Laplace transform solution of the time-dependent annular Couette flow with dynamic wall slip

• Published in: Journal of the Brazilian Society of Mechanical Sciences and Engineering 2023-11, Vol.45 (11), Article 586
• Main Authors: Ali, Ahmed E. K., Ghaleb, A. F., Abou-Dina, M. S., Helal, M. A.
• Format: Article
• Language: English
• Subjects: Boundary conditions; Circular cylinders; Couette flow; Engineering; Fluid flow; Fluidics; Industrial applications; Laplace transforms; Mechanical Engineering; Nanofluids; Perturbation methods; Polynomials; Technical Paper; Viscous fluids; Wall slip
• ISSN: 1678-5878; 1806-3691
• DOI: 10.1007/s40430-023-04498-y

The annular Couette flow has several industrial applications, particularly for the characterization of the fluid flow and deformation behavior of fluids. The inclusion of the dynamic wall slip into the flow boundary conditions seems to be necessary for an efficient continuum description of motion of nanofluidics as it reflects the importance of fluid–structure interface related phenomena. Dynamic wall slip introduces a dissipative boundary condition and thus increases the difficulties of finding solutions to related problems. In the present work we investigate the behavior of fluid flow between two infinitely long coaxial circular cylinders, when the inner cylinder is axially moving due to sudden constant velocity, while the outer cylinder is held stationary. The boundary condition on the outer cylinder is that of dynamic wall slip, in addition to the usual Navier slip. The medium considered here is a Newtonian viscous fluid. The solution of the governing equations, initial and boundary conditions for this flow is obtained using the Laplace transform technique and inversion by Laguerre polynomials. This method may be useful, when applied in conjunction with perturbation methods, to solve nonlinear Couette flow problems involving temperature changes. Numerical results are presented and discussed.