Fractional Second-Grade Fluid Flow over a Semi-Infinite Plate by Constructing the Absorbing Boundary Condition

Abstract

The modified second-grade fluid flow across a plate of semi-infinite extent, which is initiated by the plate’s movement, is considered herein. The relaxation parameters and fractional parameters are introduced to express the generalized constitutive relation. A convolution-based absorbing boundary condition (ABC) is developed based on the artificial boundary method (ABM), addressing issues related to the semi-infinite boundary. We adopt the finite difference method (FDM) for deriving the numerical solution by employing the L1 scheme to approximate the fractional derivative. To confirm the precision of this method, a source term is added to establish an exact solution for verification purposes. A comparative evaluation of the ABC versus the direct truncated boundary condition (DTBC) is conducted, with their effectiveness and soundness being visually scrutinized and assessed. This study investigates the impact of the motion of plates at different fluid flow velocities, focusing on the effects of dynamic elements influencing flow mechanisms and velocity. This research’s primary conclusion is that a higher fractional parameter correlates with the fluid flow. As relaxation parameters decrease, the delay effect intensifies and the fluid velocity decreases.

Keywords

• absorbing boundary condition
• second-grade fluid
• fractional derivative
• finite difference method