Micropolar Ferromagnetic Fluid Research Articles

Significance of solar radiation and magnetic dipole impact on micropolar ferromagnetic fluid flow via an extending surface using finite element approach

AbstractThe Galerkin finite element approach is utilized to examine the significance of magnetic dipole and solar radiation on the dynamic of micropolar ferromagnetic fluid due to extending stretch surface. The magnetic field and the significant power of magnetic dipole help to stabilize the magnetized nanoparticles inside the fluid. The solid nano‐sized particles are incorporated due to enhanced host fluid thermal conductivity, which plays a significant role in heat exchangers, modern nano‐technology, electronics chips, and materials sciences. In the present elaborated problem, with the aid of similarity transformation, the partial differential formulation is transformed into a set of dimensionless ordinary differential equations, and finds a numerical solution via finite element discretization. The detailed parametric study corresponding to various physical conditions is carried out to reveal that incremented ferromagnetic interaction variable recedes the flow speed, but it grows the thermal and microrotation distributions, and the decline in temperature is observed with the increment of ratio, viscous dissipation, and curie temperature parameters. The reliability of the Matlab code and validity of the solution has been tested with already available literature data and see a good comparison of current results.

Magnetic dipole and thermal radiation effects on hybrid base micropolar CNTs flow over a stretching sheet: Finite element method approach

The finite element method (FEM) is applied to study the impacts of prominent parameters on microrotation, velocity, and temperature to know the characteristics of the flow of incompressible water-ethylene glycol base fluids (60% water + 40% ethylene glycol) with single-wall and multiwall carbon nanotube nanoparticles micropolar ferromagnetic fluid due to porous stretching surface. A magnetic dipole of significant strength together the applied magnetic field contributes to better saturation of magnetic nanoparticles. Appropriate similarity transforms are applied to acquire the ordinary differential form of the governing non-linear partial differential equations and resulting equations are discretized in the prospectus of FEM. The detailed parametric study has been carried out, the results are presented in graphical and tabular form. The increment in the ferromagnetic interaction parameter slows down the fluid velocity but it upsurges the microrotation and thermal distribution. The multiwall carbon nanotube (MWCNT) in comparison to the single-wall carbon nanotube (SWCNT) has a greater impact on velocity and microrotation profiles also single-wall carbon nanotube (SWCNT) is compared to the multiwall carbon nanotube (MWCNT) has a greater impact on the temperature profile. The validation of the MATLAB code and the numerical scheme has been verified with an excellent comparison of present results with previous ones in the existing literature.

WITHDRAWN: Thermohaline convection in micropolar ferromagnetic fluid with Soret effect and sparsely distributed porous medium: A Brinkman model

Abstract This theoretical investigation on a horizontal micropolar ferromagnetic fluid layer with Soret effect is studied. The Brinkman porous medium is taken to analyze in the study. The geometry is considered for fluid layer whose portion of the bottom is isothermally heated from below and it is salted from above. The theory of linear stability is taken in to account to reduce the non-linear effects. The normal mode method is used to analyze the system and two free boundaries are considered. The exact solution is calculated to investigate the entire system. The thermal magnetic Rayleigh number NSC is examined analytically for sufficient large values of M 1 . An attempt is taken to analyze the porous effect on the convective system in various situations.

Penetrative Bénard-Marangoni Convection in a Micropolar Ferrofluid Layer via Internal Heating and Submitted to a Robin Thermal Boundary Conditions

Penetrative Benard-Maranagoni convection in micropolar ferromagnetic fluid layer in the presence of a uniform vertical magnetic field has been investigated via internal heating model. The lower boundary is considered to be rigid at constant temperature, while the upper boundary free open to the atmosphere is flat and subject to a convective surface boundary condition. The resulting eigenvalue problem is solved numerically by Galerkin method. The stability of the system is found to be dependent on the dimensionless internal heat source strength Ns, magnetic parameter M1, the non-linearity of magnetization parameter M3, coupling parameter N1, spin diffusion parameter N3 and micropolar heat conduction parameter N5. The results show that the onset of ferroconvection is delayed with an increase in N1 and N5 but hastens the onset of ferroconvection with an increase in M1, M3, N3 and Ns. The dimension of ferroconvection cells increases when there is an increase in M3, N1, N5 and Ns and decrease in M1 and N3.

