Search Results (15)

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. Full article

The physiological system loses thermal energy to nearby cells via the bloodstream. Such energy loss can result in sudden death, severe hypothermia, anemia, high or low blood pressure, and heart surgery. Gold and iron oxide nanoparticles are significant in cancer treatment. Thus, there is a growing interest among biomedical engineers and clinicians in the study of entropy production as a means of quantifying energy dissipation in biological systems. The present study provides a novel implementation of an intelligent numerical computing solver based on an MLP feed-forward backpropagation ANN with the Levenberg–Marquard algorithm to interpret the Cattaneo–Christov heat flux model and demonstrate the effect of entropy production and melting heat transfer on the ferrohydrodynamic flow of the Fe₃O₄-Au/blood Powell–Eyring hybrid nanofluid. Similarity transformation studies symmetry and simplifies PDEs to ODEs. The MATLAB program bvp4c is used to solve the nonlinear coupled ordinary differential equations. Graphs illustrate the impact of a wide range of physical factors on variables, including velocity, temperature, entropy generation, local skin friction coefficient, and heat transfer rate. The artificial neural network model engages in a process of data selection, network construction, training, and evaluation through the use of mean square error. The ferromagnetic parameter, porosity parameter, distance from origin to magnetic dipole, inertia coefficient, dimensionless Curie temperature ratio, fluid parameters, Eckert number, thermal radiation, heat source, thermal relaxation parameter, and latent heat of the fluid parameter are taken as input data, and the skin friction coefficient and heat transfer rate are taken as output data. A total of sixty data collections were used for the purpose of testing, certifying, and training the ANN model. From the results, it is found that the fluid temperature declines when the thermal relaxation parameter is improved. The latent heat of the fluid parameter impacts the entropy generation and Bejan number. There is a less significant impact on the heat transfer rate of the hybrid nanofluid over the sheet on the melting heat transfer parameter. Full article

The boundary layer flows exhibit symmetrical characteristics. In such cases, the flow patterns and variables are symmetrical with respect to a particular axis or plane. This symmetry simplifies the analysis and enables the use of symmetry-based boundary conditions or simplifications in mathematical models. Therefore, by using these concepts, the governing equations of the radiative flow of a hybrid nanofluid past a stretched and shrunken surface with the effect of a magnetic dipole are examined in this paper. Here, we consider copper (Cu) and alumina (Al₂O₃) as hybrid nanoparticles and use water as a base fluid. The heat transfer rate is enhanced in the presence of hybrid nanoparticles. It is observed that the heat transfer rate is increased by 10.92% for the nanofluid, while it has a 15.13% increment for the hybrid nanofluid compared to the base fluid. Also, the results reveal that the non-uniqueness of the solutions exists for a certain suction and shrinking strength. Additionally, the ferrohydrodynamic interaction has the tendency to reduce the skin friction and the heat transfer coefficients for both solution branches. For the upper branch solutions, the heat transfer rate increased over a stretching sheet but decreased for the shrinking sheet in the presence of the radiation. It is confirmed by the temporal stability analysis that one of the solutions is stable and acceptable as time evolves. Full article

In this paper, we study the laminar, incompressible, and steady flow of a biomagnetic fluid, such as blood, containing gold nanoparticles through a shrinking sheet in the presence of a magnetic dipole. This model is consistent with both the principles of magnetohydrodynamics (MHD) and ferro-hydrodynamics (FHD). An effective numerical method that is based on an iterative process, tridiagonal matrix manipulation, and a common finite difference method with central differencing is used to generate the numerical solution of obtained ordinary differential equations (ODEs). The major numerical results show that the fluid velocity decreases as the ferromagnetic number increases whereas the skin friction coefficient shows the opposite behavior. As the ferromagnetic number increases, the rate of heat transfer with ferromagnetic interaction parameter is likewise observed and shown to be decreasing. Full article

