On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domains Article First Online: 25 August 2011 Received: 02 December 2010 Accepted: 14 July 2011 DOI :
10.1007/s11012-011-9467-4

Cite this article as: Kamran, M., Imran, M., Athar, M. et al. Meccanica (2012) 47: 573. doi:10.1007/s11012-011-9467-4
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Abstract This paper concerned with the unsteady rotational flow of fractional Oldroyd-B fluid, between two infinite coaxial circular cylinders. To solve the problem we used the finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t =0^{+} , is subject to a time-dependent rotational shear. The solutions that have been obtained, presented under series form in terms of the generalized G functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B, fractional and ordinary Maxwell, fractional and ordinary second grade, and Newtonian fluids, performing the same motion, are obtained as limiting cases of general solutions.

The most important things regarding this paper to mention are that (1) we extracted the expressions for the velocity field and the shear stress corresponding to the motion of a fractional second grade fluid as limiting cases of general solutions corresponding to the fractional Oldroyd-B fluid, this is not previously done in the literature to the best of our knowledge, and (2) the expressions for the velocity field and the shear stress are in the most simplified form, and the point worth mentioning is that these expressions are free from convolution product and the integral of the product of the generalized G functions, in contrast with (Imran and Zamra in Commun. Nonlinear Sci. Numer. Simul. 16:226–238, 2011 ) in which the expression for the velocity field involving the convolution product as well as the integral of the product of the generalized G functions.

Keywords Fractional Oldroyd-B fluid Velocity field Shear stress Fractional calculus Integral transforms

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Authors and Affiliations 1. COMSATS Institute of Information Technology Wah Cantt Pakistan 2. Abdus Salam School of Mathematical Sciences GC University Lahore Lahore Pakistan