Magnetic Force Number Research Articles

Anisotropic Darcy–Brinkman Magnetic Fluid Convection under the Influence of a Time-Dependent Sinusoidal Magnetic Field

The impact of the sinusoidal mode of a magnetic field involving time fluctuations on the threshold of the ferromagnetic smart liquid convection in a saturated permeable medium is investigated using the regular perturbation technique. The Darcy–Brinkman model with anisotropic permeability is used to describe the flow through porous media. The thermal anisotropy is implemented in the energy equation. The problem might be useful in thermal engineering applications such as dynamic loudspeakers and computer hard discs and in medical applications like the treatment of tumor cells and the cell separation, to name a few. The regular perturbation technique is based on the minimum amplitude of a magnetic field modulation, and the onset criterion is dealt with in terms of a correction in the critical Rayleigh number and wavenumber. The thermal Rayleigh number correction depends on the magnetic field modulation frequency, magnetic force, anisotropies, porosity, and Prandtl number. At moderate values of the magnetic field modulation frequency, the impact of various physical factors is perceived to be noteworthy. The influences of the magnetic mechanism, Prandtl number, porosity parameter, and Brinkman number are shown to augment the destabilizing effect of the magnetic field modulation for moderate values of the frequency of a modulation. However, the destabilizing effect of the magnetic field modulation is diminished due to an increase in the values of the mechanical anisotropy parameter and thermal anisotropy parameter. The study reveals that the effect of the magnetic field modulation could be exploited to control the convective instability in an anisotropic porous medium saturated by a ferromagnetic fluid.

Oscillatory Behavior of Heat Transfer and Magnetic Flux of Electrically Conductive Fluid Flow along Magnetized Cylinder with Variable Surface Temperature

The present study deals with electrically conductive fluid flow across a heated circular cylinder to examine the oscillatory magnetic flux and heat transfer in the presence of variable surface temperature. The proposed mathematical formulation is time-dependent, which is the source of the amplitude and fluctuation in this analysis. The designed fluctuating nonlinear computational model is associated with the differential equations under specific boundary conditions. The governing equations are converted into dimensionless form by using adequate dimensionless variables. To simplify the resolution of the set of governing equations, it is further reduced. The effects of surface temperature parameter β, magnetic force number ξ, buoyancy parameter λ, Prandtl number Pr, and magnetic Prandtl parameter γ are investigated. The main finding of the current study is related to the determination of the temperature distribution for each inclination angle. It is seen that a higher amplitude of the heat transfer rate occurs as the surface temperature increases. It is also noticed that the oscillatory magnetic flux becomes more important as the magnetic Prandtl number increases at each position. The present magneto-thermal analysis is significantly important in practical applications such as power plants, thermally insulated engines, and nuclear reactor cooling.

Amplitude and oscillating assessment of thermal and magnetic boundary layer flow across circular heated cylinder with heat source/sink

The effects of heat source/sink and magnetohydrodynamics on the oscillatory and periodic quantities of heat transfer and current density characteristics of viscous fluid along the magnetized and heated circular cylinder has been investigated. The governing mathematical model in terms of partial differential equations is converted into dimensionless form. The dimensionless model is again converted into steady, real and imaginary part for oscillating results. The steady, real and imaginary part is transformed into primitive form for smooth algorithm with the help of Primitive Variable Formulation (PVF). The primitive equations are reduced into system of algebraic equations by using Finite Difference Method (FDM). The heat source/sink parameter δ, the magnetic force number ξ, the buoyancy parameter λ, magneto-Prandtl factor γ, and remaining secured factors are utilized to determine computational findings of unknown quantities. Graphs are displayed for velocity, temperature distribution and magnetic profile for all pertinent parameters by FORTRAN and Teplot 360 software. The main novelty of current work is to evaluate oscillatory and periodic quantities of heat transfer and current density by using the steady solutions. It was found that prominent results in temperature distribution are deduced at each angle with the heat source effects. It was expected physically because the heat source is used as a sporting agent to compute heat transfer performance in electrically conducting fluid. The significant amplitude of oscillation in heat transfer and current density is evaluated around every position of circular cylinder. The numerical results of skin friction are compared with existing literature with excellent agreement.