In this study, a numerical investigation of the effect of different magnetic fields on ferrofluid-fluid mixing processes in a two-dimensional microchannel is performed An improved version of smoothed particle hydrodynamics, SPH, by shifting particle algorithm and dummy particle boundary condition, is implemented to solve numerical continuity, ferrohydrodynamics-based momentum and mass transfer equations. SPH is formulated through the irregular arrangement of the nodes where the fields are approximated using the fifth-order Wendland kernel function. After validating the computational approach, the influence of the number (from one to three) of parallel electrical wires positioned perpendicular to the microchannel on the mixing efficiency is studied for the first time. It has originally been found that the mixing efficiency highly non-linearly depends on the Reynolds number and the number of electrical wires. For Re ≤ 20 the mixing efficiency is almost the same for two and three electrical wires and about two times higher than one electrical wire. For Re ≥ 80, the mixing efficiency of three wires is much higher than one and two electrical wires. Optimum performance of the micromixer is achieved with three electrical wires, since the mixer performs well on a broader range of Re than the other two studied cases. The outcomes of this study, obtained by a meshless method, are important for the industrial design of micromixers. Full article

The flow and heat characteristics of an unsteady, laminar biomagnetic fluid, namely blood containing Fe₃O₄ magnetic particles, under the influence of thermal radiation and a magnetic dipole over a cylinder with controlled boundary conditions using a group theory method are investigated in the present study. The mathematical formulation of the problem is constructed with the aid of biomagnetic fluid dynamics (BFD) which combines principles of ferrohydrodynamics (FHD) and magnetohydrodynamics (MHD). It is assumed that blood exhibits polarization as well as electrical conductivity. Additionally, the shape of the magnetic particles, namely cylindrical and spherical, is also considered. Moreover, in this model, a group theoretical transformation, namely a two-parameter group technique, is applied. By applying this group transformation, the governing system of partial differential equations (PDEs) along with applicable boundary conditions are reduced to one independent variable and, consequently, converted into a system of ordinary differential equations (ODEs) with suitable boundary conditions. An efficient numerical technique is applied to solve the resultant ODEs and this technique is based on three essential features, namely (i) a common finite differences method with central differencing, (ii) tridiagonal matrix manipulation and (iii) an iterative procedure. The flow and heat characteristics of blood-Fe₃O₄ are found to be dependent on some physical parameters such as the particle volume fraction, the ferromagnetic interaction parameter, the magnetic field parameter, and the thermal radiation parameter. An ample parametric study is accomplished to narrate the influences of such physical parameters on velocity, temperature distributions as well as the coefficient of skin friction and rate of heat transfer. From the numerical results, it is deduced that the fluid velocity is enhanced for the ferromagnetic number and the temperature profile is decreased as the ferromagnetic number is gradually increased. It is also obtained that for the cylindrical shape of magnetic particles, the fluid temperature is more enhanced than that of the spherical shape. Both the skin friction coefficient and the local Nusselt number are increased for increasing values of the ferromagnetic interaction parameter, where the heat transfer rate of blood-Fe₃O₄ is significantly increased by approximately 33.2% compared to that of pure blood, whereas the coefficient of skin friction is reduced by approximately 6.82%. Full article

The article presents the mixed finite element formulation for examining the biomagnetic fluid dynamics as governed by the Navier–Stokes equation, coupled with energy and magnetic expressions. Both ferrohydrodynamics and magnetohydrodynamics describe the additional magnetic effects. For model discretization, the Galerkin weighted residual method was performed. Departing from a good agreement with existing findings, a biomagnetic flow (blood) in a straight rectangular conduit was then simulated in the presence of a spatially changing magnetic distribution. By virtue of negligible spatial variation influence from the magnetic field, the effects of Lorentz force were not presently considered. It was further found that the model accurately exhibits the formation and distribution of vortices, temperature, and skin friction located adjacent to and remotely from the source of magnetic load following a rise in the magnetic intensity. Full article

