Unsteady Incompressible Viscoelastic Flow of a Generalised Maxwell Fluid between Two Rotating Infinite Parallel Coaxial Circular Disks

ABSTRACT

The unsteady incompressible viscous flow of a Generalised Maxwell fluid between two coaxial rotating infinite parallel circular disks is studied by using the method of integral transforms. The motion of the fluid is created by the rotation of the upper and lower circular disks with different angular velocities. A fractional calculus approach is utilized to determine the velocity profile in series form in terms of Mittag-Leffler function. The influence of the fractional as well as the material parameters on the velocity field is illustrated graphically.

Cite this paper

D. Bose and U. Basu, "Unsteady Incompressible Viscoelastic Flow of a Generalised Maxwell Fluid between Two Rotating Infinite Parallel Coaxial Circular Disks,"*Open Journal of Fluid Dynamics*, Vol. 3 No. 2, 2013, pp. 57-63. doi: 10.4236/ojfd.2013.32008.

D. Bose and U. Basu, "Unsteady Incompressible Viscoelastic Flow of a Generalised Maxwell Fluid between Two Rotating Infinite Parallel Coaxial Circular Disks,"

References

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[8] M. Kempegowda and P. M. Balagondar, “The Exact Solutions of Non-Newtonian Fluid Flow between Two Moving Parallel Disks and Stability Analysis,” Applied Mathrmatical Sciences, Vol. 6, No. 37, 2012, pp. 1827-1835.

[1] T. Von Kármán, “über Laminare und Turbulente Reibung,” Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 1, No. 4, 1921, pp. 233-255. doi:10.1002/zamm.19210010401

[2] W. G. Cochran, “The Flow Due to a Rotating Disc,” Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 30, No. 3, 1934, pp. 365-375. doi:10.1017/S0305004100012561

[3] M. A. Hossain and A. F. M. A Rahman, “The Steady Flow between Two Porous Rotating Discs in Presence of Transverse Magnetic Field,” Indian Journal of Pure and Applied Mathmatics, Vol. 15, No. 2, 1984, pp. 187-194.

[4] M. A. Hossain, A. Hossain and M. Wilson, “Unsteady Flow of Viscous Incompressible Fluid with Temperature-Dependent Viscosity Due to a Rotating Disc in Presence of Transverse Magnetic Field and Heat Transfer,” International Journal of Thermal Sciences, Vol. 40, No. 1, 2001, pp. 11-20. doi:10.1016/S1290-0729(00)01183-2

[5] T. Wenchang, P. Wenxiao and X. Mingyu, “The Unsteady Flows of a Visco-Elastic Fluid with the Fractional Maxwell Model between Two Parallel Plates,” International Journal of Non-Linear Mechanics, Vol. 38, No. 5, 2003, pp. 645-650. doi:10.1016/S0020-7462(01)00121-4

[6] S. L.Maji, N. Ghara, R. N. Jana and S. Das, “Unsteady MHD Flow between Two Eccentric Rotating Disks,” Journal of Physical Science, Vol. 13, 2009, pp. 87-96.

[7] Y. Liu, L. Zheng, X. Zhang and F. Zong, “The Oscillating Flows and Heat Transfer of a Generalized Oldroyed-B Fluid in Magnetic Field,” International Journal of Applied Mathematics, Vol. 40, 2010.

[8] M. Kempegowda and P. M. Balagondar, “The Exact Solutions of Non-Newtonian Fluid Flow between Two Moving Parallel Disks and Stability Analysis,” Applied Mathrmatical Sciences, Vol. 6, No. 37, 2012, pp. 1827-1835.