Effect of magnetic force and moderate Reynolds number on MHD Jeffrey hybrid nanofluid through peristaltic channel: application of cancer treatment

Effect of magnetic force and moderate Reynolds number on MHD Jeffrey hybrid nanofluid through peristaltic channel: application of cancer treatment

Influence of magnetic dipole on ferrohydrodynamic thin film flow over an inclined spinning surface

This study investigates the three-dimensional problem of steady ferrofluid deposition on an inclined rotating surface in the presence of a magnetic dipole. A finite element procedure is used to solve normalized ordinary differential equations derived from momentum and energy equations. The current numerical model and its solution is compared and validated against previous numerical results. The velocity and temperature field variations are a representation of the effects of magnetic field-based viscosity, magnetic polarization force, Curie temperature, and Prandtl number. In addition, some common errors in the similarity transformation for inclined rotating disk flows are addressed in the present study. The results show that the magnetic field-dependent viscosity generated by the magnetic torque in the current flow reduces the velocity of the thin film liquid in all directions, including rotational flow (radial, tangential, and axial) and inclined flow (drainage and induced). Moreover, the local heat transfer between the fluid and the surface of the rotating disk increases with a rise in the ferromagnetic interaction number and Prandtl number. These findings imply that ferrofluids could be effective for cooling electronic devices in the presence of a magnetic dipole.

Effects of Dufour and thermal diffusion on unsteady MHD free convection and mass transfer flow through an infinite vertical permeable sheet

In this paper, the effects of Dufour and thermal diffusion and on unsteady MHD (magnetohydrodynamic) free convection and mass transfer flow through an infinite vertical permeable sheet have been investigated numerically. The non-dimensional governing equations are solved numerically by using the superposition method with the help of “Tec plot” software. The numerical solution regarding the non-dimensional velocity, temperature, and concentration variables against the non-dimensional coordinate variable has been carried out for various values of pertinent numbers and parameters like the suction parameter left( {v_{0} } right), Prandtl number left( {P_{r} } right), magnetic parameter left( M right), Dufour number left( {D_{f} } right), Soret number left( {S_{0} } right), Schmidt number left( {S_{c} } right), and for constant values of modified local Grashof number left( {G_{{text{m}}} } right) and local Grashof number left( {G_{r} } right).The velocity field decreases for increasing the suction parameter which is focusing on the common fact that the usual suction parameter stabilizing the effect on the boundary layer growth. The thermal boundary layer thickness becomes thinner for rising values of the Dufour and Soret numbers. The skin friction enhances for uplifting values of Soret number and Dufour number but reduces for moving suction parameter, Magnetic force number, Prandtl number, and Schmidt number. The heat transfer rate increases for increasing the suction parameter, Dufour number, Prandtl number, and Soret number. The mass transfer rate increases for enhancing the values of suction parameter, Magnetic force number, Soret number, and Prandtl number but decreases for Dufour number and Schmidt number.

Spectral computation of reactive bi-directional hydromagnetic non-Newtonian convection flow from a stretching upper parabolic surface in non-Darcyporous medium

