Theoretical and numerical investigation of an applied magnetic field on mixed convection flow of a biofluid through a vertical plate using contained heating or cooling is observed in this study. The mathematical formulation is that of the full Biomagnetic Fluid Dynamics (BFD) model which deals with on the ferrohydrodynamics (FHD) and magnetohydrodynamics (MHD)principle. In this work, the study is performed on a specific biofluid, viz. human blood. Assume that the magnetization very linearly with magnetic field strength, temperature dependency of dynamic viscosity and thermal conductivity is noticed. A system of non-linear equations with appropriate boundary condition is obtained by familiarizing suitable non-dimensional variables in the physical problem. For the numerical solution, we used finite difference method which is based on an efficient technique is applied in the problem. Computations for flow profiles, local skin friction coefficient and local heat transfer coefficient are performed with the magnetic parameter Mn, the viscosity/temperature parameter theta(r) and the thermal/conductivity parameter S-& lowast;. The effect of the localized heating or cooling is examined. The computational results presented graphically and have been validated in an appropriate manner. The study reveals that the impact of a magnetic field for blood flow in arteries is found significantly. The results presented bear the promise of valuable applications in physiology, medicine and bioengineering.

In engineering and medical applications, heat flow and transfer over a wedge are important phenomena that happen often. Consequently, it is important to look at the fluid’s heat and flow properties over a wedge. In the presence of a magnetic dipole, this study investigated the flow and heat transfer of a biomagnetic fluid containing magnetic particles over a wedge. Furthermore, in this inquiry, blood is taken into account as the base fluid and Ni-ZnFe2O4 as the magnetic particles. The controlling partial differential equations are transformed into ordinary differential equations using suitable-self similarity variables. These equations are then solved in MATLAB using the bvp4c technique. The impact of physical parameters, such as ferromagnetic interaction, power-law index, and particle volume fraction is visually displayed for temperature, velocity profiles, and the rate of heat transfer, skin friction. The calculated findings show that the power-law index parameter increases fluid velocity while the ferromagnetic interaction parameter and particle volume fraction decrease it. Additionally, it is shown that while skin friction and the rate of heat transfer decrease with increasing ferromagnetic interaction parameter values. Analysis of these phenomena is intended to aid in the identification of potential real-world applications in a variety of engineering domains, such as magnetic drug delivery, cancer treatment, and reduction of blood flow during surgeries. Numerical results have been compared with prior research to assess the accuracy of the current model and have been determined to be an excellent agreement.

The use of nanoparticles, the biological phenomenon has lately been found to play a key role in engineering and biomedical applications including the separation of specified molecules, magnetic targeting of drugs, diagnostic methods such as MRI, CT scan, the treatment of hyperthermia or hypothermia, etc. Motivating by the above applications, the current study is designed and presents a novel mathematical model to analyze the behavior of blood-based ternary hybrid nanofluid under the influence of magnetic dipole with variable fluid properties over a stretching sheet. Silicon Dioxide ( SiO_2 ), Iron Oxide ( Fe_3O_4 ) and Copper ( Cu ) are considered nanoparticles, with blood as the base fluid. Similarity transformations are used to convert the partial differential equations into ordinary differential equations, which are numerically solved by using the finite difference method, consisting of the central differencing method, a tridiagonal matrix manipulation, and an iterative method. The most important results of this investigation of different non-dimensional physical factors are velocity, temperature, skin friction, and the Nusselt number. It was noted that by elevating the figures of variations in viscosity, thermal conductivity, magnetic field parameter, and ferromagnetic interaction parameter, fluid axial velocity decreased. Also found that the rate of heat transfer increased by 4.51

