# Analytical Solution of Transient Flow of Fractional Oldroyd-B Fluid between Oscillating Cylinders

## DOI:

https://doi.org/10.21015/vtm.v10i2.1184## Abstract

This paper investigates the fractional Oldroyd-B ﬂuid ﬂow across two interminable coaxial cylinders, where the ﬂuid’s motion is generated by the oscillatory movement of cylinders and the oscillating pressure gradient. The proﬁle of velocity and shear stress of the ﬂow is derived with the assistance of Caputo fractional derivative utilizing an analytical technique, ﬁnite Hankel transform and Laplace transforms. The semi-analytical solution is then displayed as generalized functions of G and R satisfying fundamental constitutive equations and all initial and boundary conditions. To validate the results, some limitations have been imposed on the determined equations and the results have been contrasted against previous results. Moreover, the inﬂuence of various parameters on the ﬂow of fractionalized Oldroyd-B ﬂuid is investigated and depicted graphically.

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*VFAST Transactions on Mathematics*,

*10*(2), 21–33. https://doi.org/10.21015/vtm.v10i2.1184

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