Fractional order analysis of unsteady pressure-driven flow in an annulus with momentum slip

Abstract

Nearly all deformed materials possess both elastic and viscous properties through concurrent storage and dissipation of mechanical vitality. This type of novel functional fluid undergoing deformation is crucial in describing hydrodynamically the general behavior of the fluid. Thus, the working fluid carries memory attribute stored in the particles. The fractional order model for circumferentially pressure-driven flow of viscous fluid in an annulus with momentum slip is investigated theoretically. In particular, an exponentially decaying/growing pressure is considered. For the purpose of this study, the Atangana–Baleanu fractional order model is employed. A solution approach to the fractionalized model is by utilizing Laplace transformation and Tzou’s algorithm for numerical Laplace inversion. It was found that a decisive factor in boosting the speed of flow is suppressing the memory effect of the fluid particle. Also, the instability of the flow can be controlled by enhancing the memory effect.

Keywords

• Atangana–Baleanu fractional model
• Exponential pressure
• Fractional calculus
• Pressure-driven flow
• Slip boundaries
• Unsteady