This research concentrates on the 2-D, steady, laminar, viscous, incompressible boundary layer flow of a biomagnetic fluid containing two different magnetic particles (CoFe2O4andFe3O4) over a continuously moving horizontal plate in the presence of a magnetic field generated by a magnetic dipole. For the mathematical formulation the comprehensive concept of Biomagnetic Fluid Dynamics (BFD) is adopted incorporating the principles of FerroHydroDynamics (FHD) and MagnetoHydroDynamics (MHD). The physical problem which is constituted by a coupled system of Partial Differential Equations (PDEs) along with corresponding boundary conditions, is transformed into a coupled system of nonlinear Ordinary Differential Equations (ODEs) subject to analogous boundary conditions by establishing newly simplified similarity transformations. The transformed ODEs along with the boundary conditions are then solved numerically by introducing an efficient numerical technique based on a finite difference algorithm. Verification of this work has been also done by comparing the obtained results with previously published results and found in quite good agreement. The significant effects caused by the variation of the governing parameters such as the skin friction, heat transfer rate and wall pressure are presented more intricately. It has been contemplated that including magnetic particles with pure blood enhances the impact of the magnetic field on the flow, temperature and pressure profiles which could be of interest engineering implementations, like, magnetic drug delivering in blood cells, separating RBCs (Red Blood Cells), controlling the flow of blood during surgeries, treating cancer by producing magnetic hyperthermia etc.

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.

Theoretical and numerical investigation of an applied magnetic field on mixed convection flow of a biofluid through a vertical plate using contained heating or cooling is observed in this study. The mathematical formulation is that of the full Biomagnetic Fluid Dynamics (BFD) model which deals with on the ferrohydrodynamics (FHD) and magnetohydrodynamics (MHD) principle. In this work, the study is performed on a specific biofluid, viz. human blood. Assume that the magnetization very linearly with magnetic field strength, temperature dependency of dynamic viscosity and thermal conductivity is noticed. A system of non-linear equations with appropriate boundary condition is obtained by familiarizing suitable non-dimensional variables in the physical problem. For the numerical solution, we used finite difference method which is based on an efficient technique is applied in the problem. Computations for flow profiles, local skin friction coefficient and local heat transfer coefficient are performed with the magnetic parameter Mn, the viscosity/temperature parameter θr and the thermal/conductivity parameter S∗. The effect of the localized heating or cooling is examined. The computational results presented graphically and have been validated in an appropriate manner. The study reveals that the impact of a magnetic field for blood flow in arteries is found significantly. The results presented bear the promise of valuable applications in physiology, medicine and bioengineering.

The study of flow and heat transfer of biomagnetic fluid past a stretching sheet has a significant importance in a number of bio-medical and engineering applications including cancer treatment, drug delivery, magnetic resonance imaging, reducing blood flow during surgeries etc. Owing to these applications, the aim of the present paper is to study an electrically non-conducting Newtonian biomagnetic fluid in the presence of a magnetic dipole over an extendable sheet subject to velocity slip. The governing steady boundary layer equations with the help of similarity transformations were converted into a set of highly non-linear ordinary differential equations which are then computationally solved by applying the bvp4c function technique in MATLAB software. The results show that blood velocity and temperature can remarkably be influenced by the variation of ferromagnetic parameter. As the ferromagnetic parameter increases, the rate of heat transfer of blood is increased while coefficient of skin friction is reduced. We hope that this study could be useful in cancer treatment as well as in drug administration.

This investigations covers the numerical analysis of a steady biomagnetic fluid flow (BFD) that passed through a two dimensional stretching sheet under the influence of magnetic dipole. The effect of fluid variable viscosity and thermal conductivity are also taken into consideration as assumed to vary as linear function of temperature. Our model mathematically formulated for BFD namely blood which consist of principles of magnetohydrodynamic (MHD) and ferrohydrodynamic (FHD), where blood treated as an electrically conducting fluid as well as polarization. Using similarity transformations, the governing system of partial differential equations are transferred into system of ordinary differential equations (ODE). The resulting coupled non linear ODE is numerically solved by employing bvp4c function technique available in MATLAB software. The effects of pertinent parameters namely ferromagnetic interaction parameter, magnetic field parameter, mixed convection parameter, viscosity variation parameter, Prandtl number, thermal conductivity parameter etc are plotted and discussed adequately for velocity and temperature profile as well as skin friction coefficient and rate of heat transfer. The results revels that velocity profile decreases as enhanced values of ferromagnetic number whereas temperature profile increased. Also found that skin friction coefficient reduces and rate of heat transfer increases by increasing values of thermal conductivity parameter and viscosity variation parameter. For numerical validation a comparisons has been made for some specific values with previous investigators. We hope that the present analysis will present in bio-medical and bio-engineering sciences.

