A computational approach for the unsteady flow of maxwell fluid with Caputo fractional derivatives

Abstract

In this paper, the velocity field and the time dependent shear stress of Maxwell fluid with Caputo fractional derivatives in an infinite long circular cylinder of radius R is discussed. The motion in the fluid is produced by the circular cylinder. The fluid is initially at rest and at time t=0+, cylinder begins to oscillate with the velocity fsinωt, due to time dependent shear stress acting on the cylinder tangentially. The hybrid technique used in this paper for the solution of the problem has less computational efforts and time cost as compared to other commonly used methods. The obtained solutions are in transformed domain, which are expressed in terms of modified Bessel functions I0(·) and I1(·). The inverse Laplace transformation has been calculated numerically by using MATLAB package. The semi analytical solutions for Maxwell fluid with fractional derivatives are reduced to the similar solutions for Newtonian and ordinary Maxwell fluids as limiting cases. In the end, numerical simulations have been performed to analyze the behavior of fractional parameter α, kinematic viscosity ν, relaxation time λ, radius of the circular cylinder R and dynamic viscosity μ on our obtained solutions of velocity field and shear stress. Keywords: Shear stress, Maxwell fluid, Laplace transformation, Velocity field, Modified Bessel function