OHAM and FEM solutions of concentric n-layer flows of incompressible third-grade fluids in a horizontal cylindrical pipe
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This paper examines the concentric n-layer flows for incompressible third-grade fluids through a horizontal cylindrical pipe. Such flows of multilayer fluids have a wide variety of applications in petroleum and chemical industries. The approximate solutions for velocity fields of multilayer flows are presented by the application of optimal homotopy asymptotic method and Galerkin’s finite element method. Further, it is shown that a unique maximum velocity always exists in the core of the pipe for any number of fluid layers. The effects of suitable parameters on the velocity profiles are presented graphically for multilayer flows.
Keywordsn-layer flows Concentric flow Third-grade fluids OHAM and FEM Approximate solutions
The authors are grateful to the anonymous referee for a careful checking of the details and for helpful comments that improved this paper. Also the authors are highly thankful to the University of Management and Technology, Lahore, Pakistan, for supporting and facilitating.
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Conflict of interest
The authors declare that there is no conflict of interest regarding the publication of this paper.
- 15.Gul T, Shah RA, Islam S, Ullah M, Khan MA, Zaman A, Haq Z (2014) Exact solution of the two thin film non-Newtonian immiscible fluids on a vertical belt. J Basic Appl Sci Res 4(6):283–288Google Scholar
- 18.Siddiqui AM, Azim QA, Rana MA (2010) On exact solutions of concentric n-layer flows of viscous fluids in a pipe. Nonlinear Sci Lett A 1(1):93–102Google Scholar
- 34.Iqbal S, Siddique I (2012) Galerkin’s finite element method for solving special forth-order boundary-value problem. Sci Int 24(4):333–336Google Scholar
- 35.Iqbal S, Abualnaja KM (2014) Galerkin’s finite element formulation for thin film flow of a third grade fluid down an inclined plane. Sci Int 26(4):1403–1405Google Scholar