Magnetic particles are essential in materials science, biomedical, bioengineering, heat exchangers due to their exceptional thermal conductivity and unique properties. This work aims to model and analyze the biomagnetic fluid flow and heat transfer, namely the flow of blood with magnetic particles (Fe3O[Formula: see text] induced by stretching cylinder with linear and nonlinear stretching velocities. Additionally, this study investigates the impact of particles diameter and their spacing under the influence of ferrohydrodynamics (FHD) principle. The collection of partial differential equations is transformed using similarity transformations to produce the theoretically stated ordinary differential system. An efficient numerical technique, which is further based on common finite difference method with central differencing, a tridiagonal matrix manipulation and an iterative procedure are used to solve the problem numerically. The major goal of this extensive study is to enhance heat transformation under the influence of numerous parameters. There have been numerous displays of the velocity profile, temperature distribution, local skin friction factor and rate of heat transfer in terms of the appearing physical parameters. It is observed that variation in velocity and temperature distributions is the cause of increasing the ferromagnetic interaction parameter and the size of magnetic particles. The enhancement of particle diameter causes an increment in the skin friction while the rate of heat transfer declines. For verifying purposes, a comparison is also shown with previously published scientific work and found to possess suitable accuracy.

This study goal is to examine the flow of two-dimensional biomagnetic Maxwell fluid past a nonlinearly stretched sheet while it is subject to an applied magnetic field that is produced by the presence of a magnetic dipole. Assumedly, the fluids magnetization M varies linearly with temperature T and magnetic field strength H. Consideration is given to the effects of magnetohydrodynamics (MHDs) and ferrohydrodynamics (FHDs) on the flow. The controlling nonlinear partial differential equation is presented with similarity transformations to change it into coupled ordinary differential equations. These equations are then numerically solved with the help of common finite differences method. The influence of the addressed problem parameters, namely, magnetic parameter [Formula: see text], ferromagnetic parameter [Formula: see text], Deborah number [Formula: see text] and nonlinear stretching parameter [Formula: see text] on the flow profile is discussed with the help of graphical demonstration. The obtained results show that the fluid velocity increases near the wall but its reverse after a fixed point from the wall with increases nonlinearity stretching parameter. The study also demonstrates that as the magnetic field intensity increases, the temperature distributions increase while the fluid velocity decreases. It was also discovered that, in contrast to the situation of pure hydrodynamics, the effect of MHD or FHD interaction is to slow down the fluid velocity. By making numerous comparisons with previously published work, the numerical method accuracy is examined, and the comparisons show that the results are generally in good accord. Along with the flow parameters, physical parameters like the dimensionless Nusselt number and the skin friction coefficient are shown. The study will be crucial for applications in medicine.

The key objective of the present study is to elaborate the concept of boundary layer flow and heat transfer of magnetohydrodynamics namely Cu-water nanofluid flow towards an exponentially shrinking sheet with aid of mathematical modeling and computation. The present mathematical model is investigated under the influence of thermal radiation and suction. Using exponential form of similarity variables, the system of partial differential equations (PDEs) are converted in to a set of ordinary differential equations (ODEs). The resulting nonlinear ODEs are computationally solved by using a two-point boundary value problem numerical technique, which constitutes with common finite difference method. The influence of physical parameters such as magnetic field parameter, Eckert number, suction parameter, radiation parameter are described in details with the help of graphical demonstration of velocity and temperature distributions, coefficient of skin fiction and rate of heat transfer. Computational results reveal that after suspension of nanoparticles into base fluid as water fluid temperature raised significantly compare to that of pure fluid. It is also observed that for rising values of magnetic field parameter, thermal radiation, particles volume fraction fluid temperature distribution significantly improved; whereas opposite phenomena is true for suction parameter and Prandtl number. The rate of heat transfer accelerated with Eckert number, Prandtl number, while coefficient of skin friction boost with thermal radiation parameter. For verifying purposes, a comparison has been shown between present results and the computational results of previous studies and found a very close agreement.

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