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 (Fe 3 O[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.

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.

The main contribution of the current work is a numerical and mathematical investigation of the effects of magnetic dipole and electrical conductivity on the heat and flow transfer of biomagnetic fluid over a non-linear stretched sheet with variable thickness. Static magnetic fields are produced by magnetic dipoles, which are used in medical a pplications such as MRI, drug administration, and cancer therapy. Additionally, the impact of non-linear heat source/sink features was examined in the study, leading to an interesting phenomenon. The PDEs are attenuated to nonlinear ODEs with dealing appropriate similarity variables. These resultant ODEs are computed by developing an effective method emerged on the application of the finite differences technique. In the end, this section offers a summary of the implications resulting from different physical limitations on blood flow, including variable thickness and power index effects. It was discovered that the rise in Kelvin and Lorentz forces in the boundary layer significantly affected blood flow. The current findings for the biomagnetic fluid model are novel and inventive since they effectively expand upon the issues previously addressed by previously published scientific documentation.

The aim of present research is to endorse the interactions of magnetohydrodynamics and ferrohydrodynamics on biomagnetic fluid flow- namely the flow of blood with magnetic particles over a cylinder with prescribed heat flux. The transformation of group theoretic approach namely one parameter group method is applied in this paper. By applying this method, the number of independent variables are reduced into one and the set of partial differential equations reduces to a system of ordinary differential equations along with boundary conditions. The results are presented graphically for blood-Fe3O4 and blood-CoFe2O4. The numerical simulation for ordinary differential equations is presented by applying an efficient numerical technique which based on common finite difference method along with central differencing, a tridiagonal matrix manipulation and an iterative procedure. The graphical results disclose that the presence of ferromagnetic number enhanced the temperature and more effectively for CoFe2O4 magnetic particles than Fe3O4. A reduction in blood velocity has been observed for magnetic particles volume fraction. Moreover, the rate of heat transfer enhanced for larger values of magnetic particles volume fraction and attained highest for CoFe2O4. The results compared with the previous literature and shows an excellent agreement, which assures the validity of the analysis. The novelty of the present problem is to study the biomagnetic fluid by taking magnetic particles using group theoretical method.

Magnetic particles have grown appeal due to their ability to in changing the thermophysical properties of biomagnetic fluid, particularly blood, which are more tied to practical applications. The current work uses the well-known MHD blood flow with magnetic particles because of its noteworthy function in medical applications. Therefore, the aim of the current study focuses on studying the significance of electrically conducting blood flow with Fe 3 O 4 magnetic particles subject to exponentially stretching cylinder. A mathematical form is introduced in the system of partial differential equation forms which consists with momentum equation and temperature equation and reduced into a nonlinear form of coupled ordinary differential equations by applying a similarity framework. The computational solution of the given problem has been obtained by utilizing a parametric continuation method (PCM) built in MATLAB package. The impacts of episodic parameters such as particles volume fraction, curvature parameter, and magnetic field parameter are discussed and depicted graphically via velocity and temperature distributions. A tabular form is also presented for the skin friction coefficient and the rate of heat transfer. It has been observed that blood velocity fall down due to enhancement of magnetic field parameter and particles volume fraction; whereas temperature profile increased in this case. The obtained results also indicates that for rising values of curvature parameter, skin friction coefficient decreases but rate of heat transfer boost up. To ensure the validity of numerical scheme, a comparison of the present results are made with previous published studies. It has been perceived that present study are in good agreement with previous studies under some special cases. We hope that the current study will be beneficial in targeted drug delivery, cancer treatment, imaging, and tumor therapy.

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.