This paper presents a mathematical model for bi-directional convection magnetohydrodynamic (MHD) tangent hyperbolic nanofluid flow from the upper horizontal subsurface of a stretching parabolic surface to a non-Darcian porous medium, as a simulation of nanocoating. Chemical reaction, activation energy and thermo solutal buoyancy effects are included. The Darcy–Brinkman–Forchheimer model is deployed which permits the analysis of inertial (second order) porous drag effects. The Buongiorno nanoscale model is deployed which includes Brownian motion and thermophoresis effects. The dimensionless, transformed, nonlinear, coupled ordinary differential equations are solved by implementing the spectral relaxation method (SRM). Validation with previous studies is included. The numerical influence of key parameters on transport characteristics is evaluated and visualized graphically. Velocity is elevated (and momentum boundary layer thickness is reduced) with increasing wall thickness parameter, permeability parameter, Forchheimer parameter, Weissenberg (rheological) parameter and modified Hartmann (magnetic body force) number. Velocity enhancement is also computed with increment in stretching rate parameter, rheological power-law index, thermal Grashof number, and species (solutal) Grashof number, and momentum boundary layer thickness diminishes. Temperature is suppressed with increasing stretching rate index and Prandtl number whereas it is substantially elevated with increasing Brownian motion and thermophoresis parameters. Velocity and temperature profiles are reduced adjacent to the parabolic surface with larger wall thickness parameter for stretching rate index [Formula: see text]1, whereas the reverse behavior is observed for stretching rate index [Formula: see text]1. Nanoparticle concentration magnitude is depleted with larger numeric of Lewis number and the Brownian motion parameter, whereas it is enhanced with greater values of the stretching index and thermophoresis parameter. The nanoparticle concentration magnitude is reduced with an increase in chemical reaction rate parameter whereas it is boosted with activation energy parameter. Skin friction, Nusselt number and Sherwood number are also computed. The study is relevant to electromagnetic nanomaterials coating processes with complex chemical reactions.

Magnetic force effects on peristaltic transport of hybrid bio-nanofluid (Au[sbnd]Cu nanoparticles) with moderate Reynolds number: An expanding horizon

This work investigates the magnetic force and nonlinear thermal radiation on hybrid bio-nanofluid flow in a peristaltic channel under the influence of an applied magnetic field with high and low Reynolds number. Gold and copper nanoparticles are taken into account. Momentum, Maxwell, and heat with nonlinear thermal radiation and heat source think equations are considered in the dimensionless form without any approximation as a system of nonlinear partial differential equations. The expressions of velocity, induced magnetic field components, magnetic pressure, stream function, magnetic force, joule heating, shear stress, and Nusselt number have been obtained using the Adomian decomposition method. Influences of miscellaneous physical and biomedical parameters including moderate Reynolds, magnetic Reynolds, hybrid nanofluid volume fraction, Hartmann, dimensionless wavenumber, electric field stress, nonlinear thermal radiation, and internal heat generation absorption parameters on velocity, induced magnetic field components, magnetic pressure, normal component of the pressure gradient, heat distribution shear stress on the walls and Nusselt number are plotted and examined. During the investigation, it is found that the gold nanofluid has the highest velocity compared with hybrid, copper, and base fluid, while the hybrid nanofluid has a high magnetic force. The nonlinear thermal radiation is rising the heat distribution for hybrid nanofluid

Effects of nonlinear thermal radiation over magnetized stagnation point flow of Williamson fluid in porous media driven by stretching sheet

AbstractIn this study, the stagnation point flow of a magnetized Williamson fluid past a stretching sheet in the presence of nonlinear thermal radiation and buoyancy effect is studied. The present situation is remodeled using similarity transformation that transforms the flow model of partial differential equations into the set of nonlinear ordinary differential equations. The fourth‐order Runge‐Kutta scheme and shooting method are employed to solve these reduced equations. The effects of various associated parameters over the velocity and temperature profiles are plotted and the outcome of each associated parameter is discussed through graphs. The key findings are noted as follows: the velocity profile declines with an increase in the magnetic force number, and an increment in buoyancy parameter leads to the increase in the boundary layer thickness and decrease in the thickness of the thermal boundary layer.

