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The onset of convection in a ferrofluid-saturated porous layer has been investigated using a local thermal nonequilibrium (LTNE) model by allowing the solid phase to transfer heat via a Cattaneo heat flux theory while the fluid phase to transfer heat via usual Fourier heat-transfer law. The flow in the porous medium is governed by modified Brinkman-extended Darcy model. The instability of the system is discussed exactly for stress-free boundaries, while for rigid-ferromagnetic/paramagnetic boundaries the results are obtained numerically using the Galerkin method. The presence of Cattaneo effect introduces oscillatory convection as the preferred mode of instability contrary to the occurrence of instability via stationary convection found in its absence. Besides, oscillatory ferroconvection is perceived when the solid thermal relaxation time parameter exceeds a threshold value and increase in its value is to hasten the oscillatory onset. The effect of different boundary conditions on the instability of the system is noted to be qualitatively same. The paper aims to discuss these issues.

The investigators would follow the procedure of Straughan (2013) to obtain the expression for Rayleigh number. The Brinkman-extended Darcy model is used to describe the flow in a porous medium. The investigators have used a Galerkin method to obtain the numerical results for rigid-ferromagnetic/paramagnetic boundaries, while the instability of the system is discussed exactly for stress-free boundaries.

The Cattaneo–LTNE porous ferroconvection has been analyzed for different velocity and magnetic boundary conditions. The Brinkman-extended Darcy model is used to describe the flow in a porous medium. The effect of different types of velocity and magnetic boundary conditions on the instability of the system has been highlighted. The instability of the system is discussed exactly for stress-free boundaries, while for rigid-ferromagnetic/paramagnetic boundaries the results are obtained numerically using the Galerkin method.

The novelty of the present paper is to combine LTNE and second sound effects in solids on thermal instability of a ferrofluid-saturated porous layer by retaining the usual Fourier heat-transfer law in the ferrofluid. The Brinkman-extended Darcy model is used to describe the flow in a porous medium. The effect of different types of velocity and magnetic boundary conditions on the instability of the system is discussed.

The purpose of this paper is to explore a model for thermal convection in a plane layer when the density-temperature relation in the buoyancy term is quadratic. A heat source/sink varying in a linear fashion with a vertical height expressed as z was allowed, functioning as a heat sink in an area of the layer and as a heat source in the remainder.

First, the authors present the governing equations of motion and derive the associated perturbation equations. Second, the authors introduce the linear and nonlinear analysis of the system. Third, the authors transform the system to velocity-vorticity-potential formulation and introduce a numerical study of the problem in three dimensions.

First, the linear instability and nonlinear stability thresholds are derived. Second, the linear instability thresholds accurately predict the onset of instability. Third, the required time to arrive at the steady state increases as Ra tends to Ra_L . Fourth, the authors find that the convection has three different interesting patterns.

With the modernday need for heat transfer or insulation devices in industry, particularly those connected with nanotechnology, the usefulness of a mathematical analysis of such resonance became apparent. Thus, this study is believed to be of value.

Numerical computations were performed for the heat transfer and fluid flow characteristics of natural convection with an internal vertical channel composed by a pair of parallel plates in a rectangular enclosure. The inner plates and the bounding wall of the enclosure were maintained at uniform but different temperatures. The plates were symmetrically arranged. Unsteady computation was performed to simulate the evolution process of the natural convection developing from the zero initial field. The cases of Ra = 2 × 10⁴, 2 × 10⁵ and 10⁶ were studied. A symmetrical steady solution was achieved for the case of Ra = 2 × 10⁴. For Ra = 2 × 10⁵ and 10⁶, time dependent asymmetrical processes were observed. The flow oscillating process seemed to be more complex at Ra = 2 × 10⁵ than that at Ra = 10⁶, which is quasi‐periodic with two frequencies.