Energy transport intensification is a major challenge in various technical applications including heat exchangers, solar collectors, electronics, and others. Simultaneously, the control of energy transport and liquid motion allows one to predict the development of the thermal process. The present work deals with the computational investigation of nanoliquid thermogravitational energy transport in a square region with hot cylinders along walls under non-uniform magnetic influences. Two current-carrying wires as non-identical magnetic sources are set in the centers of two heated half-cylinders mounted on the bottom and left borders, while the upper wall is kept at a constant low temperature. Buongiorno’s model was employed with the impact of Brownian diffusion and thermophoresis. Governing equations considering magnetohydrodynamic and ferrohydrodynamic theories were solved by the finite element technique. The effects of the magnetic sources strengths ratio, Lewis number, Hartmann number, magnetic number, buoyancy ratio, Brownian motion characteristic, and thermophoresis feature on circulation structures and heat transport performance were examined. For growth of magnetism number between 0 and ${10}^3$ one can find an increment of heat transfer rate for the half-cylinder mounted on the bottom wall and a reduction of heat transfer rate for the half-cylinder mounted on the left wall, while for an increase in magnetism number between ${10}^3$ and ${10}^4$, the opposite effects occur. Moreover, a rise in the Lewis number characterizes the energy transport degradation. Additionally, an intensification of energy transport could be achieved by a reduction of the thermophoresis parameter, while the Brownian diffusion factor and buoyancy ratio have a negligible influence on energy transport. Furthermore, the heat transfer rate through the half-cylinder mounted on the bottom wall declines with an increase in the magnetic sources strengths ratio. Full article

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. Full article

In the present study, the two-dimensional jet flow of Fe₃O₄-H₂O nanofluid was numerically investigated in a microchannel. The main objective of this article was to study the impact of permanent magnets on both ferromagnetic hydrodynamic and thermal behavior. A ferromagnetic hydrodynamic model, which includes the Brown effect and thermophoretic effect, was applied to simulate the problem through solving momentum, energy, and volume fraction equations. In this regard, different results, including the velocity vector, temperature distribution, and Nusselt number, were analyzed. Moreover, the influence of Kelvin force, inlet opening, permanent magnets position, and Reynolds number were studied on the jet flow and heat transfer. The obtained results demonstrate these factors significantly affect the jet flow and heat transfer of Fe₃O₄-H₂O nanofluid in the microchannel. Moreover, it was found that the magnetic field originating from permanent magnets can effectively solve the problem of local high temperature on the wall at low inlet opening. The heat transfer gain was the most obvious when the position of the permanent magnet was close to the microchannel entrance. When inlet opening and permanent magnets position are 1/4 and 1, respectively, the heat transfer gain was largest, reaching 35.2%. Full article

Because of the floating magnetic nanomaterial, ferrofluids have magneto-viscous properties, enabling controllable temperature changes as well as nano-structured fluid characteristics. The study’s purpose is to evolve and solve a theoretical model of bioconvection nanofluid flow with a magnetic dipole effect in the presence of Curie temperature and using the Forchheimer-extended Darcy law subjected to a vertical cone surface. The model also includes the nonlinear thermal radiation, heat suction/injection, viscous dissipation, and chemical reaction effects. The developed model problem is transformed into nonlinear ordinary differentials, which have been solved using the homotopy analysis technique. In this problem, the behavior of function profiles are graphically depicted and explained for a variety of key parameters. For a given set of parameters, tables representthe expected numerical values and behaviors of physical quantities. The nanofluid velocity decreases as the ferrohydrodynamic, local inertia, and porosity parameters increase and decrease when the bioconvection Rayleigh number increases. Many key parameters improved the thermal boundary layer and temperature. The concentration is low when the chemical reaction parameter and Schmidt number rises. Furthermore, as the bioconvection constant, Peclet and Lewis numbers rise, so does the density of motile microorganisms. Full article

