Unsteady flow of viscoelastic fluid with the fractional K-BKZ model between two parallel plates

In the present paper, we investigate the unsteady flow of a viscoelastic fluid between two parallel plates which is generated by the impulsively accelerated motion of the bottom plate. Based on the result of (Jaishankar and McKinley, 2014), the fractional K-BKZ constitutive equation is obtained from the fractional Maxwell model. Using respectively the fractional Maxwell model and fractional K-BKZ model, the unidirectional flows between two plates are simulated and compared. The velocity field and shear stress of the flows are calculated by developing efficient finite difference schemes. The results show that the fluid with the fractional Maxwell model gradually loses the viscoelasticity, but the fluid with the fractional K-BKZ model continues to preserve the viscoelasticity. The dependence of the flow velocity on various parameters of the fractional K-BKZ model is analyzed graphically.