Wire coating analysis with Oldroyd 8-constant fluid by optimal homotopy asymptotic method. (English) Zbl 1238.76034

Summary: The wire coating in a pressure type die with the bath of Oldroyd 8-constant fluid with pressure gradient is investigated. The non-linear ordinary differential equation in dimensionless form is obtained, which is solved for the velocity profile using the Optimal Homotopy Asymptotic Method (OHAM). The effect of Dilatant constant \(\alpha \), the Psendoplastic constant \(\beta \), and the pressure gradient on velocity distribution and shear stress is studied. Shear stress is examined under the effect of the viscosity parameter \(\eta _{0}\). Moreover, the volume flow rate and average velocity is carefully studied with changing the domain (thickness) of the polymer and varying the parameter \(\alpha ,\beta \) and the pressure gradient.


76M25 Other numerical methods (fluid mechanics) (MSC2010)
76A10 Viscoelastic fluids
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
Full Text: DOI


[1] Akter, S.; Hashmi, M.S.J., Analysis of polymer flow in a canonical coating unit: power law approach, Prog. org. coat., 37, 15-22, (1999)
[2] S. Akter, M.S.J. Hashmi, Plasto-hydrodynamic pressure distribution in a tapered geometry wire coating unit, in: Proceedings of the 14th Conference of the Irish Manufacturing Committee, IMC14, Dublin, 1997, pp. 331-340.
[3] Siddiqui, A.M.; Haroon, T.; Khan, H., Wire coating extrusion in a pressure-type die \(n\) flow of a third grade fluid, Int. J. nonlinear sci. numer. simul., 10, 2, 247-257, (2009)
[4] Fenner, R.T.; Williams, J.G., Analytical methods of wire coating die design, Trans. plast. inst. (London), 35, 701-706, (1967)
[5] Sajjid, M.; Siddiqui, A.M.; Hayat, T., Wire coating analysis using MHD Oldroyd 8-constant fluid, Internat. J. engrg. sci., 45, 381-392, (2007)
[6] Marinca, V.; Herişanu, N., Optimal homotopy perturbation method for strongly nonlinear differential equations, Nonlinear sci. lett. A, 1, 3, 273-280, (2010) · Zbl 1222.65089
[7] Marinca, V.; Herişanu, N.; Nemes, I., An optimal homotopy asymptotic method with application to thin film flow, Cent. eur. J. phys., 6, 3, 648-653, (2008)
[8] Herişanu, N.; Marinca, V.; Dordea, T.; Madescu, G., A new analytical approach to nonlinear vibration of an electrical machine, Proc. rom. acad. ser. A, 9, 3, 229-236, (2008)
[9] Marinca, V.; Herişanu, N.; Bota, C.; Marinca, B., An optimal homotopy asymptotic method applied to steady flow of a fourth-grade fluid past a porous plate, Appl. math. lett., 22, 245-251, (2009) · Zbl 1163.76318
[10] Marinca, V.; Herişanu, N., Application of optimal homotopy asymptotic method for solving nonlinear equations arising in heat transfer, Int. commun. heat mass transfer, 35, 710-715, (2008)
[11] Herişanu, N.; Marinca, V., Accurate analytical solutions to oscillators with discontinuities and fractional-power restoring force by means of the optimal homotopy asymptotic method, Comput. math. appl., 60, 1607-1615, (2010) · Zbl 1202.34072
[12] Islam, S.; Shah, Rehan Ali; Ali, Ishtiaq, Optimal homotopy asymptotic solutions of Couette and Poiseuille flows of a third grade fluid with heat transfer analysis, Int. J. nonlinear sci. numer. simul., 11, 6, 389-400, (2010)
[13] Ali, Javed; Islam, S.; Islam, Sirajul; Zaman, Gul, The solution of multipoint boundary value problems by the optimal homotopy asymptotic method, Comput. math. appl., 59, 2000-2006, (2010) · Zbl 1189.65154
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.