Influence of Magnetic Field and Porous Medium on Taylor–Couette Flows of Second Grade Fluids Due to Time-Dependent Couples on a Circular Cylinder

Dumitru Vieru () and Constantin Fetecau
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Dumitru Vieru: Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India
Constantin Fetecau: Academy of Romanian Scientists, 3 Ilfov, 050044 Bucharest, Romania

Mathematics, 2025, vol. 13, issue 13, 1-20

Abstract: Axially symmetric Taylor–Couette flows of incompressible second grade fluids induced by time-dependent couples inside an infinite circular cylinder are studied under the action of an external magnetic field. The influence of the medium porosity is taken into account in the mathematical modeling. Analytical expressions for the dimensionless non-trivial shear stress and the corresponding fluid velocity were determined using the finite Hankel and Laplace transforms. The solutions obtained are new in the specialized literature and can be customized for various problems of interest in engineering practice. For illustration, the cases of oscillating and constant couples have been considered, and the steady state components of the shear stresses were presented in equivalent forms. Numerical schemes based on finite differences have been formulated for determining the numerical solutions of the proposed problem. It was shown that the numerical results based on analytical solutions and those obtained with the numerical methods have close values with very good accuracy. It was also proved that the fluid flows more slowly and the steady state is reached earlier in the presence of a magnetic field or porous medium.

Keywords: second grade fluids; Taylor–Couette flows; time-dependent torques; exact solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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