Exact solutions for a viscoelastic fluid with the generalized Oldroyd-B model

In this paper, the generalized Oldroyd-B model with the fractional calculus approach is used. Exact analytic solutions for the velocity and the stress fields in term of the Fox HH-function are obtained by using the discrete Laplace transform for two types of flows of a viscoelastic fluid, namely, (i) flow due to impulsive motion in the presence of a constant pressure gradient and (ii) flow induced by an impulsive pressure gradient. The influence of various parameters of interest on the velocity and shear stress has been shown and discussed through several graphs. Moreover, a comparison between Oldroyd-B and generalized Oldroyd-B fluids is also made.