Oscillating Flows of Fractionalized Second Grade Fluid with Slip Effects

Abstract

This paper examines the fractionalized second grade fluid due to oscillating plate under slip condition. The discrete Laplace transform technique is employed to compute the analytical solutions for the equations of motion. The velocity field and shear stress are computed. In order to write them in compact form, the Wright generalized hyper geometric function is used and written as addition of slip and no slip contributions. The closed-form solutions for ordinary second grade and Newtonian fluids carrying out the similar motion are achieved. The computations for fractional and ordinary second grade fluids without slip effect are also achieved as a special case. Furthermore, the impact of various parameters such as the slip, fractional and material parameters on the motion of fractionalized second grade fluid will be explained through graphs. Finally, a comparison among the Newtonian fluids, ordinary second grade fluids and fractionalized second grade fluids is also carried out.