Abstract The biomagnetic fluid (blood) flow with magnetic particles over an inclined stretched cylinder in the presence of a magnetic dipole is numerically studied. The effect of thermal radiation and heat source/sink are taken into consideration. For the mathematical formulation of the present problem both magnetization (polarization) and electrical conductivity of blood are taken into consideration. Consequently, the mathematical formulation of Biomagnetic Fluid Dynamics (BFD) is utilized, where both principles of magnetohydrodynamics (MHD) and ferrohydrodynamics (FHD) are taken into account. The governing non-linear partial differential equations are transformed into ordinary differential equations by using a similarity approach. The numerical solution is obtained by employing the bvp4c function in MATLAB R2018b software. The results are presented graphically and discussed for various parameters that are involved in this problem. Considering the electrical conductivity and magnetization of blood with magnetic particles, the effect of magnetohydrodynamic interaction parameter and ferrohydrodynamic interaction parameter on velocity and temperature profiles are discussed. One of the major findings is that the rate of heat transfer and skin friction coefficient are increased and decreased, respectively with increasing values of the volume fraction. It is obtained that the effect of the magnetic field is significantly enchased by the presence of the magnetic particles to blood.

Magnetic fluids with magnetic field effect mediated by magnetic particles such as NiZnFe 3 O 4 into base fluid like blood ignite new medical applications interests. Magnetic particles are investigated due to their remarkable properties like as exceptional thermal conductivity, which is considered one of the vital in modern nanotechnology to improve the thermal properties as coolants in heat transfer equipment such as drug administration, cancer treatment, and electronic cooling system. Therefore, the research on novel heat transfer of biomagnetic fluids is extremely potent and inspiring. Hence, the present computational study investigates a NiZnFe 3 O 4 –blood magnetic fluids steady heat and flow transmission mechanisms performance past a swirling stretchable cylinder. In addition, due to the difference in rotation between NiZnFe 3 O 4 and blood for the purposes of the effects of rotational viscosity in flow, a magnetic field is applied in both radial and tangential directions. The governing equations describing the physical problem accompanied by boundary conditions have been transformed into a dimensionless form using a suitable similarity transformation. With the aid of the MATLAB computer program, the modified system of nonlinear ordinary differential equations has been computationally resolved using a precise numerical technique known as the parametric continuation method to explore the significance of pertinent physical parameters. With the use of graphs and tabular representations, the role of emerging physical factors in this model, including the Reynolds number, effective magnetization number, ferromagnetic interaction parameter, and particle volume fraction, is described in opposition to the flow and heat fields. The numerical results ultimately demonstrate that, when adding magnetic particles to base fluid (blood), which is superior to conventional fluids, Reynolds number and magnetization force play a key influence in the flow distributions and improvement of heat transfer. It is seen that fluid velocity reduced with enhancement values of ferromagnetic interaction parameter, and particles’ volume fraction. Additionally, it is discovered that for Reynolds number, particles’ volume fraction, and effective magnetization number, the rate of heat transfer is increased. With authors’ best information, till to date, the study of heat and flow transmission of blood with NiZnFe 3 O 4 particles under magnetic field effect over swirling extended cylinder has not been attempted by anyone. Sooth to say, the findings of this paper are entirely original and such numerical outcomes were never published by any scholar researchers. The present model can be applicable in medical sectors especially in drug delivery, cancer treatment, separation, and magnetic resonance imaging.

A two-dimensional (2D) steady boundary layer flow along with heat transfer of a self-similar biomagnetic fluid over a permeable moving flat plate has been taken into consideration in this work. The flow is contemplated to be embedded by a magnetic dipole of sufficient magnetic strength. Transpiration as well as movement along the wall is also regarded. By imposing the appropriate similarity technique, the governing equations are converted into a system of coupled nondimensional equations. An efficient numerical technique has been incorporated to solve these dimensionless coupled nonlinear ordinary differential equations. The existence of dual solutions along with their stability has been established with the consideration of stability analysis. We discovered from our analysis that two solutions exist (one stable and another unstable) for the arbitrary values of transpiration, movement velocity and biomagnetic interaction parameters on flow and physical parameters. The attained results are demonstrated graphically and in tabular form. For the validity of our numerical scheme, we compared our findings with others previously published and found significant agreement.