Effect of induced magnetic field and linear / non-linear vertical stretching sheet on mixed convection Jeffrey fluid near a stagnation-point flow through a porous medium with suction or injection

The present study deals with the effect of induced magnetic field on mixed convective near a stagnation point flow with linear / non-linear vertical stretching sheet of Jeffrey fluid flow through porous medium in the presence of slip flow regime. The set of governing non-linear coupled partial differential equations are transformed into a set of non-linear coupled ordinary differential equations using suitable similarity transformations, which are then solved numerically using Runge-Kutta fourth order in association with shooting technique in MATLAB. The effects of non-dimensional parameters such as Jeffrey parameter, magnetic force number, magnetic Prandtl number, magnetic parameter, suction/injection parameter, slip velocity parameter, linear or non-linearity parameter, permeability parameter, velocity ratio parameter, Prandtl number, thermal radiation parameter and Eckert number on velocity, induced magnetic field and temperature are presented graphically while the skin friction and local Nusselt number are represented numerically.

Modeling of hybrid nanofluid behavior within a permeable media involving buoyancy effect

In current report, hybrid nanofluid free convection within a permeable media has been modeled via CVFEM including magnetic effect. To obtain the momentum equations, permeability​ was involved via Non-Darcy model. Hybrid nanoparticle (Fe3O4+MWCNT) with base fluid of water has been considered. Source term of radiation impact was incorporated. To obtain various outcomes, influences of Darcy number, magnetic force, radiation parameter and Rayleigh number on nanomaterial behavior have been implemented. Outcomes illustrated that average Nusselt number enhance significantly with both Rayleigh and Darcy number as well as thermal radiation, however it decrease with Hartmann number and Darcy number affect significantly the velocity profile for the Hybrid nanofluid.

Gaseous slip flow affected by inclined low magnetic field using second‐order boundary conditions

AbstractIn this study, asymptotic solutions of a near continuum gaseous slip flow in two‐dimensional rectangular microchannels under the effect of electromagnetic force are presented. An inclined magnetic field was assumed in this study. Nondimensional equations were obtained that relate the pressure ratio, Mach number, magnetic Reynolds number, magnetic force number, and Reynolds number. The asymptotic solutions for the compressible, laminar, and steady flow were obtained by applying second‐order slip velocity and temperature jump wall boundary conditions. It was found that the electric and magnetic field with inclined angle had significant effects on the flow properties. The solutions obtained here using the second‐order boundary conditions result in tangible improvement over those obtained using first‐order boundary conditions. We compared our solutions against the numerical solutions that were provided in the literature and showed that our solutions were in good agreement with the numerical solution.

Study of non-isothermal incompressible flow and heat flux of nano-ferrofluid with induced magnetic induction

Presently we have studied the nonlinear magnetohydrodynamic convective boundary-layer flow of water- based nano-ferrofluid adjacent to a non-isothermal stretching sheet. Three different ferrofluid suspensions are considered, namely water containing magnetite (Fe3O4), (Mn − Zn)and cobalt ferrite (CoFe2O4) ferriteferro-particles. Magnetic field is sufficiently strong to induce induction effects. Applying similarity transformations, the boundary region equations for mass, momentum, magnetic induction and energy are reduced to coupled, multi-degree, nonlinear differential equations. The non-dimensional boundary value problem is then solved computationally under specified wall and free stream conditions, with Maple quadrature and shooting techniques. Non-isothermal as well as constant heat flux cases are examined. The key parameters emerging in the model are the reciprocal of magnetic Prandtl number, Prandtl number, the reciprocal of magnetic body force parameter, heat source/sink parameter, nano-particle volume fraction and power-law index. The influence of these parameters on flow fields like velocity, temperature, and gradient of magnetic stream function for different ferro-particle cases, is presented graphically. Detailed elucidation of the results is also included. Validation is conducted with a finite element method (FEM). Significantly greater temperatures are observed for magnetite ferro-particles as compared with cobalt or Manganese-Zinc ferroparticles. Stream function (Magnetic) is found to be suppressed with increasing power-law index. With increasing magnetic force number there is a substantial elevation in induced magnetic field. Increasing reciprocal of magnetic Prandtl number i.e. decreasing magnetic Prandtl number leads to a depression in velocity i.e. flow deceleration, for the Fe3O4 − H2O magnetite ferrofluid. The study proposed here is of concern to the processing of nano-ferro-materials.

