An Analytical and Semi-analytical Study of the Oscillating Flow of Generalized Burgers’ Fluid through a Circular Porous Medium

Unsteady oscillatory flow of generalized Burgers’ fluid in a circular channel tube in the porous medium is investigated under the influence of time-dependent trapezoidal pressure gradient given by an infinite Fourier series. An exact analytical expression for the solution for the fluid velocity and the shear stress are recovered by using the similarity arguments together with the integral transforms. The solution is verified with a semi-analytical solution obtained by employing the Stehfest's method. Using the software Mathcad, numerical calculations have been carried out, and results are presented in graphical illustrations in order to analyze the effects of various fluid parameters on the fluid motion. As expected, with the increase in the permeability of the porous medium, the drag force decreases, which results in an increase in the velocity profile for all kinds of fluid models (a generalized Burgers’ fluid, a Burgers’ fluid, a Maxwell fluid, and an Oldroyd-B fluid). Moreover, it has been observed that the material constants of the generalized Burgers’ fluid, as well as the Burgers’ fluid, are other important factors that enhance the flow velocity performance of the fluid. The velocity-time variation for the generalized Burgers’ fluid, the Oldroyd-B fluid, and the Newtonian fluid is similar to the trapezoidal waveform, whereas it is different for the Burgers’ and Maxwell fluid.