Effect of Sparse Distribution Pores in Thermohaline Convection in a Micropolar Ferromagnetic Fluid

Thermoconvective instability in multi-component fluids has wide range of applications in heat and mass transfer. This paper deals with the theoretical investigation on a horizontal fluid layer of micropolar ferromagnetic fluid heated from below and salted from above saturating a porous medium subjected to a transverse uniform magnetic field using Brinkman model. The salt is a ferromagnetic salt which modifies the magnetic field established. The effect of salinity has been included in the magnetization and density of the ferromagnetic fluid. A theory of linear stability analysis and normal mode technique have been carried out to analyze the onset of convection for a fluid layer contained between two free boundaries for which exact solution is obtained and the stationary and oscillatory instabilities have been carried out for various physical quantities. The results are depicted graphically and the stabilizing and destabilizing behaviors are studied.

Modelling micropolar ferromagnetic fluid flow due to stretching of an elastic sheet

The flow of a micropolar ferromagnetic liquid due to stretching of an elastic sheet in the presence of a magnetic dipole is investigated. The focus of the study is on the magneto-thermo mechanical interaction and heat transfer at the stretching sheet. Two different boundary heating conditions, namely prescribed surface temperature (PST) and prescribed surface heat flux (PHF) are considered in the analysis. The momentum and thermal energy equations are formulated as an eight parameter problem that is solved numerically using the shooting method with Runge-Kutta-Fehlberg and Newton-Raphson schemes. Extensive computation of the velocity and temperature profiles are presented for a wide range of values of fluid and system parameters. The skin friction and heat transfer characteristics for the ferromagnetic fluid are investigated for different values of the governing parameters. It was found, among other interesting phenomenon, that the primary effect of the magneto-thermo mechanical interaction is to decelerate the fluid motion as compared to the pure hydrodynamic case.

Linear stability of triple-diffusive convection in micropolar ferromagnetic fluid saturating porous medium

The triple-diffusive convection in a micropolar ferromagnetic fluid layer heated and soluted from below is considered in the presence of a transverse uniform magnetic field. An exact solution is obtained for a flat fluid layer contained between two free boundaries. A linear stability analysis and a normal mode analysis method are carried out to study the onset convection. For stationary convection, various parameters such as the medium permeability, the solute gradients, the non-buoyancy magnetization, and the micropolar parameters (i.e., the coupling parameter, the spin diffusion parameter, and the micropolar heat conduction parameter) are analyzed. The critical magnetic thermal Rayleigh number for the onset of instability is determined numerically for a sufficiently large value of the buoyancy magnetization parameter M1. The principle of exchange of stabilities is found to be true for the micropolar fluid heated from below in the absence of the micropolar viscous effect, the microinertia, and the solute gradients. The micropolar viscous effect, the microinertia, and the solute gradient introduce oscillatory modes, which are non-existent in their absence. Sufficient conditions for the non-existence of overstability are also obtained.

Thermal convective instability in a micropolar ferromagnetic fluid saturated porous layer heated from below

Thermal convective instability in a micropolar ferromagnetic fluid saturated porous layer heated from below

Effect of Gravity Modulation on the Onset of Ferroconvection in a Densely Packed Porous Layer