Entropy generation analysis for thermomagnetic convection of paramagnetic fluid inside a porous enclosure in the presence of magnetic quadrupole field

The entropy generation characteristics for thermomagnetic convection in a porous cavity filled with paramagnetic air in the presence of a magnetic quadrupole field are investigated numerically using a finite volume method. The vertical walls of the porous cavity are maintained at different temperatures, whereas the horizontal walls are insulated. The Darcy–Brinkman–Forchheimer model is used for mathematical formulation of the fluid flow in porous media. Thermal, frictional and total entropy generation and Bejan number for a selected range of magnetic force number (γ = 1–100), Darcy number (Da = 5 × 10−4–5 × 10−2) and Rayleigh number (Ra = 104–106) are examined for both cases: (1) with gravity and (2) without gravity. The results indicate that the magnetic field had little or no effect on the total entropy generation for the lower values of Darcy number and the process is dominated by the heat transfer irreversibility. In contrast, the magnetic force provokes various irreversibilities to rise as a result of improved convection at higher Darcy numbers, and the irreversibility is dominated by the viscous effects. This work may give an insight into the design-related concept of entropy generation for various thermal systems and clarifying energy loss.

Modeling magnetic nanopolymer flow with induction and nanoparticle solid volume fraction effects: Solar magnetic nanopolymer fabrication simulation

A mathematical model is presented for the nonlinear steady, forced convection, hydromagnetic flow of electro-conductive magnetic nanopolymer with magnetic induction effects included. The transformed two-parameter, non-dimensional governing partial differential equations for mass, momentum, magnetic induction and heat conservation are solved with the local non-similarity method subject to appropriate boundary conditions. Keller’s implicit finite difference “box” method is used to validate solutions. Computations for four different nanoparticles and three different base fluids are included. Silver nanoparticles in combination with various base fluids enhance temperatures and induced magnetic field and accelerate the flow. An elevation in magnetic body force number decelerates the flow, whereas an increase in magnetic Prandtl number elevates the magnetic induction. Furthermore, increasing nanoparticle solid volume fraction is found to substantially boost temperatures. Applications of the study arise in advanced magnetic solar nanomaterials (fluids) processing technologies.

Lattice Boltzmann method for thermomagnetic convection and entropy generation of paramagnetic fluid in porous enclosure under magnetic quadrupole field

In this study, thermomagnetic convection in a porous cavity filled with paramagnetic fluid under a magnetic quadrupole field is studied using lattice Boltzmann method (LBM), and the corresponding entropy generation is analyzed. The horizontal walls of the porous enclosure are adiabatic, and the temperatures of the vertical walls are different. The effects of Darcy number (Da), porosity (ε), and magnetic force number (γ) on the heat transfer, fluid flow, and entropy generation characteristics are investigated. The results show that, as the magnetic force number increases, the flow is strengthened. The local Nusselt numbers (Nuloc) increase and the average Bejan number (Beave) decreases under the non-gravitational condition. Nuloc change a little along the hot wall due to the lower value of Darcy number and higher values of Darcy number lead to higher buoyancy forces, Nuloc change significantly under the gravitational or non-gravitational condition. Moreover, the average Nusselt number (Nuave) and total entropy generation (Stotal) slightly decrease at first and thereafter increase when the magnetic force dominates the entire domain under the gravitational condition. It is also observed that, when ε0 = ε1 = 0.5, γ > 10, the average Nusselt number (Nuave) is significantly higher than in the other cases. Furthermore, the average Nusselt number (Nuave) reaches its minimum value when ε0 = ε1 = 0.5, γ = 4.

