## THERMAL SCIENCE

International Scientific Journal

### THE ANALYTIC SOLUTIONS FOR THE UNSTEADY ROTATING FLOWS OF THE GENERALIZED MAXWELL FLUID BETWEEN COAXIAL CYLINDERS

**ABSTRACT**

In this paper, we consider the unsteady rotating flow of the generalized Maxwell fluid with fractional derivative model between two infinite straight circular cylinders, where the flow is due to an infinite straight circular cylinder rotating and oscillating pressure gradient. The velocity field is determined by means of the combine of the Laplace and finite Hankel transforms. The analytic solutions of the velocity and the shear stress are presented by series form in terms of the generalized G and R functions. The similar solutions can be also obtained for ordinary Maxwell and Newtonian fluids as limiting cases.

**KEYWORDS**

PAPER SUBMITTED: 2019-08-03

PAPER REVISED: 2020-01-15

PAPER ACCEPTED: 2020-01-20

PUBLISHED ONLINE: 2020-11-27

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**Issue 6**, PAGES [4041 - 4048]

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