Influence of Magnetic Dipole on Biomagnetic Fluid Flow Past a Thin Needle Under the Interaction of Magnetohydrodynamics and Ferrohydrodynamics Using Lie Group Analysis

To shed light on the steady biomagnetic fluid flow past a thin needle under the combined influence of ferrohydrodynamics and magnetohydrodynamics, an analysis has been conducted. The intricate scenario above investigates how blood flow along a thin needle is impacted by the presence of a magnetic dipole. The described system of partial differential equations is converted into a set of ordinary differential equations. Using scaling symmetry transformations produced via Lie group analysis, ordinary differential equations are reported in this study. An effective numerical strategy emerged on the finite difference method is used to numerically solve the resulting equations. A graphic representation of the major effects of different physical non-dimensional parameters on the temperature, velocity profiles, coefficient of skin friction, rate of heat transfer, and Sherwood number is presented. The current findings specify that the velocity profiles decrease under ferromagnetic interaction parameter and magnetic field parameter while thermal distribution positively changes under the effect of under ferromagnetic interaction parameter and magnetic field parameter. The concentration profiles behave negatively with the Schmidt number and power law index quantity. Additionally, the current study reveals that the ferromagnetic interaction and magnetic field parameters increase the blood rate of heat transfer, skin friction coefficient, and Sherwood number. The comparison with earlier results gives a reliability of present results.