The purpose of this paper is to determine the thermo-gravitational convective state of a non-Fourier fluid layer of the single-phase-lagging type, heated from below. Unlike existing methodologies, the spectral modes are not imposed arbitrarily. They are systematically identified by expanding the spectral coefficients in terms of the relative departure in the post-critical Rayleigh number (perturbation parameter). The number and type of modes is determined to each order in the expansion. Non-Fourier effects become important whenever the relaxation time (delay in the response of the heat flux with respect to the temperature gradient) is of the same order of magnitude as process time.

In the spectral method the flow and temperature fields are expanded periodically along the layer and orthonormal shape functions are used in the transverse direction. A perturbation approach is developed to solve the nonlinear spectral system in the post-critical range.

The Nusselt number increases with non-Fourier effect as suggested in experiments in microscale and nanofluid convection.

Unlike existing nonlinear formulations for RB thermal convection, the present combined spectral-perturbation approach provides a systematic method for mode selection.

The purpose of this paper is to study analytically and numerically the effect of a transverse magnetic field on the separation of species induced in an inclined rectangular porous cavity saturated with an electrically conducting mixture.

The porous layer is assumed homogeneous and submitted from its long sides to uniform heat fluxes and to a magnetic field of strength B. The Darcy model combined with the Boussinesq approximation are used to study the heat and solute transfer in the medium. An analytical solution is developed on the basis of the parallel flow approximation. Numerical simulations are also performed in order to validate the analytical solution. The controlling parameters of this problem are the thermal Rayleigh number, the inclination of the enclosure, the separation parameter, the Hartmann number and the Lewis number.

For given values of the thermal Rayleigh number, the inclination of the enclosure, the separation parameter and the Lewis number, there is an optimal magnetic field which leads to a maximum of separation. At relatively high Rayleigh numbers, where convection destroys the separation process, it is possible, with an optimal choice of the Hartman number, to recover a good level of separation.

Since the problem is governed by several parameters (five parameters), only the Darcy model was used in this study instead of the Darcy-Brinkman extended model even if the latter model allows to cover the pure fluid and Darcy porous media as limiting cases.

In separation experiments, it is very difficult technically to work with small Rayleigh numbers due to technical difficulties. However, the process of separations is canceled at high Rayleigh number by the strength of convection which causes a mixing in the binary mixture. This study shows that, by using adequate combinations of the controlling parameters, it becomes possible to reach a good level of separation even at relatively high Rayleigh numbers.

Optimum choice of the magnetic field and the inclination of the cavity may lead to a good level of the separation process. For large Lewis numbers, the separation vanishes far above and far below the optimal Ha. However, for small Lewis numbers, an important level of separation is maintained for any Ha located below the optimal value of the latter parameter.

The purpose of this paper to analyze the effect of Soret with heat and mass transfer on an unsteady two-dimensional Magnetohydrodynamics flow through a porous medium under the influence of the uniform transverse magnetic field in a rotating parallel plate is considered.

A mathematical model was developed using the slip conditions under unsteady state situations. Analytical expressions for the velocity, temperature and concentration profiles, wall shear stress, rates of heat and mass transfer and volumetric flow rate were obtained and computationally discussed with respect to the non-dimensional parameters. Further, the velocity reduces with increasing Hartmann number M and increases with Grashof number Gr and permeability parameter K.

It is observed that temperature reduces with an increase in Prandtl number Pr and ω. It is noted that the thermal radiation increases with increase in Soret number Sr, Schmidt number Sc, Prandtl number pr and ω.

Concentration decreases with an increase in radiation parameter R and chemical reaction parameter Kc.

