×

zbMATH — the first resource for mathematics

Wire coating analysis by withdrawal from a bath of Sisko fluid. (English) Zbl 1137.76009
Summary: We analyze the wire coating by withdrawal from a bath of Sisko fluid. The relevant equations are first modelled and then solved by utilizing the homotopy analysis method. The convergence of the obtained series solution is carefully analyzed. We also discuss the influence of non-Newtonian parameter on velocity, volume flow rate, radius of coated wire, shear stress at the surface of the wire and the force required to pull the wire.

MSC:
76A05 Non-Newtonian fluids
76M25 Other numerical methods (fluid mechanics) (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Denn, M.M., Process fluid mechanics, (1980), Prentice-Hall England Cliffs, New Jersy
[2] Middleman, S., Fundamentals of polymer processing, (1977), McGraw-Hill New York
[3] Akter, S.; Hashmi, M.S.J., Analysis of polymer flow in a conical coating unit: a power law approach, Prog. org. coat., 37, 15-22, (1999)
[4] S. Akter, M.S.J. Hashmi, Plasto-hydrodynamic pressure distribution in a tepered geometry wire coating unit. in: Proceedings of 14th Conference of the Irish Manufacturing Committee (IMC 14) Dublin, 1997, pp. 331-340.
[5] Fetecau, C.; Fetecau, C., Unsteady flows of Oldroyd-B fluids in a channel of rectangular cross-section, Int. J. non-linear mech., 40, 1214-1219, (2005) · Zbl 1287.76045
[6] Fetecau, C.; Fetecau, C., On some axial Couette flows of non-Newtonian fluids, Z. angew. math. phys. (ZAMP), 56, 1098-1106, (2005) · Zbl 1096.76003
[7] Fetecau, C.; Fetecau, C., Starting solutions for some unsteady unidirectional flows of a second grade fluid, Int. J. eng. sci., 43, 781-789, (2005) · Zbl 1211.76032
[8] Fetecau, C.; Fetecau, C., Starting solutions for the motion of a second grade fluid due to longitudinal and torsional oscillations of a circular cylinder, Int. J. eng. sci., 44, 788-796, (2006) · Zbl 1213.76014
[9] Hayat, T.; Khan, M.; Ayub, M., The effect of slip condition on flows of an Oldroyd-6 constant fluid, J. comput. appl. math., 202, 402-413, (2007) · Zbl 1147.76550
[10] Hayat, T.; Ali, N.; Asghar, S., Hall effects on peristaltic flow of a Maxwell fluid in a porous medium, Phys. lett. A., 363, 397-403, (2007) · Zbl 1197.76126
[11] Hayat, T.; Sajid, M., On the analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder, Phys. lett. A., 361, 316-322, (2007) · Zbl 1170.76307
[12] Hayat, T.; Abbas, Z.; Sajid, M., Series solution for the upper-convected Maxwell fluid over a porous stretching plate, Phys. lett. A., 358, 396-406, (2006) · Zbl 1142.76511
[13] Baris, S.; Dokuz, M.S., Flow of a binary mixture of incompressible Newtonian fluids in a rectangular channel, Int. J. eng. sci., 43, 171-188, (2003) · Zbl 1211.76049
[14] Baris, S.; Dokuz, M.S., Three dimensional stagnation point flow of a second grade fluid towards a moving plate, Int. J. eng. sci., 44, 49-58, (2006)
[15] S.J. Liao, The proposed homotopy analysis technique for the solution of non-linear problems, Ph.D Thesis, Shanghai Jiao Tong University, 1992.
[16] Liao, S.J., Beyond perturbation: introduction to homotopy analysis method, (2003), Chapman and Hall/CRC Press Boca Raton
[17] Liao, S.J., On the homotopy analysis method for nonlinear problems, Appl. math. comput., 147, 499-513, (2004) · Zbl 1086.35005
[18] Sajid, M.; Hayat, T.; Asghar, S., Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt, Nonlinear dyn., 50, 27-35, (2007) · Zbl 1181.76031
[19] Hayat, T.; Sajid, M., Analytic solution for axisymmetric flow and heat transfer of a second grade fluid past a stretching sheet, Int. J. heat mass transfer, 50, 75-84, (2007) · Zbl 1104.80006
[20] Liao, S.J., A new branch of solutions of boundary-layer flows over an impermeable stretched plate, Int. J. heat mass transfer, 48, 2529-2539, (2005) · Zbl 1189.76142
[21] Liao, S.J., An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate, Comm. non-linear sci. numer. simm., 11, 326-339, (2006) · Zbl 1078.76022
[22] Cheng, J.; Liao, S.J.; Pop, I., Analytic series solution for unsteady mixed convection boundary layer flow near the stagnation point on a vertical surface in a porous medium, Transport porous media, 61, 365-379, (2005)
[23] Hayat, T.; Khan, M.; Ayub, M., On the explicit analytic solutions of an Oldroyd 6-constant fluid, Int. J. eng. sci., 42, 123-135, (2004) · Zbl 1211.76009
[24] M. Sajid, A.M. Siddiqui, T. Hayat, Wire coating analysis using MHD Oldroyd 8-constant fluid, Int. J. Eng. Sci., in press.
[25] Hayat, T.; Khan, M.; Asghar, S., Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid, Acta mech., 168, 213-232, (2004) · Zbl 1063.76108
[26] Liao, S.J., On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluid over a stretching sheet, J. fluid mech., 488, 189-212, (2003) · Zbl 1063.76671
[27] Abbas, Z.; Sajid, M.; Hayat, T., MHD boundary layer flow of an upper-convected Maxwell fluid in a porous channel, Theor. comput. fluid dyn., 20, 229-238, (2006) · Zbl 1109.76065
[28] Abbasbandy, S., The application of homotopy analysis method to nonlinear equations arising in heat transfer, Phys. lett. A., 360, 109-113, (2006) · Zbl 1236.80010
[29] Tan, Y.; Abbasbandy, S., Homotopy analysis method for quadratic recati differential equation, Comm. non-linear sci. numer. simul., 45, 381-392, (2007)
[30] S. Abbasbandy, F.S. Zakaria, Soliton solutions for the fifth order KdV equation with the homotopy analysis method, Nonlinear Dyn., in press. · Zbl 1170.76317
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.