Magnetohydrodynamic Motions of Oldroyd-B Fluids in Infinite Circular Cylinder That Applies Longitudinal Shear Stresses to the Fluid or Rotates Around Its Axis

Dumitru Vieru (), Constantin Fetecau and Zulkhibri Ismail
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Dumitru Vieru: Department of Theoretical Mechanics, Technical University of Iasi, 700050 Iasi, Romania
Constantin Fetecau: Academy of Romanian Scientists, 3 Ilfov, 050044 Bucharest, Romania
Zulkhibri Ismail: Centre for Mathematical Sciences, College of Computing and Applied Sciences, Universiti Malaysia Pahang Al-Sultan Abdullah, Lebuh Persiaran Tun Khalil Yaacob, Kuantan 26300, Pahang, Malaysia

Mathematics, 2024, vol. 12, issue 20, 1-16

Abstract: Two classes of magnetohydrodynamic (MHD) motions of the incompressible Oldroyd-B fluids through an infinite cylinder are analytically investigated. General expressions are firstly established for shear stress and velocity fields corresponding to the motion induced by longitudinal shear stress on the boundary. For validation, the expression of the shear stress is determined by two different methods. Using an important remark regarding the governing equations for shear stress and fluid velocity corresponding to the two different motions, this expression is then used to provide the dimensionless velocity field of the MHD motion of the same fluids generated by a cylinder that rotates around its symmetry axis. Obtained results can generate exact solutions for any motion of this kind of Oldroyd-B fluids. Consequently, both types of motions are completely solved. For illustration, some case studies are considered, and adequate velocity fields are provided. The steady-state components of these velocities are presented in different forms whose equivalence is graphically proved. The influence of the magnetic field on the fluid behavior is graphically investigated. It was found that the fluid flows slower, and a steady state is earlier reached in the presence of a magnetic field. The fluid behavior when shear stress is given on the boundary is also investigated.

Keywords: Oldroyd-B fluids; unsteady MHD motions; circular cylinder; general solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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