Effects of Coriolis force and different basic temperature gradients on Marangoni ferroconvection

The effect of Coriolis force and different forms of basic temperature gradients on the onset of Marangoni ferroconvection in a horizontal layer of ferrofluid is investigated theoretically. The lower boundary is assumed to be rigid-isothermal, while the upper free boundary on which the surface tension acts is non-deformable and insulating to temperature perturbations. The Galerkin technique is used to obtain the critical stability parameters. It is shown that convection sets in as oscillatory motions provided that the Prandtl number is less than unity. A mechanism for suppressing or augmenting Marangoni ferroconvection by rotation, nonlinearity of magnetization and different forms of basic temperature gradients is discussed in detail. It is found that the inverted parabolic temperature profile indicates a reinforcement of stability, whereas the step function temperature profile indicates a diminution of stability. Comparisons of results between the present and the existing ones are made under the limiting conditions and good agreement is found

Effect of Cubic Temperature Profiles on Ferro Convection in a Brinkman Porous Medium

The effect of cubic temperature profiles on the onset ferroconvection in a Brinkman porous medium in presence of a uniform vertical magnetic field is studied. The lower and upper boundaries are taken to be rigid-isothermal and ferromagnetic. The Rayleigh-Ritz method with Chebyshev polynomials of the second kind as trial functions is employed to extract the critical stability parameters numerically. The results indicate that the stability of ferroconvection is significantly affected by cubic temperature profiles and the mechanism for suppressing or augmenting the same is discussed in detail. It is observed that the effect of Darcy number magnetic number and nonlinearity of the fluid magnetization parameter is to hasten, while an increase in the ratio of viscosity parameter and Biot number is to delay the onset of ferroconvection in a Brinkman porous medium. Further, increase in and decrease in is to decrease the size of the convection cells

Effects of quadratic drag and throughflow on double diffusive convection in a porous layer

The linear stability theory is used to investigate analytically the effects of quadratic drag and vertical throughflow on double diffusive convection in a horizontal porous layer using the Forchheimer-extended Darcy equation. The boundaries of the porous layer are considered to be either impermeable or porous, but perfect conductors of heat and solute concentration. Conditions for the occurrence of stationary and oscillatory convection are obtained using the Rayleigh-Ritz method. Stability boundaries are drawn in the Rayleigh numbers plane and the throughflow is found to influence the mode of instability. It is found that, irrespective of the nature of boundaries, a small amount of throughflow in either of its direction destabilizes the system; a result which is in contrast to the single component system. © 2005 Elsevier Ltd. All rights reserved

Penetrative ferroconvection via internal heating in a saturated porous layer with constant heat flux at the lower boundary

A model for penetrative ferroconvection via internal heat generation in a ferrofluid saturated porous layer is explored. The BrinkmanLapwood extended Darcy equation with fluid viscosity different from effective viscosity is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed to be rigid-paramagnetic and insulated to temperature perturbations, while at upper stress-free boundary a general convective-radiative exchange condition on perturbed temperature is imposed. The resulting eigenvalue problem is solved numerically using the Galerkin method. It is found that increasing in the dimensionless heat source strength N s, magnetic number M 1 Darcy number Da and the non-linearity of magnetization parameter M 3 is to hasten, while increase in the ratio of viscosities �, Biot number Bi and magnetic susceptibility � is to delay the onset of ferroconvection. Further, increase in Bi, Da -1 and N s and decrease in �, M 1 and M 3 is to diminish the dimension of convection cells. © 2011 Elsevier B.V

Onset of Benard-Marangoni Ferroconvection with Internal Heat Generation

The effect of internal heat generation on the onset of Benard-Marangoni convection in a horizontal ferrofluid layer heated from below in the presence of a uniform vertical magnetic field is studied. The lower boundary is rigid and the upper free boundary is assumed to be flat and undeformable. Both the boundaries are considered to be perfectly insulated to temperature perturbations and the resulting eigenvalue problem is solved numerically using the Galerkin technique as well as analytically by regular perturbation technique with wave number as a perturbation parameter. It is observed that the analytical results agree well with those obtained numerically. It is noted that the combined effect of magnetic Rayleigh number and dimensionless internal heat source strength is to reinforce together and to hasten the onset of Benard-Marangoni ferroconvection compared to their presence in isolation. In addition, the nonlinearity of fluid magnetization is found to have no influence on the criterion for the onset of ferroconvection. Some existing results are reproduced as particular cases from the present study

Effect of Coriolis Force on Bénard–Marangoni Convection in a Rotating Ferrofluid Layer with MFD Viscosity

The simultaneous effect of Coriolis force due to rotation and magnetic field dependent (MFD) viscosity on the onset of Bénard-Marangoni convection in a horizontal ferrofluid layer in the presence of a uniform vertical magnetic field is studied. The lower boundary is rigid while the upper free boundary is open to the atmosphere and at which the temperature-dependent surface tension effect is allowed for. The Galerkin technique is employed to extract the critical stability parameters numerically. The results show that the onset of Bénard-Marangoni ferroconvection is delayed with an increase in the MFD viscosity parameter , Taylor number T a, magnetic susceptibility χ and Biot number Bi but opposite is the case with an increase in the value of magnetic numberM1 and nonlinearity of fluid magnetization M3. Further, increase inM1, M3 and decrease in , T a, χ and Bi is to decrease the size of the convection cells. Comparisons of results between the present and the existing ones are made under the limiting conditions and good agreement is found

Onset of Thermogravitational Convection in a Ferrofluid Layer with Temperature Dependent Viscosity

The onset of thermogravitational convection in a horizontal ferrofluid layer is investigated with viscosity depending exponentially on temperature. The bounding surfaces of the ferrofluid layer are considered to be either stress free or rigid-ferromagnetic and insulated to temperature perturbations. The resulting eigenvalue problem is solved numerically using the Galerkin technique and also by a regular perturbation technique for different types of velocity boundary conditions, namely free-free, rigid-rigid, and lower rigid- upper free. It is observed that increasing the viscosity parameter, ΛΛ, and the magnetic number, M1M1, is to hasten the onset of ferroconvection, while the nonlinearity of fluid magnetization, M3M3, is found to have no influence on the stability of the system. The critical stability parameters are found to be the same in the limiting cases of either no magnetic forces or no buoyancy forces

Onset of Benard-Marangoni ferroconvection with a convective surface boundary condition: The effects of cubic temperature profile and MFD viscosity

The combined effects of basic cubic temperature profiles and magnetic field dependent (MFD) viscosity on the onset of Benard-Marangoni convection in a ferrofluid layer are studied. The lower boundary is rigid-isothermal, while the upper free boundary open to the atmosphere is flat and subject to a general thermal boundary condition. The Galerkin technique is employed to extract the critical stability parameters numerically. The results indicate that the basic cubic temperature profiles have a profound influence on the stability characteristics of the system and can be effectively used to either suppress or augment the onset of Benard-Marangoni ferroconvection. Besides, increasing the magnetic Rayleigh number and the nonlinearity of magnetization hastens, while an increase in the Biot number and MFD viscosity parameter delays the onset of Benard-Marangoni ferroconvection. The existing results in the literature are obtained as particular cases from the present study. (C) 2013 Elsevier Ltd. All rights reserved

Onset of convection in a sparsely packed porous layer with throughflow

The onset of Rayleigh-​Benard convection in a sparsely packed porous layer with vertical throughflow is investigated using Brinkman's modification of the Darcy flow model with fluid viscosity different from effective viscosity. The crit. Rayleigh nos. are obtained for free-​free, rigid-​rigid and rigid-​free boundaries which are insulated to temp. perturbations. It is noted that an increase in the value of viscosity ratio is to delay the onset of convection. Further, it is obsd. that the throughflow can be used either to suppress or augment convection, depending on the nature of boundaries and also on the values of phys. parameters

Ferromagnetic convection in a rotating ferrofluid saturated porous layer

The effect of Coriolis force on the onset of ferromagnetic convection in a rotating horizontal ferrofluid satd. porous layer in the presence of a uniform vertical magnetic field is studied. The boundaries are considered to be either stress free or rigid. The modified Brinkman-​Forchheimer-​extended Darcy equation with fluid viscosity different from effective viscosity is used to characterize the fluid motion. The condition for the occurrence of direct and Hopf bifurcations is obtained anal. in the case of free boundaries, while for rigid boundaries the eigenvalue problem has been solved numerically using the Galerkin method. Contrary to their stabilizing effect in the absence of rotation, increasing the ratio of viscosities, Λ, and decreasing the Darcy no. Da show a partial destabilizing effect on the onset of stationary ferromagnetic convection in the presence of rotation, and some important observations are made on the stability characteristics of the system. Moreover, the similarities and differences between free-​free and rigid-​rigid boundaries in the presence of buoyancy and magnetic forces together or in isolation are emphasized in triggering the onset of ferromagnetic convection in a rotating ferrofluid satd. porous layer. For smaller Taylor no. domain, the stress-​free boundaries are found to be always more unstable than in the case of rigid boundaries. However, this trend is reversed at higher Taylor no. domain because the stability of the stress-​free case is increased more quickly than the rigid case