Unsteady flow of a Burgers’ fluid with Caputo fractional derivatives: A hybrid technique

Abstract

The shear stress and velocity field related to the oscillatory motion of a fractional Burgers’ fluid model in an infinitely circular cylinder are examined using modified Bessel equation and Laplace transformation. The fluid is at rest initially and after t=0+, because of shear, it instantly starts to move along the axis of cylinder. The procured results are expressed in modified Bessel fields I0(·) and I1(·) and fulfill both initial and boundary conditions. Inverse Laplace transformation has been found numerically using Matlab software. In the end, numerical simulations have been performed to analyze the behavior of fractional parameter α, similarity parameter β, relaxation time λ1, retardation time λ3, radius of the circular cylinder R and material parameter λ2 on our obtained solutions of velocity field and shear stress. The comparison between numerical and exact results are also presented in graphical and tabular form. Keywords: Laplace transformation, Velocity field, Burgers’ fluid, Stehfest’s algorithm, Shear stress