Open AccessAnalytical Solutions for the Flow of a Fractional Second Grade Fluid due to a Rotational Constantly Accelerating Shear
Author(s) -
Muhammad Kamran,
Muhammad Imran,
Muhammad Athar
Publication year - 2012
Publication title -
isrn mathematical analysis
Language(s) - English
Resource type - Journals
eISSN - 2090-4665
pISSN - 2090-4657
DOI - 10.5402/2012/374670
Subject(s) - laplace transform , fluid motion , newtonian fluid , cylinder , flow (mathematics) , mathematical analysis , generalized newtonian fluid , fluid dynamics , mathematics , boundary value problem , exact solutions in general relativity , equations of motion , shear (geology) , shear flow , non newtonian fluid , herschel–bulkley fluid , mechanics , hankel transform , motion (physics) , classical mechanics , physics , bessel function , geometry , shear rate , rheology , materials science , thermodynamics , composite material
Exact analytic solutions are obtained for the flow of a generalized second grade fluid in an annular region between two infinite coaxial cylinders. The fractional calculus approach in the governing equations of a second grade fluid is used. The exact analytic solutions are constructed by means of Laplace and finite Hankel transforms. The motion is produced by the inner cylinder which is rotating about its axis due to a constantly accelerating shear. The solutions that have been obtained satisfy both the governing equations and all imposed initial and boundary conditions. Moreover, they can be easily specialized to give similar solutions for second grade and Newtonian fluids. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between the three models, is underlined by graphical illustrations.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom