Ferromagnetic Convection Research Articles

Linear Study of Ferromagnetic Convection in Nanofluids Under the Effect of Variable Viscosity

Linear Study of Ferromagnetic Convection in Nanofluids Under the Effect of Variable Viscosity

Oscillatory convection in viscoelastic ferrofluid layer: Linear and non-linear stability analyses

The problem of ferroconvection in a viscoelastic fluid layer is studied with the aim to investigate oscillatory motions. In this article, a stability analysis for both linear and nonlinear systems is carried out. In the linear stability analysis, the expressions for steady and oscillatory Rayleigh numbers are obtained and the effects of magnetic as well as viscoelastic parameters on the onset of viscoelastic ferromagnetic convection are investigated numerically. From the analysis, we found that the magnetic number (M_1), the stress relaxation time (lambda_1) and the nonlinearity of magnetization (M_3) have destabilizing influences on the onset of ferroconvection, whereas the strain retardation time (lambda_2) has stabilizing influence. In the weakly nonlinear stability analysis, the formula for heat transfer rate in terms of the Nusselt number is derived for oscillatory convection. From the analyses, we found that for increasing values of the magnetic number, stress relaxation time and nonlinearity of magnetization, the heat transfer rate rises, whereas it decreases for larger values of the strain retardation time. Moreover, the pitchfork bifurcation analysis yields that in order to reach the stable positions, the value of amplitude increases as the stress relaxation time increases, whereas a reverse trend is observed for the strain retardation time.

Effect of Gravitation Modulation on Viscoelastic Nonlinear Ferro-Convection

Abstract This paper examines a nonlinear investigation of viscoelastic ferromagnetic convection under gravity modulation. A weakly nonlinear instability has been investigated using the perturbation method. Based on the Oldroyd model for ferrofluids, the constitutive equations of the flow model were developed. The coupled system of the Khayat-Lorenz model developed and was numerically solved in the presence of gravity modulation. Heat transfer results are examined for nonlinear theory and neutral stability curves for linear theory. The nonlinear PDE system is transformed into a nonlinear ODE system with similarity transformations up to the second term. The dual effect of the gravity modulation includes stabilizing and destabilizing.

Linear and weakly non-linear stability analysis of oscillatory convection in rotating ferrofluid layer

In the present paper, the problem of ferroconvection in the presence of uniform vertical rotation is considered to investigate the linear and weakly non-linear oscillatory stability. Two-dimensional convective roll instability is discussed with finite-amplitude disturbances. For linear stability, as a first-order problem, the expressions for Rayleigh numbers for stationary and oscillatory convection are derived and the effects of Coriolis force and magnetic parameters on the onset of ferromagnetic convection are studied, numerically. In weakly nonlinear oscillatory analysis, the second-order and third-order stability problems are discussed and the complex Ginzburg-Landau equation describing the amplitude of convection cell in rotating ferrofluid is derived and consequently, the expression for Nusselt number representing the heat transfer rate is obtained. From the present analysis, we observed that the rotation has the usual stabilizing effect on the linear stability in ferroconvection, however, the magnetic number (M1) and the measure of nonlinearity of magnetization (M3) both have a destabilizing effect on the onset of linear instability. Also, we found that for non-linear convection, the heat transfer rate (the Nusselt number) increases with increasing values of Taylor number, magnetic number, and the measure of nonlinearity of magnetization.

The Effect of Magnetic Field Dependent Viscosity on Ferromagnetic Convection in a Rotating Sparsely Distributed Porous Medium - Revisited

The effect of magnetic field dependent (MFD) viscosity on the thermal convection in a ferrofluid layer saturating a sparsely distributed porous medium has been investigated by using the Darcy-Brinkman model in the simultaneous presence of a uniform vertical magnetic field and a uniform vertical rotation. A correction is applied to the study of Vaidyanathan <i>et al</i>. [11] which is very important in order to predict the correct behavior of MFD viscosity. A linear stability analysis has been carried out for stationary modes and oscillatory modes separately. The critical wave number and critical Rayleigh number for the onset of instability, for the case of free boundaries, are determined numerically for sufficiently large values of the magnetic parameter <i>M</i><i>1</i>. Numerical results are obtained and are illustrated graphically. It is shown that magnetic field dependent viscosity has a destabilizing effect on the system for the case of stationary mode and a stabilizing effect for the case of oscillatory mode, whereas magnetization has a destabilizing effect.

