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Z. Naturforsch. 69a, 232 – 238
(2014)
doi:10.5560/ZNA.2014-0022
First Exact Solutions for Flows of Rate Type Fluids in a Circular Duct that Applies a Constant Couple to the Fluid
1 Department of Theoretical Mechanics, Technical University of Iasi, Iasi 700050, Romania
2 Abdus Salam School of Mathematical Sciences, GC University, Lahore 54600, Pakistan
3 Department of Mathematics, Technical University of Iasi, Iasi 700050, Romania
4 Academy of Romanian Scientists, Bucuresti 050094, Romania
Received March 10, 2014 / published online May 21, 2014
Reprint requests to: Const. F.; E-mail:
c_fetecau@yahoo.com
Rotational flow of an Oldroyd-B fluid induced by an infinite circular cylinder that applies a constant couple to the fluid is studied by means of integral transforms. Such a problem is not solved in the existing literature for rate type fluids and the present solutions are based on a simple but important remark regarding the governing equation for the non-trivial shear stress. The solutions that have been obtained satisfy all imposed initial and boundary conditions and can easy be reduced to the similar solutions corresponding to Maxwell, second-grade, and Newtonian fluids performing the same motion. Finally, the influence of material parameters on the velocity and shear stress distributions is graphically underlined.
Key words: Oldroyd-B Fluid; Circular Duct; Constant Couple; Exact Solutions.