In this study, we examined the biomagnetic flow and heat transfer of an incompressible electrically conductive fluid (blood) containing gold nanoparticles over a stretching sheet in the presence of a magnetic dipole. In this problem, both principles of magnetohydrodynamics (MHD) and ferrohydrodynamics (FHD) were adopted. Biot number and slip and suction parameters were taken into consideration. The nonlinear partial differential equations were transformed into ordinary differential equations by implementing similarity transformations. The numerical solution was attained by utilizing the bvp4c function technique in MATLAB R2018b software. The influence of pertinent parameters involved in this model, such as ferromagnetic parameter, magnetic field parameter, Grashof number, Eckert number, suction parameter, Biot number, slip parameter and Prandtl number, on the dimensionless velocity, temperature, skin friction and heat transfer rate were analyzed numerically and are represented graphically. Among the numerous results, it was observed that increment in ferromagnetic parameter and Prandtl number results in decrement of the velocity and temperature, respectively. For some values of the parameters, a comparison with the results of other documents in the literature is also made. Full article

The effect of non-Newtonian biomagnetic power-law fluid in a channel undergoing external localised magnetic fields is investigated. The governing equations are derived by considering both effects of Ferrohydrodynamics (FHD) and Magnetohydrodynamics (MHD). These governing equations are difficult to solve due to the inclusion of source term from magnetic equation and the nonlinearity of the power-law model. Numerical scheme of Constrained Interpolation Profile (CIP) is developed to solve the governing equations numerically. Extensive results carried out show that this method is efficient on studying the biomagnetic and non-Newtonian power-law flow. New results show that the inclusion of power-law model affects the vortex formation, skin friction and heat transfer parameter significantly. Regardless of the power-law index, the vortex formation length increases when Magnetic number increases. The effect of this vortex however decreases with the inclusion of power-law where in the shear thinning case, the arising vortex is more pronounced than in the shear thickening case. Furthermore, increasing of power-law index from shear thinning to shear thickening, decreases the wall shear stress and heat transfer parameters. However for high Magnetic number, the wall shear stress and heat transfer parameters increase especially near the location of the magnetic source. The results can be used as a guide on assessing the potential effects of radiofrequency fields (RF) from electromagnetic fields (EMF) exposure on blood vessel. Full article

Ferro liquids derive their magneto–viscous behavior from the suspended magnetic nanomaterial that enables tunable changes in temperature, as well as nano-structured fluid characteristics. A theoretical model that depicts the bioconvection flow of cross nanofluid with a magnetic dipole subjected to a cylindrical surface was developed and numerically solved. The model encountered nonlinear thermal radiation, activation energy, and second order slip. The flow equations were reduced and are presented in dimensionless forms, and they were solved numerically using the shooting technique, which is a built-in feature of MatLab. The model encountered symmetrical constraints for predicting velocity, temperature, concentration, and gyrotactic microorganism distribution and profiles. Moreover, the numerical values were computed for local Nusselt number, local Sherwood number, and motile density number against each physical parameter. Full article

This investigated the time-dependent, two-dimensional biomagnetic fluid (blood) flow (BFD) over a stretching sheet under the action of a strong magnetic field. Blood is considered a homogeneous and Newtonian fluid, which behaves as an electrically conducting magnetic fluid that also exhibits magnetization. Thus, a full BFD formulation was considered by combining both the principles of magnetization and the Lorentz force, which arise in magnetohydrodynamics and ferrohydrodynamics. The non-linear governing equations were transformed by using the usual non-dimensional variables. The resulting system of partial differential equations was discretized by applying a basic explicit finite differences scheme. Moreover, the stability and convergence analysis were performed to obtain restrictions that were especially for the magnetic parameters, which are of crucial importance for this problem. The acquired results are shown graphically and were examined for several values of the dimensionless parameters. The flow and temperature distributions were increased as the values of the magnetic parameters were increased. With the progression in time, the flow profile and temperature distribution were also increased. It is hoped that the results of this problem will be used for high targeting efficiency toward determining the maximum values of magnetic field for which accurate flow predictions could be made using a very simple numerical scheme. Full article