Effects of slip on oscillating fractionalized Maxwell fluid

Abstract

The flow of an incompressible fractionalized Maxwell fluid induced by an oscillating plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid. The solutions obtained for the velocity field and the associated shear stress, written in terms of H-functions, using discrete Laplace transform, satisfy all imposed initial and boundary conditions. The no-slip contributions, that appeared in the general solutions, as expected, tend to zero when slip parameter θ → 0. Furthermore, the solutions for ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained as limiting cases of general solutions. The solutions for fractionalized and ordinary Maxwell fluids for noslip condition also obtained as a special cases and they are similar to the solutions of classical Stokes’ first problem of fractionalized and ordinary Maxwell fluid, if oscillating parameter ω = 0. Finally, the influence of the material, slip and the fractional parameters on the fluid motion, as well as a comparison among fractionalized Maxwell, ordinary Maxwell and Newtonian fluids is also analyzed by graphical illustrations.

Keywords

• maxwell fluid
• fractional derivative
• slip effects
• oscillating flows
• exact solutions
• velocity field
• shear stress
• discrete laplace transforms
• 76a05
• 76a10