2002).

DOI: https://doi.org/10.1016/s0096-3003(01)00184-9

[18] A.M. Wazwaz, A reliable modification of Adomian decomposition method, Appl. Math. Comp., 102, pp.77-86, (1999).

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