Mass Transfer in Magnetohydrodynamic Oscillatory Flow of Casson Liquid Through a Porous Horizontal Channel with Velocity Slip

Zaheer Abbas ¹, Muhammad Shakib Arslan ^1*, Muhammad Yousuf Rafiq ¹, Jafar Hasnain ²

This study demonstrated the understanding of Casson fluid dynamics under magnetic fields and slip conditions aids in optimizing cooling systems and enhancing biomedical applications.

Abstract

Background: Casson liquid, a non-Newtonian fluid, exhibits unique rheological properties characterized by a yield stress below which it behaves as a solid, and above which it flows like a viscous fluid. These fluids show a shear-thinning behavior, where viscosity decreases with an increasing shear rate, making them relevant in various industrial and biological processes. Understanding the dynamics of Casson fluid flow under different conditions, such as in the presence of magnetic fields (MHD), permeable media, or chemical reactions, is essential for optimizing systems in fields ranging from biomedical applications to chemical engineering. Methods: This study investigates the mass transfer in magnetohydrodynamic oscillatory flow of a Casson liquid through a porous horizontal channel with velocity slip. The governing nonlinear partial differential equations were transformed into ordinary differential equations using similarity transformation. The exact solutions were obtained using Mathematica to analyze the effects of various physical parameters, including the Hartmann number, Schmidt number, wall expansion ratio, and slip parameter on flow dynamics. Results: The results indicate that an increase in the Reynolds number enhances velocity at the lower wall while reducing it at the upper wall. An increase in the wall expansion ratio leads to higher velocity at the center of the channel and lower velocity near the plate edges, modeling arterial dilation effects. The fluid parameter and slip parameter significantly influence velocity profiles, impacting flow dynamics relevant to biological and engineering applications. The Hartmann effect showed that velocity decreases at the channel center, demonstrating the importance of magnetic field strength in controlling fluid flow. Conclusion: This study offers insights into the behavior of Casson fluid flows in oscillating and porous environments, which are applicable to biomedical and industrial processes. The findings can be used to optimize cooling systems in electronic devices, enhance the design of medical devices, and improve treatments involving magnetic fields. Additionally, this insight can be applied in developing more efficient drug delivery systems that rely on the flow of therapeutic fluids through narrow channels or porous media.

Keywords: Casson liquid, Magnetohydrodynamics, Oscillatory flow, Porous channel, Velocity slip

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