Open AccessOn Unsteady Flow of a Viscoelastic Fluid Through Rotating Cylinders
Author(s) -
Madeeha Tahir,
Muhammad Naeem,
Rabia Safdar,
Dumitru Vieru,
Muhammad Imran,
Naeem Sadiq
Publication year - 2017
Publication title -
open journal of mathematical sciences
Language(s) - English
Resource type - Journals
eISSN - 2616-4906
pISSN - 2523-0212
DOI - 10.30538/oms2017.0001
Subject(s) - fractional calculus , laplace transform , newtonian fluid , viscoelasticity , mathematical analysis , herschel–bulkley fluid , mathematics , flow (mathematics) , constitutive equation , non newtonian fluid , classical mechanics , generalized newtonian fluid , shear stress , vector field , calculus (dental) , physics , mechanics , geometry , viscosity , shear rate , finite element method , thermodynamics , medicine , dentistry
The fractional calculus approach is used in the constitutive relationship model of fractional Maxwell fluid. Exact solutions for the velocity field and the adequate shear stress corresponding to the rotational flow of a fractional Maxwell fluid, between two infinite coaxial circular cylinders, are obtained by using the Laplace transform and finite Hankel transform for fractional calculus. The solutions that have been obtained are presented in terms of generalized Gb,c,d(·, t) and Rb,c(·, t) functions. In the limiting cases, the corresponding solutions for ordinary Maxwell and Newtonian fluids are obtained from our general solutions. Furthermore, the solutions for the motion between the cylinders, when one of them is at rest, are also obtained as special cases from our results. Finally, the influence of the material parameters on the fluid motion is underlined by graphical illustrations. AMS Mathematics Subject Classification : 76A05.
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