Numerical simulations have been performed for three‐dimensional natural convection of water near its maximum‐density (cold water) inside rectangular enclosures with differential heating at the vertical (left and right) walls. The horizontal (top and bottom) walls and the lateral (front and rear) walls are taken as insulated. Computations are performed for the buoyancy‐driven convection of cold water with density inversion parameter θ_m = 0.5 in the enclosures with aspect ratio (height/width) A_y = 8 and depth ratios (depth/width) A_z = 0.5, 1, and 2. The influence of the depth ratio on the onset of oscillatory convection in a cold‐water‐filled enclosure is investigated. The presence of the lateral walls tends to suppress the onset of unsteadiness in the convective flow. The main features of the oscillatory convection flow and temperature fields as well as the instability mechanism in the three‐dimensional enclosure were similar to those found in the two‐dimensional model. However, there exists a strong three‐dimensionality in the spatial distribution of the fluctuation amplitude. With the decrease of the depth ratio, the damping effect of the lateral walls becomes increasingly pronounced, leading to a reduced heat transfer rate.

The stability of two‐dimensional natural convection of water near its density maximum (cold water) inside a vertical rectangular enclosure with an aspect ratio of eight is investigated via a series of direct numerical simulations. The simulations aim to clarify, under the influence of density inversion, the physical nature of the instability mechanism responsible for the laminar buoyancy‐driven flow transition from a steady state to an oscillatory state in the enclosure filled with cold water. Two values of the density inversion parameter, _m= 0.4 and 0.5, where the density inversion of cold water may exert strong influence on the flow, are considered in the present study. The results show that the transition from steady state to periodically oscillatory convection arises in the cold‐water‐filled enclosure through a Hopf bifurcation. The oscillatory convection in the water‐filled enclosure for both values of _m is found to feature an oscillatory multicellular structure within the contra‐rotating bicellular flow regions. A traveling wave motion accordingly results along the maximum density contour, which demarcates the contra‐rotating bicellular flows in the enclosure. For both cases the nature of transition into unsteadiness is found to be buoyancy‐driven. The critical Rayleigh number for the bifurcation at _m = 0.4 is found to be markedly higher than that at _m = 0.5.

This paper aims to investigate the onset of convection, heat and mass transports in a sparse porous layer saturated with chemically reactive binary fluid mixture heated and salted from below under the influence of Soret and Dufour effects.

The Brinkman model is used for momentum equation. Linear stability analysis based on normal mode technique is used to evaluate the onset threshold for stationary and oscillatory convection. In weak-nonlinear theory, the truncated Fourier series method is used. The resulting system of differential equations is solved numerically by using the Runge–Kutta fourth-order method.

Because of the competition between the processes of thermal, solute diffusions, chemical reaction and cross-diffusions, the onset of instability is via oscillatory mode instead of stationary. The effect of dissolution/precipitation of reactive component and the cross-diffusions on the stability, heat and mass transports is investigated.

By the proper adjustment of underlying parameters, the onset of convection can either be advanced or delayed as per the requirement. Therefore, the present investigation forms a useful tool for regulating the onset of convection.

The effect of magnetic field dependent (MFD) viscosity on the onset of convection in a ferromagnetic fluid layer heated from below saturating rotating porous medium in the presence of vertical magnetic field is investigated theoretically by using Darcy model. The resulting eigen value problem is solved using the regular perturbation technique. Both stationary and oscillatory instabilities have been obtained. It is found that increase in MFD viscosity and increase in magnetic Rayleigh number is to delay the onset of ferroconvection, while the nonlinearity of fluid magnetization has no influence on the stability of the system.

The thermal perturbation method is employed for analytical solution. 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 impermeable boundaries for which an exact solution is obtained.

The conditions for the system to stabilize both by stationary and oscillatory modes are studied. Even for the oscillatory system of particular frequency dictated by physical conditions, the critical Rayleigh numbers for oscillatory mode of the system were found to be greater than for the stationary mode. The system gets destabilized for various physical parameters only through stationary mode. Hence, the analysis is restricted to the stationary mode. To the Coriolis force, the Taylor number T_a is calculated to discuss the results. It is found that the system stabilizes through stationary mode for values of and for oscillatory instability is favored for Ta > 104. Therefore the Taylor number T_a leads to stability of the system. For larger rotation, magnetization leads to destabilization of the system. The MFD viscosity is found to stabilize the system.

This research paper is new and original.