Non-Newtonian Casson Fluid through a Porous Rotating Channel with Seepage Flow

Abstract

Rotating channels represent complex geometries that play a crucial role in various engineering applications, including the optimization of blood flow simulators, filtra-tion systems, and chemical reactors. In these systems, non-Newtonian fluids, such as Casson fluid, exhibit unique flow characteristics, especially when subjected to rotational and porous conditions. This study focuses on the steady, laminar flow of incompressible Casson fluid through a rotating channel filled with porous material, where a uniform angular velocity is applied and seepage occurs at the upper wall of the channel. The governing equations for this flow are derived from the Darcy–Brinkman model, and through the use of similarity transformations, these equations are converted into a sixth-order ordinary differential equation (ODE). The analytical solution to this ODE is obtained, providing insights into the behavior of the fluid under the given conditions. The impact of the Casson parameter on the primary, secondary, and seepage velocities is thoroughly analyzed, with particular attention paid to the influence of rotational effects in a porous medium. Graphical represen-tations are employed to illustrate the flow behavior and highlight the significant changes in velocity profiles due to variations in the Casson parameter. This com-prehensive analysis contributes to a deeper understanding of non-Newtonian fluid dynamics in rotating porous channels, with potential applications in engineering fields such as biomedicine, environmental engineering, and industrial fluid systems.