The stability of a horizontal porous layer of a ferromagnetic fluid heated from below is studied when the fluid layer is subject to a time-periodic body force. Modified Darcy law is used to describe the fluid motion. The effect of gravity modulation is treated by a perturbation expansion in powers of the amplitude of modulation. The stability of the system, characterized by a correction Rayleigh number, is determined as a function of the frequency of modulation, magnetic parameters, and Vadasz number. It is found that subcritical instability is possible for low frequency g-jitter and that the magnetic and g-jitter mechanisms work against each other for small and moderate values of frequency of modulation. The effect of Vadasz number is shown to be reinforcing the influence of gravity modulation for small and moderate values of frequency. The magnetic, porous and modulation effects disappear altogether for sufficiently large values of the frequency of modulation. Keywords-Ferromagnetic fluid, Gravity modulation, Perturbation method, Porous layer, Stability. Gupta and Gupta (3) investigated thermal instability in a layer of ferromagnetic fluid subject to coriolis force and permeated by a vertical magnetic field. It is substantiated that overstability cannot occur if the Prandtl number is greater than unity. Gotoh and Yamada (4) investigated the linear convective instability of a ferromagnetic fluid layer heated from below and confined between two horizontal ferromagnetic boundaries. The Galerkin technique is used and the Legendre polynomials are taken as the trial functions. It is shown that the magnetization of the boundaries and the nonlinearity of fluid magnetization reduce the critical Rayleigh number and the effects of magnetization and buoyancy forces are shown to compensate each other. Blums (5) examined the possibility of having convection in ferromagnetic fluids as a result of magneto- diffusion of colloidal particles which give rise to non-uniform magnetization. Stiles and Kagan (6) examined the thermoconvective instability of a horizontal layer of ferrofluid in a strong vertical magnetic field. Their work also questioned the satisfactory agreement claimed to exist between the experiments and the theoretical model of Finlayson which has been generalized by them. Odenbach (7) investigated the convective flow generated by the interaction of a magnetic field gradient with a gradient in magnetization in a magnetic fluid. This gradient was caused by the diffusion of the magnetic particles in the field gradient. Aniss et al. (8) investigated the effect of a time-sinusoidal magnetic field on the onset of convection in a horizontal magnetic fluid layer heated from above. The Floquet theory is used to determine the convective threshold for free-free and rigid-rigid cases. The possibility to produce a competition between the harmonic and subharmonic modes at the onset of convection is discussed. Abraham (9) investigated the Rayleigh-Benard problem in a micropolar ferromagnetic fluid layer in the presence of a vertical uniform magnetic field analytically. It is shown that the micropolar ferromagnetic fluid layer heated from below is more stable as compared with the classical Newtonian ferromagnetic fluid. The effect of radiative heat transfer on ferroconvection has been studied by Maruthamanikandan (10) using the linear stability analysis. Consideration is given to two asymptotic cases, viz., transparent and opaque layers of fluid. The critical values marking the onset of convection are obtained using the Galerkin technique. Bajaj (11) considered thermosolutal convection in magnetic fluids in the presence of a vertical magnetic field and bifrequency vertical vibrations. The regions of parametric instability have been obtained using the Floquet theory. Ramanathan and Muchikel (12) investigated the effect of temperature-dependent viscosity on ferroconvective instability in a porous medium. It is found that the stationary mode of instability is

The Onset of Ferromagnetic Convection in a Micropolar Ferromagnetic Fluid Layer Heated from Below

The onset of ferromagnetic convection in a micropolar ferromagnetic fluid layer heated from below in the presence of a uniform applied vertical magnetic field has been investigated. The rigid-isothermal boundaries of the fluid layer are considered to be either paramagnetic or ferromagnetic and the eigenvalue problem is solved numerically using the Galerkin method. It is noted that the paramagnetic boundaries with large magnetic susceptibility χ delays the onset of ferromagnetic convection the most when compared to very low magnetic susceptibility as well as ferromagnetic boundaries. Increase in the value of magnetic parameter M1 and spin diffusion (couple stress) parameter N3 is to hasten, while increase in the value of coupling parameter N1 and micropolar heat conduction parameter N5 is to delay the onset of ferromagnetic convection. Further, increase in the value of M1, N1, N5 and χ as well as decrease in N3 is to diminish the size of convection cells.

Effect of dust particles on a layer of micropolar ferromagnetic fluid heated from below saturating a porous medium

The problem of the effect of dust particles on the thermal convection in micropolar ferromagnetic fluid saturating a porous medium subject to a transverse uniform magnetic field has been investigated theoretically. Linear stability analysis and normal mode analysis methods are used to find an exact solution for a flat micropolar ferromagnetic fluid layer contained between two free boundaries. In case of stationary convection, the effect of various parameters like medium permeability, dust particles, non-buoyancy magnetization, coupling parameter, spin-diffusion parameter and micropolar heat conduction parameter are analyzed. For sufficiently large values of magnetic parameter M 1 , the critical magnetic thermal Rayleigh number for the onset of instability is determined numerically and results are depicted graphically. It is also observed that the critical magnetic thermal Rayleigh number is reduced solely because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the micropolar ferromagnetic fluid saturating a porous medium heated from below in the absence of micropolar viscous effect, microinertia and dust particles.

