# The Role of Slip Velocity in Fractional MHD Casson Fluid Flow within Porous Cylinder

## Authors

• Wan Faezah Wan Azmi Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
• Ahmad Qushairi Mohamad Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
• Lim Yeou Jiann Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia
• Sharidan Shafie Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia

## Keywords:

Casson Fluid, Caputo-Fabrizio Fractional Derivative, MHD, Slip Velocity Cylinder

## Abstract

Numerous academics are intrigued by exploring the fractional Casson fluid model due to its enhanced precision compared to the traditional fluid model. However, many researchers have successfully tackled the analytical solution for the fractional fluid model while overlooking the impact of boundary slip. Hence, this study aims to tackle the challenge of describing the Casson fluid behaviour with fractional properties in a cylindrical domain, considering the influence of slip velocity at the boundaries. Furthermore, magnetohydrodynamics (MHD) had been introduced into the analysis and considered a porous medium resembling a blood clot or fatty plaque. The Caputo-Fabrizio fractional derivative is employed to establish the dimensionless governing equation. Subsequently, we solve it analytically using the Laplace transform in conjunction with finite Hankel transform techniques. A thorough examination follows the graphical presentation of the analytical solution in the context of relevant parameters. The findings illustrate those higher values of the Casson parameter, slip velocity parameter, Darcy number, and fractional parameter lead to an augmentation in fluid velocity. Conversely, an escalation in magnetic parameters causes a reduction in fluid velocity. These findings can be utilized to validate the accuracy of numerical results. The findings of this study hold considerable importance in enhancing our understanding of human blood flow, especially in scenarios where a velocity gradient occurs between blood particles and the stretching motion of arteries.

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