Numerical study on magnetic control of boundary layers in non-Newtonian flows over stretching cylinders using Keller box analysis

This article presents an analysis of the magnetic field’s effects on two-dimensional, two-directional, incompressible, and steady third-grade fluid flow over a stretched circular cylinder. A mathematical model describing the behavior of third-grade fluid in the cylindrical coordinate system is developed, accounting for nonlinear differential conditions. To simplify the analysis, appropriate transformations are applied to convert the fractional differential conditions into ordinary differential conditions. The resulting nonlinear differential framework is solved using the Keller Box method. The influences of several novel parameters on the velocity are depicted and examined. Furthermore, the expression for the skin-friction coefficient is computed and provided. The comparison of the obtained results with existing literature is made and found in good accordance. Through comprehensive numerical simulations and analytical derivations, this study contributes to the understanding of magnetic field control in boundary layers of third-grade fluid over stretching cylinders, with implications for a wide range of practical applications in engineering and fluid dynamics. The stronger influence of the magnetic field, indicating an increase in the Hartmann number, corresponds to suppression of thermal and solutal transport, thereby leading to a decrease in the temperature and concentration gradients. Conversely, the velocity profile exhibits an increase, indicating enhanced fluid motion under the influence of the magnetic field. This behavior is consistent with the magnetohydrodynamic effects, where the Lorentz force induced by the magnetic field alters the fluid flow, resulting in changes in the velocity distribution while impacting temperature and concentration gradients.