Practical Insight of Ferroconvection in Heterogeneous Brinkman Porous Medium

Ferromagnetic fluids are made up of magnetic particles, which are suspended in a carrier liquid such as water, hydrocarbon (mineral oil or kerosene) or fluorocarbon with a surfactant to avoid clumping. Worldwide many literature revealed that, the ferromagnetic fluids application has been diversified in nature and widely used in engineering, technology, agricultural, animal and biomedical sciences etc. (evidence based medicine for cancer patients, fertigation in agriculture). Now a days, the driven applications are using in developing countries. The ferromagnetic fluids analytical applications are very limited scope in Indian scenario due to paucity of literature and technological gap. In the essence of this research gap the present study undertaking to demonstrate the various applications of ferroconvection in a heterogeneous Brinkman porous medium on theoretical basis. The resulting eigenvalue problem is solved numerically using the Galerkin method. The effects of vertical heterogeneity of permeability, Darcy parameter, Magnetic Rayleigh number, nonlinearity of magnetization, and internal heat source on the onset of ferromagnetic convection is investigated.

Ferromagnetic Convection in a Densely Packed Porous Medium with Magnetic-Field-Dependent Viscosity – Revisited

Abstract The effect of magnetic-field-dependent (MFD) viscosity on the thermal convection in a ferromagnetic fluid in the presence of a uniform vertical magnetic field is investigated for a fluid layer saturating a densely packed porous medium using the Darcy model. A correction is applied to the model by Sunil et al. [Z. Naturforsch. 59, 397 (2004)], which is very important to predict the correct behaviour of MFD viscosity. A linear stability analysis is carried out for stationary modes. The critical wave number and critical Rayleigh number for the onset of instability, for the case of free boundaries, are determined numerically for sufficiently large values of the magnetic parameter M 1. Numerical results are obtained and illustrated graphically. It is shown that MFD viscosity has stabilizing effect on the system, whereas medium permeability has a destabilizing effect.

Brinkman ferroconvection

PurposeThe simultaneous effects of local thermal non-equilibrium (LTNE) and vertical heterogeneity in permeability on the onset of ferromagnetic convection in a Brinkman porous medium are analyzed in the presence of a uniform vertical magnetic field. The eigenvalue problem is solved numerically using shooting method for isothermal rigid-ferromagnetic boundaries for various forms of vertically stratified permeability function Γ(z). The effect of vertically stratified permeability is found to either hasten or delay the onset of ferromagnetic convection. The deviation in the critical Rayleigh number between different forms of Γ(z) is found to be not so significant with an increase in the Darcy number. It is observed that the general quadratic variation of Γ(z) has more destabilizing effect on the system when compared to the constant permeability porous medium case. Besides, the influence of LTNE and magnetic parameters on the criterion for the onset of ferromagnetic convection has been assessed in detail. The paper aims to discuss these issues.Design/methodology/approachFerroconvection in a porous medium has been analyzed considering heterogeneity in the permeability of the porous medium. The resulting eigenvalue problem has been solved numerically using shooting method as well as Galerkin method for realistic boundary conditions.FindingsThe novelty of the present study lies in understanding the effect of heterogeneity in the permeability of the porous medium on control of ferroconvection in a porous medium. In analyzing the problem, realistic boundary conditions are considered and the resulting eigenvalue problem is solved numerically using shooting method as well as Galerkin method.Originality/valueControl of ferroconvection in a porous medium is an important feature in heat transfer-related problems and many mechanisms are being used to understand this aspect in the literature. The novelty of the present study lies in recognizing the effect of heterogeneity in the permeability of the porous medium on control of ferroconvection. This fact has been analyzed in detail for various forms of heterogeneity functions using numerical techniques by considering realistic boundary conditions.

On estimating the complex growth rates in ferromagnetic convection with magnetic-field-dependent viscosity in a rotating sparsely distributed porous medium

It is proved analytically that the complex growth rate of an arbitrary oscillatory motion of growing amplitude in ferromagnetic convection with magnetic-field-dependent viscosity in a rotating sparsely distributed porous medium for the case of free boundaries is located inside a semicircle in the right half of the plane whose centre is at the origin of the coordinate system and whose radius depends on the Rayleigh number, Prandtl number, Taylor number, and magnetic number. Bounds for the case of rigid boundaries are also derived.

On Estimating the Complex Growth Rates in Ferromagnetic Convection with Magnetic-Field-Dependent Viscosity in a Rotating Sparsely Distributed Porous Medium

On Estimating the Complex Growth Rates in Ferromagnetic Convection with Magnetic-Field-Dependent Viscosity in a Rotating Sparsely Distributed Porous Medium

Effect of vertical heterogeneity on the onset of ferroconvection in a Brinkman porous medium

The onset of ferroconvection in a Brinkman porous medium is studied for different forms of vertical heterogeneity permeability function Γ(z). The eigenvalue problem is solved numerically using the Galerkin method for isothermal/insulated rigid-ferromagnetic boundary conditions. It is observed that the onset of ferromagnetic convection can be either hastened or delayed depending on the type of heterogeneity of the porous medium as well as thermal boundary conditions. The effect of increasing magnetic number is to hasten the onset of ferroconvection for all choices of Γ(z). Although the measure of nonlinearity of magnetization is to hasten the onset of ferroconvection in the case of isothermal boundaries, it shows no influence on the onset criterion when the boundaries are insulated. Further, the deviation in critical Darcy–Rayleigh number between different forms of Γ(z) is found to be not so significant with an increase in the Darcy number.

Ferromagnetic Convection in a Heterogeneous Porous Medium

The effect of vertical heterogeneity of permeability on the onset convection in a horizontal layer of magnetized ferrofluid-saturated Darcy porous medium is investigated. Four different forms of vertical heterogeneity permeability function \({\Gamma (z)}\) are considered for discussion. The eigenvalue problem is solved numerically using the Galerkin method for three types of temperature boundary conditions namely, (i) isothermal, (ii) insulated to temperature perturbations, and (iii) lower insulated to temperature perturbations and upper isothermal. The general quadratic variation in the vertical heterogeneity of permeability is to hasten the onset of ferromagnetic convection compared with other forms of \({\Gamma(z)}\). The measure of nonlinearity of magnetization and the magnetic susceptibility is found to influence the onset if the boundaries are either isothermal or lower insulated and upper isothermal. Increasing the magnetic number is to augment the onset of ferromagnetic convection. The system is more stabilizing when the boundaries are isothermal and least stable for insulated ones. Compared to the homogeneous porous medium case, the critical wave number is higher if the permeability of the porous medium is heterogeneous and the boundaries are isothermal.

On Exchange of Stabilities in Ferromagnetic Convection in a Rotating Ferrofluid Saturated Porous Layer

In the present paper, first of all, it is proved that the ‘principle of the exchange of stabilities’ is not, in general valid, for the case of free boundaries and then a sufficient condition is derived for the validity of this principle in ferromagnetic convection, for the case of free boundaries, in a horizontal ferrofluid saturated porous layer in the presence of a uniform vertical magnetic field and uniform rotation about the vertical axis.

