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Heat transfer by laminar flow of a third grade fluid in wire coating analysis with temperature dependent and independent viscosity

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Abstract

The flow of a third grade fluid in between the continuum (wire) and conical die is considered for wire coating analysis. The analysis is based on perturbation technique. The Reynolds’s and Vogel’s model are accounted for the temperature dependent viscosity. The influence of Reynolds’s model parameter m and Vogel’s model parameters, α and B is investigated carefully on solution of the problem. It is investigated that the velocity profile oscillates about r for the case of temperature dependent viscosity for the parameters m, α, β and B.

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References

  1. Caswell B., Tanner R.J.: Polym. Eng. Sci. 18(5), 417–421 (1978)

    Article  Google Scholar 

  2. Basu S.: J. Polym. Eng. Sci. 21, 1128–1137 (1981)

    Article  Google Scholar 

  3. Denn M.M.: Process Fluid mechanics. Prentice-Hall, England cliff (1980)

    Google Scholar 

  4. Middleman S.: Fundamentals of polymer processing. McGraw-Hill, New York (1977)

    Google Scholar 

  5. McKelvey J.M.: Polymer processing. John Wiley and Sons, New York (1962)

    Google Scholar 

  6. Paton J.B., Squire P.H., Darnell W.H., Cash F.M., Carley J.F.: Processing of thermoplastic materials, pp. 269–299. Reinhold Pub. Corp., New York (1959)

    Google Scholar 

  7. Bagley E.B., Storey S.H.: Wire Wire Prod. 38, 1104 (1963)

    Google Scholar 

  8. 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)

    Article  Google Scholar 

  9. Akter, S., Hashmi, M.S.J.: Plasto-hydrodynamic pressure distribution in a tepered geometry wire coating unit, pp. 331–340. In: Proceedings of the 14th Conference of the Irish manufacturing committee (IMC14), Dublin (1997)

  10. Siddiqui A.M., Haroon T., Khan H.: Wire coating extrusion in a Pressure-type Die n flow of a third grade fluid. Int. J. Non linear Sci. Numer. Simul. 10(2), 247–257 (2009)

    Article  Google Scholar 

  11. Nafeh A.H.: Perturbation methods. Willy, New York (1973)

    Google Scholar 

  12. Nayfeh A.H.: Introduction to perturbation techniques. Wiley, New York (1979)

    Google Scholar 

  13. Armbruster D, Perturbation methods bifurcation theory and computer algebraic. Springer (1987)

  14. He J.H.: Homotopy perturbation technique. Comput. Method. Appl. Mech. Eng. 178(3–4), 257–262 (1999)

    Article  MATH  Google Scholar 

  15. He J.H.: Homotopy perturbation method: a new nonlinear analytical technique. Appl. Math. Comput. 135, 73–79 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  16. He J.H.: A coupling method of a homotopy technique and a perturbation technique for non-linear problems. Int. J. Non linear Mech. 35, 37–43 (2000)

    Article  MATH  Google Scholar 

  17. Odibat, Z.M.: A new modification of the homotopy perturbation for linear and non-linear operators, Appl. Math. Comput. doi:10.1016/j.amc(2006).11.188

  18. Moini M.: Modified homotopy perturbation method for solving linear and non linear Schrödinger equations. Int. J. Pure Appl. Math. 49(4), 489–495 (2008)

    MathSciNet  MATH  Google Scholar 

  19. Herisanu N., Marinca V., Dordea T., Madescu G.: A new analytic approach to nonlinear vibration of an electrical machine. Proc. Roman Acad. 9(3), 229–236 (2008)

    Google Scholar 

  20. Herisanu N., Marinca V.: An iterative procedure with application to Van der Pol oscillator. Int. J. Nonlinear Sci. Numer. Simul. 10, 353–361 (2009)

    Article  Google Scholar 

  21. Herisanu N., Marinca V.: Explicit analytical approximation to large-amplitude non-linear oscillations of a uniform cantilever beam carrying an intermediate lumped mass and rotary inertia. Meccanica 45, 847–855 (2010)

    Article  MathSciNet  Google Scholar 

  22. Marinca V., Herisanu N., Nemes I.: An optimal homotopy asymptotic method with application to thin film flow. Cent. Europ. J. Phys. 6(3), 648–653 (2008)

    Article  Google Scholar 

  23. Marinca V., Herisanu N.: Optimal homotopy perturbation method for strongly nonlinear differential equations. Non linear Sci. Lett. A. 1(3), 273–280 (2010)

    Google Scholar 

  24. Marinca, V., Herisanu, N.: Non-linear dynamic analysis of an electrical machine rotor- bearing system by the optimal homotopy perturbation method. Comput. Math. Appl., doi:10.1016/j.camwa.08.0562010

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Correspondence to Rehan Ali Shah.

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Shah, R.A., Islam, S., Siddiqui, A.M. et al. Heat transfer by laminar flow of a third grade fluid in wire coating analysis with temperature dependent and independent viscosity. Anal.Math.Phys. 1, 147–166 (2011). https://doi.org/10.1007/s13324-011-0011-4

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  • DOI: https://doi.org/10.1007/s13324-011-0011-4

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