Linear stability of double-diffusive convection in a micropolar ferromagnetic fluid saturating a porous medium

This paper deals with the theoretical investigation of the double-diffusive convection in a micropolar ferromagnetic fluid layer heated and soluted from below saturating a porous medium subjected to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained. A linear stability analysis theory and normal mode analysis method have been carried out to study the onset of convection. The influence of various parameters like medium permeability, solute gradient, non-buoyancy magnetization and micropolar parameters (i.e. coupling parameter, spin diffusion parameter and micropolar heat conduction parameter) has been analyzed on the onset of stationary convection. The critical magnetic thermal Rayleigh number for the onset of instability is also determined numerically for sufficiently large values of buoyancy magnetization parameter M 1 and results are depicted graphically. The principle of exchange of stabilities is found to hold true for the micropolar ferromagnetic fluid saturating a porous medium heated from below in the absence of micropolar viscous effect, microinertia and solute gradient. The oscillatory modes are introduced due to the presence of the micropolar viscous effect, microinertia and solute gradient, which were non-existent in their absence. In this paper, an attempt is also made to obtain the sufficient conditions for the non-existence of overstability.

Double-diffusive convection in a micropolar ferromagnetic fluid

This paper deals with the theoretical investigation of the double-diffusive convection in a micropolar ferromagnetic fluid layer heated and soluted from below subjected to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained. A linear stability analysis theory and normal mode analysis method have been carried out to study the onset of convection. The influence of various parameters like solute gradient, non-buoyancy magnetization and micropolar parameters (i.e. coupling parameter, spin diffusion parameter and micropolar heat conduction parameter) has been analyzed on the onset of stationary convection. The critical magnetic thermal Rayleigh number for the onset of instability is also determined numerically for sufficiently large values of buoyancy magnetization parameter M 1 and results are depicted graphically. The principle of exchange of stabilities is found to hold true for the micropolar ferromagnetic fluid heated from below in the absence of micropolar viscous effect, microinertia and solute gradient. The oscillatory modes are introduced due to the presence of the micropolar viscous effect, microinertia and solute gradient, which were non-existent in their absence. In this paper, an attempt is also made to obtain the sufficient conditions for the non-existence of overstability.

Marginal stability of micropolar ferromagnetic fluid saturating a porous medium

This paper deals with the theoretical investigation of the marginal stability of a micropolar ferromagnetic fluid layer heated from below saturating a porous medium subjected to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained using a linear stability analysis theory and normal mode analysis method. For the case of stationary convection, the effect of various parameters such as medium permeability, non-buoyancy magnetization, coupling parameter, spin diffusion parameter and micropolar heat conduction has been analysed. The critical magnetic thermal Rayleigh number for the onset of instability is also determined numerically for sufficiently large values of the magnetic parameter M1 and the results are depicted graphically. The principle of exchange of stabilities is found to hold true for the micropolar ferromagnetic fluid saturating a porous medium heated from below in the absence of the micropolar viscous effect and microinertia. The oscillatory modes are introduced due to the presence of the micropolar viscous effect and microinertia, which were non-existent in their absence. Sufficient conditions for the non-existence of overstability are also obtained.

Effect of rotation on a layer of micropolar ferromagnetic fluid heated from below saturating a porous medium

This paper deals with the theoretical investigation of the effect of rotation on a layer of micropolar ferromagnetic fluid heated from below saturating a porous medium subjected to a transverse uniform magnetic field. For a flat fluid layer contained between two free boundaries, an exact solution is obtained using a linear stability analysis theory and normal mode analysis method. For the case of stationary convection, the effect of various parameters like medium permeability, rotation, non-buoyancy magnetization, coupling parameter, spin diffusion parameter and micropolar heat conduction has been analyzed. The critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for sufficiently large values of magnetic parameter M 1 and results are depicted graphically. The principle of exchange of stabilities is found to hold true for the micropolar ferromagnetic fluid saturating a porous medium heated from below in the absence of micropolar viscous effect, microinertia and rotation. The oscillatory modes are introduced due to the presence of the micropolar viscous effect, microinertia and rotation, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained.

Rayleigh–Benard convection in a micropolar ferromagnetic fluid

The problem of Rayleigh–Benard convection in a micropolar ferromagnetic fluid layer permeated by a uniform, vertical magnetic field is investigated analytically with free–free, isothermal, spin-vanishing, magnetic boundaries. The influence of the various micropolar and magnetization parameters on the onset of stationary convection has been analysed. It is observed that the micropolar ferromagnetic fluid layer heated from below is more stable as compared with the classical Newtonian ferromagnetic fluid. The nature of influence of the magnetization parameters on convection in the micropolar ferromagnetic fluid is similar to that in the case of Newtonian ferromagnetic fluids. The influence of the micropolar parameters on convection in the ferromagnetic case is akin to its role in the non-magnetic fluid case. The critical wave number is found to be insensitive to the changes in the micropolar fluid parameters, but sensitive to the magnetization parameters.