Exact solutions for the unsteady rotational flow of a generalized second grade fluid through a circular cylinder

M Athar,M Imran,M Kamran

doi:10.15388/na.15.4.14315

M Athar, M Imran + Show 1 more

Open Access

https://doi.org/10.15388/na.15.4.14315

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Abstract

Here the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized second grade fluid within an infinite circular cylinder are determined by means of the Laplace and finite Hankel transforms. At time t = 0 the fluid is at rest and the motion is produced by the rotation of the cylinder around its axis with a time dependent angular velocity Ωt. The solutions that have been obtained are presented under series form in terms of the generalized G-functions. The similar solutions for the ordinary second grade and Newtonian fluids, performing the same motion, are obtained as special cases of our general solution.

Highlights

Many materials such as drilling mud, certain oils and greases, blood and many emulsions have been used as non-Newtonian fluids
One of the recent advances in the theoretical studies in rheology is the development of one-dimensional fractional derivative models
The one-dimensional fractional derivative Maxwell model has been found very useful in modeling the linear viscoelastic response of polymer solutions and melts

Summary

Introduction

Many materials such as drilling mud, certain oils and greases, blood and many emulsions have been used as non-Newtonian fluids. Amongst the many models which have been treated as non-Newtonian behavior, the fluids of differential type have received special attention [1,2,3]. One of the recent advances in the theoretical studies in rheology is the development of one-dimensional fractional derivative models. The simplicity of their form and the fact that they can be used to study shear-thinning, have opened the way for the solution to a series of engineering problems. The similar solutions for the ordinary second grade and Newtonian fluids, performing the same motion, are obtained as special cases of our general solution

Governing equations

Flow through a circular cylinder

Calculation of the velocity field

Calculation of the shear stress

Conclusion