B-SPLINE COLLOCATION SIMULATION OF NON-LINEAR TRANSIENT MAGNETIC NANOBIO-TRIBOLOGICAL SQUEEZE-FILM FLOW

A mathematical model is presented for magnetized nanofluid bio-tribological squeeze-film flow between two approaching disks. The nanofluid comprises a suspension of metal oxide nanoparticles with an electrically-conducting base fluid, making the nanosuspension responsive to applied magnetic field. The governing viscous momentum, heat and species (nanoparticle) conservation equations are normalized with appropriate transformations which renders the original coupled, non-linear partial differential equation system into a more amenable ordinary differential boundary value problem. The emerging model is shown to be controlled by a number of parameters, viz nanoparticle volume fraction, squeeze number, Hartmann magnetic body force number, disk surface transpiration parameter, Brownian motion parameter, thermophoretic parameter, Prandtl number and Lewis number. Computations are conducted with a B-spline collocation numerical method. Validation with previous homotopy solutions is included. The numerical spline algorithm is shown to achieve excellent convergence and stability in non-linear bio-tribological boundary value problems. The interaction of heat and mass transfer with nanofluid velocity characteristics is explored. In particular, smaller nanoparticle (high Brownian motion parameter) suspensions are studied. The study is relevant to enhanced lubrication performance in novel bio-sensors and intelligent knee joint (orthopaedic) systems.

Lattice Boltzmann method for thermomagnetic convection of paramagnetic fluid in square cavity under a magnetic quadrupole field

Numerical study was performed for a better understanding on thermomagnetic convection under magnetic quadrupole field utilizing the lattice Boltzmann method. Present problem was examined under non-gravitational and gravitational conditions for a wide range of magnetic force number from 0 to 1000. Vertical walls of the square cavity were heated differentially while the horizontal walls were assumed to be adiabatic. Distributions of the flow and temperature field were clearly illustrated. Under non-gravitational condition, the flow presents a two-cellular structure with horizontal symmetry, and the average Nusselt number increases with the augment of magnetic force number. Under gravitational condition, two-cellular structure only occurs when the magnetic field is relatively strong, and the average Nusselt number decreases at first and then rises with the enhancing magnetic field. Results show that the magnetic field intensity and the Rayleigh number both have significant influence on convective heat transfer, and the gravity plays a positive role in heat transfer under weak magnetic field while a negative one for magnetic force numbers larger than 1×105.

Entropy Generation and Natural Convection of Air under a Magnetic Quadrupole Field in a Square Enclosure

The natural convection and entropy generation of air are numerically investigated in a two-dimensional square enclosure under a magnetic quadrupole field. In this study. The finite-volume method is applied to solve the coupled equation for flow, energy and entropy generation. Simulations are conducted to obtain solutions in terms of streamlines, isotherms, local entropy generation contours, total entropy generation, Bejan number for various ranges of the magnetic force parameter and Rayleigh number in a nongravitational field. Two symmetric cells with the same strength but opposite rotation directions are observed with the flow filed. Total entropy generation increases with increasing the magnetic force number. However, the average Bejan number holds the reverse trend. The magnetic field has a broad spectrum of applications in engineering areas to control natural convection. The local and total entropy generation presented in this study can be useful addition where one wants to minimize the irreversibility of the system.

Numerical simulation of thermomagnetic convection of cold water near its density maximum in a square enclosure under a magnetic quadrupole field

Natural convection of cold water near its density maximum in a square enclosure is studied numerically under the influence of a magnetic quadrupole field without gravity. A generalized model which includes a non-Boussinesq parabolic density–temperature relationship is established. The governing equations in primitive variables are discretized using the finite-volume method and solved using the SIMPLE algorithm. The effects of magnetic force number, Rayleigh number and density inversion parameter on flow and heat transfer characteristics are analyzed. The results show that the primary flow pattern depends mainly on the density inversion parameter. Multi-cellular flow structures are observed for certain ranges of density inversion parameter independent of the value of Rayleigh number and magnetic force number. The heat transfer changes non-monotonically under combined actions of the quadrupole magnetic field and density inversion.