Influence of time-fractional derivatives on the boundary layer flow of Maxwell fluids

Abstract

Unsteady flows of an upper-convected Maxwell fluid, in two-dimensional boundary layer approximation are studied. Governing equations of the boundary layer flow are reduced to a non-linear partial differential equation by using the stream function. The Maxwell model, described by the fractional differential equations with time-fractional Caputo-Fabrizio derivatives is approached. Analytical solutions for the velocity components are determined using the generalized method of separation of variables coupled with the Laplace transform method. The velocity components are determined for the fractional Maxwell fluids and for ordinary Maxwell fluids. The fluid behaviour is significantly changed by the fractional parameter. It is found that, after a critical time value, the fractional fluids become slower than the ordinary fluid. There is possible to find a vortex sheet for ordinary Maxwell fluids, but not there for fractional Maxwell fluids.