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Targeted magnetic drug delivery (TMDD) is a promising approach relevant to multimodal cancer therapy. A majority of the TMDD models represent a mixture of blood and nanoparticles as a one-phase solution. However, in many cases it is an oversimplistic assumption. The existing two-phase models are usually one-way coupled, i.e. the blood flow has an impact on the MN flow. However, the inverse impact of the MNs on the the blood is not included. To eliminate these drawbacks the model is governed by two–way coupled momentum and temperature equations for the blood flow and the MN. The numerical procedure invokes the stream function–vorticity formulation and an efficient numerical procedure. The model, validated by experimental results, has been applied to analyze the formation of vortices generated by a combination of the magnetic force (MF) and the drag force (DF). The model also simulates the zones of TMDD and the corresponding changes in the vorticity. Finally, the model includes the impact of the size and concentration of the MNs on the temperature of the blood. These important scenarios cannot be analyzed by the earlier models.

The flow and heat transfer of a steady, viscous biomagnetic fluid containing magnetic particles caused by the swirling and stretching motion of a three-dimensional cylinder has been investigated numerically in this study. Because fluid and particle rotation are different, a magnetic field is applied in both radial and tangential directions to counteract the effects of rotational viscosity in the flow domain. Partial differential equations are used to represent the governing three-dimensional modeled equations. With the aid of customary similarity transformations, this system of partial differential equations is transformed into a set of ordinary differential equations. They are then numerically resolved utilizing a common finite differences technique that includes iterative processing and the manipulation of tridiagonal matrices. Graphs are used to depict the physical effects of imperative parameters on the swirling velocity, temperature distributions, skin friction coefficient, and the rate of heat transfer. For higher values of the ferromagnetic interaction parameter, it is discovered that the axial velocity increases, whereas temperature and tangential velocity drop. With rising levels of the ferromagnetic interaction parameter, the size of the axial skin friction coefficient and the rate of heat transfer are both accelerated. In some limited circumstances, a comparison with previously published work is also handled and found to be acceptably accurate.

Many problems in fluid mechanics describe the change in the flow under the effect of electromagnetic forces. The present study explores the behaviour of an electric conducting, Newtonian fluid flow applying the magnetohydrodynamics (MHD) and ferrohydrodynamics (FHD) principles. The physical problems for such flows are formulated by the Navier–Stokes equations with the conservation of mass and energy equations, which constitute a coupled non-linear system of partial differential equations subject to analogous boundary conditions. The numerical solution of such physical problems is not a trivial task due to the electromagnetic forces which may cause severe disturbances in the flow field. In the present study, a numerical algorithm based on a finite volume method is developed for the solution of such problems. The basic characteristics of the method are, the set of equations is solved using a simultaneous direct approach, the discretization is achieved using the finite volume method, and the solution is attained solving an implicit non-linear system of algebraic equations with intense source terms created by the non-uniform magnetic field. For the validation of the overall algorithm, comparisons are made with previously published results concerning MHD and FHD flows. The advantages of the proposed methodology are that it is direct and the governing equations are not manipulated like other methods such as the stream function vorticity formulation. Moreover, it is relatively easily extended for the study of three-dimensional problems. This study examines the Hartmann flow and the fluid flow with FHD principles, that formulate MHD and FHD flows, respectively. The major component of the Hartmann flow is the Hartmann number, which increases in value the stronger the Lorentz forces are, thus the fluid decelerates. In the case of FHD fluid flow, the major finding is the creation of vortices close to the external magnetic field source, and the stronger the magnetic field of the source, the larger the vortices are.

Of concern in the paper is a theoretical investigation of boundary layer flow of a biomagnetic fluid and heat transfer on a stretching/shrinking sheet in the presence of a magnetic dipole. The problem has been treated mathematically by using Lie group transformation. The governing nonlinear partial differential equations are thereby reduced to a system of coupled nonlinear ordinary differential equations subject to associated boundary conditions. The resulting equations subject to boundary conditions are solved numerically by using bvp4c function available in MATLAB software. The plots for variations of velocity, temperature, skin friction and heat transfer rate have been drawn and adequate discussion has been made. The study reveals that the problem considered admits of dual solutions in particular ranges of values of the suction parameter and nonlinear stretching/shrinking parameter. A stability analysis has also been carried out and presented in the paper. This enables one to determine which solution is stable that can be realized physically, and which is not. The results of the present study have been compared with those reported by previous investigators to ascertain the validity/reliability of the computational results.

The study of biomagnetic fluid flow and heat transfer containing magnetic particles through an unsteady stretching/shrinking cylinder was numerically investigated in this manuscript. Biomagnetic fluid namely blood taken as base fluid and CoFe2O4 as magnetic particles. Where blood acts as an electrically conducting fluid along with magnetization/polarization. The main concentration is to study a time-dependent biomagnetic fluid flow with magnetic particles that passed through a two dimensional stretching/shrinking cylinder under the influence of thermal radiation, heat source and partial slip condition which has not been studied yet as far as best knowledge of authors. This model is consistent with the principles of magnetohydrodynamic and ferrohydrodynamic. The flow equations, such as momentum, energy which is described physically by a system of coupled, nonlinear partial differential equation with appropriate boundary conditions and converted into a nonlinear system of ordinary differential equations by using suitable similarity transformations. The resultant ODEs numerically solved by applying by applying an efficient numerical technique based on a common finite differencing method along with central differencing, tridiagonal matrix manipulation and an iterative procedure. The values assigned to the parameters are compatible with human body conditions. The numerous results concerning velocity, temperature and pressure field, as well as the skin friction and the rate of heat transfer, are presented for the parameters exhibiting physical significance, such as ferromagnetic interaction parameter, magnetic field parameter, volume fraction, unsteady parameter, curvature parameter, etc. The main numerical findings are that the fluid velocity is decreased as the ferromagnetic number is enhanced gradually in both stretching or shrinking cases whereas, the opposite behavior is found for the skin friction coefficient. The rate of heat transfer with ferromagnetic interaction parameter was also monitored and found that opposite behavior occurs for stretching and shrinking cases. Comparisons were made to check the accuracy of the present numerical results with published literature and found to be in excellent agreement. Hopefully, this proposed model will control the blood flow rate, as well as the rate of heat transfer, such as magnetic hyperthermia.