This paper presents a study of visco-elastic flow of an
incompressible generalized Oldroyd-B fluid between two infinite parallel plates
in which the constitutive equation involves fractional order time derivative.
The solutions of field equations are being obtained for the motion of the said
fluid between two parallel plates where the lower plate starts to move with
steady velocity and the upper plate remains fixed in the first problem and the
upper plate oscillates with constant frequency and the other being at rest in
the second problem. The exact solutions for the velocity field are obtained by
using the Laplace transform and finite Fourier
Sine transform technique in terms of Mittag Leffler and generalised functions.
The analytical expression for the velocity fields are derived and the effect of
fractional parameters upon the velocity field is depicted graphically.
K. R. Rajagopal and A. S. Gupta, “On a Class of Exact Solutions to the Equations of Motion of a Second Grade Fluid,” International Journal of Engineering Science, Vol. 19, No. 7, 1981, pp. 1009-1014.
M. Khan, T. Hayat and S. Asgar, “Exact Solution for MHD Flow of a Generalised Oldroyed-B Fluid with Modified Darcy’s Law,” International Journal of Engineering Science, Vol. 44, No. 5-6, 2006, pp. 333-339.
C. Fetecau, M. Khan, C. Fetecau and H. Qi, “Exact Solutions for the Flow of a Generalised Oldroyed-B Fluid Induced by a Suddenly Moved Plate between Two Side Walls Perpendicular to the Plate,” Proceedings of the Romanian Academy, Series A, Vol. 11, 2010, pp. 3-10.
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, p. 4.