Brinkman ferromagnetic convection in a porous layer: Effect of MFD viscosity and magnetic boundaries

In the present study, the effect of magnetic field dependent (MFD) viscosity and different types of magnetic boundaries on the onset of ferromagnetic convection in a horizontal layer of Brinkman porous medium is investigated numerically using the Galerkin method. The simultaneous and isolation presence of buoyancy and magnetic forces on the stability characteristics of the system are emphasized. The study reveals that the linear stability of the system depends significantly on the types of magnetic boundaries. The rigid-paramagnetic boundaries are found to be preferred to the ferromagnetic ones in suppressing ferromagnetic convection. Besides, the system is more stable when the magnetic forces alone are present. In addition, increasing MFD viscosity parameter λ and decreasing magnetic number M1 and nonlinearity of fluid magnetization parameter M3 is to inhibit the onset of ferromagnetic convection in a porous medium. The critical wave number is found to be independent of λ, but increasing M1 and χ as well as decreasing M3 is to reduce the size of convection cells. At higher values of M3, the critical Rayleigh number and the corresponding wave number coincide for different magnetic boundaries.

On the characterization of non-oscillatory motions in ferromagnetic convection with magnetic field dependent viscosity in a rotating porous medium

Abstract In the present paper, a sufficient condition is derived for the validity of the “principle of the exchange of stabilities” in ferromagnetic convection with magnetic field dependent viscosity, for the case of free boundaries, in porous medium in the presence of a uniform vertical magnetic field and uniform rotation about the vertical axis.

On arresting the complex growth rates in ferromagnetic convection with magnetic field dependent viscosity in a rotating ferrofluid layer

It is proved analytically that the complex growth rate ω=ωr+iωi (ωrandωi are respectively the real and imaginary parts of ω) of an arbitrary oscillatory motion of growing amplitude in ferromagnetic convection, with magnetic field dependent viscosity, in a rotating ferrofluid layer for the case of free boundaries, must lie inside a semicircle in the right half of the ωrωi- plane whose center is at the origin and (radius)2=max{(RM1/Pr),Ta}, where R is the Rayleigh number, M1 is the magnetic number, Pr is the Prandtl number and Ta is the Taylor number. Further, bounds for the case of rigid boundaries are also derived separately.

On Exchange of Stabilities in Ferromagnetic Convection in a Rotating Porous Medium

On Exchange of Stabilities in Ferromagnetic Convection in a Rotating Porous Medium

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.

On stationary convection and oscillatory motions in ferromagnetic convection in a ferrofluid layer

It is shown analytically that the ‘principle of the exchange of stabilities’ (PES), in general, is not valid in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries and hence a sufficient condition is derived for the validity of the PES. Upper bounds for the complex growth rate are then obtained. It is proved that the complex growth rate σ=σr+iσi (where σr and σi are, respectively, the real and imaginary parts of σ) of an arbitrary oscillatory motion of growing amplitude, in ferromagnetic convection in a ferrofluid layer, for the case of free boundaries lies inside a semicircle in the right half of the σrσi-plane whose center is at the origin and (radius)2=RM1/Pr, where R is the Rayleigh number,M1 is the magnetic number and Pr is the Prandtl number. Further, bounds for the case of rigid ferromagnetic boundaries are also derived separately.

Ferromagnetic Convection in a Heterogeneous Darcy Porous Medium Using a Local Thermal Non-equilibrium (LTNE) Model

The combined effects of vertical heterogeneity of permeability and local thermal non-equilibrium (LTNE) on the onset of ferromagnetic convection in a ferrofluid saturated Darcy porous medium in the presence of a uniform vertical magnetic field are investigated. A two-field model for temperature representing the solid and fluid phases separately is used. The eigenvalue problem is solved numerically using the Galerkin method for different forms of permeability heterogeneity function Γ(z) and their effect on the stability characteristics of the system has been analyzed in detail. It is observed that the general quadratic variation of Γ(z) with depth has more destabilizing effect on the system when compared to the homogeneous porous medium case. Besides, the influence of LTNE and magnetic parameters on the criterion for the onset of ferromagnetic convection is also assessed.