Analysis of Magneto Hydrodynamic Flow with Wall Injection Using Fractional Derivative

Document Type : Original Article

Authors

Mohammad Tolami ¹

Akbar Nazari Golshan ²

Seyyed Salman Nourazar ¹

¹ Energy Conversion Department, Faculty of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran

² Department of Physics, Faculty of Basic Sciences, Shahed University, Tehran, Iran

10.22067/jacsm.2025.91367.1309

Abstract

The aim of this study is to investigate the injection of mutable velocity flow from the walls into the magneto hydrodynamic flow. A dominant term of tangential velocity is considered and the remaining terms are ignored and the first order derivative with respect to r is replaced by a fractional derivative. The equation is transformed into a nonlinear ordinary differential equation with fractional derivative using the similarity transformation method and solved using semi-analytical and numerical methods. The results show that increasing Re causes a significant increase in the values of the dimensionless velocity and radial velocity in the center of the channel, while a slight decrease is observed in the regions closer to the walls, but in the regions very close to the walls it is almost unchanged. Increasing Ha leads to a significant decrease in the maximum velocity. the velocity vector lines at fixed radial positions become more uniform. Increasing the Ha also leads to the appearance of two smaller maximum velocities in the vicinity of the channel walls.

Keywords

Jeffrey-Hamel Flow

Convergent and Divergent Channel

Injection

Magneto Hydrodynamic Flow

Fractional Derivative

Semi-Analytical Method

Subjects

• Fluid mechanics

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