Stability of plane Poiseuille and Couette flows of Navier–Stokes–Voigt fluid

Shankar, B. M.; Shivakumara, I. S.

doi:10.1007/s00707-023-03624-0

Cited by 10 publications

(1 citation statement)

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“…In work [24], it was shown that the governing equations for velocity and non-trivial shear stress related to some isothermal MHD unidirectional flows of second grade fluids in a porous medium have identical forms. Shankar and Shivakumara [25] investigated the temporal stability of the plane Poiseuille and Couette flows of a Navier-Stokes-Voigt-type viscoelastic fluid. Recently, Fetecau and Vieru [26] obtained the general solutions for MHD flows of incompressible second grade fluids between infinite horizontal parallel plates which are embedded in a porous medium.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions to the Unsteady Poiseuille Flow of a Second Grade Fluid with Slip Boundary Conditions

Baranovskii

2024

Polymers

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This paper deals with an initial-boundary value problem modeling the unidirectional pressure-driven flow of a second grade fluid in a plane channel with impermeable solid walls. On the channel walls, Navier-type slip boundary conditions are stated. Our aim is to investigate the well-posedness of this problem and obtain its analytical solution under weak regularity requirements on a function describing the velocity distribution at initial time. In order to overcome difficulties related to finding classical solutions, we propose the concept of a generalized solution that is defined as the limit of a uniformly convergent sequence of classical solutions with vanishing perturbations in the initial data. We prove the unique solvability of the problem under consideration in the class of generalized solutions. The main ingredients of our proof are a generalized Abel criterion for uniform convergence of function series and the use of an orthonormal basis consisting of eigenfunctions of the related Sturm–Liouville problem. As a result, explicit expressions for the flow velocity and the pressure in the channel are established. The constructed analytical solutions favor a better understanding of the qualitative features of time-dependent flows of polymer fluids and can be applied to the verification of relevant numerical, asymptotic, and approximate analytical methods.

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Section: Introductionmentioning

confidence: 99%