Finite Larmor radius effect on thermosolutal instability of a plasma in porous medium

The thermosolutal instability of a plasma in porous medium is considered in the presence of finite Larmor radius effect. The finite Larmor radius, stable solute gradient and magnetic field introduce oscillatory modes in the systems which were nonexistent in their absence. For stationary convection, the finite Larmor radius and stable solute gradient have stabilizing effects on the thermosolutal instability in porous medium. In presence of finite Larmor radius effect, the medium permeability has a destabilizing (or stabilizing) effect and the magnetic field has a stabilizing (or destabilizing) effect under certain condition whereas in the absence of finite Larmor radius effect, the medium permeability and the magnetic field have destabilizing and stabilizing effects, respectively, on thermosolutal instability of a plasma in porous medium. The sufficient conditions for nonexistence of overstability are obtained.The financial assistance to Mr. Sunil in the form of Senior Research Fellowship of the Council of Scientific and Industrial Research (CSIR), New Delhi is gratefully acknowledged.     

The onset of Darcy-Brinkman thermosolutal convection in a horizontal porous media

On the basis of Brinkman model, the onset of double-diffusive (thermosolutal) convection with a reaction term in a horizontal sparsely packed porous media is studied using the normal mode analysis. The effects of Brinkman term, the reaction term, the normalized porosity ε and Lewis number Le on the Rayleigh number for stationary and oscillatory case are presented graphically. The Darcy number destabilize the system in case of both stationary and oscillatory mode. The effects of Lewis number and reaction term depend on the value of the values of solutal Rayleigh number. Furthermore, some results of Darcy model can be recovered in limit cases.     

Nonlinear effects in the convective instability of a binary mixture in a porous medium near threshold

An amplitude equation is derived near threshold for both the stationary and the oscillatory instabilities and an oscillatory behavior in time for the Nusselt and the Froude number is predicted for the oscillatory instability.     

Rayleigh convective instability in a cloud medium

The problem of convective instability of an atmospheric layer containing a horizontally finite region filled with a cloud medium is considered. Solutions exponentially growing with time, i.e., solitary cloud rolls or spatially localized systems of cloud rolls, have been constructed. In the case of axial symmetry, their analogs are convective vortices with both ascending and descending motions on the axis and cloud clusters with ring-shaped convective structures. Depending on the anisotropy of turbulent exchange, the scale of vortices changes from the tornado scale to the scale of tropical cyclones. The solutions with descending motions on the axis can correspond to the formation of a tornado funnel or a hurricane eye in tropical cyclones.     

Heat and mass transfer of MHD convective boundary layer flow past a stretching porous wall embedded in a porous medium

The hydromagnetic convective boundary layer flow past a stretching porous wall embedded in a porous medium with heat and mass transfer in the presence of a heat source and under the influence of a uniform magnetic field is studied. Exact solutions of the basic equations of motion, heat and mass transfer are obtained after reducing them to nonlinear ordinary differential equations. The reduced equations of heat and mass transfer are solved using a confluent hypergeometric function. The effects of the flow parameters such as a suction parameter (N), magnetic parameter (M), permeability parameter (K _p ), wall temperature parameter (r), wall concentration parameter (n), and heat source/sink parameter (Q) on the dynamics are discussed. It is observed that the suction parameter appears in the boundary condition ensuring the variable suction at the surface. Transverse component of the velocity increases only when magnetic field strength exceeds certain value, but the thermal boundary layer thickness and concentration distribution increase for all values. Results presented in this paper are in good agreement with the work of the previous author and also in conformity with the established theory.     

The instability of fronts in a porous medium

We use a random choice numerical method to analyze the instability of a front separating two fluids in a porous medium. We observe a linear instability and a catastrophic finite amplitude instability. A qualitative analogy with problems involving a transition to turbulence is pointed out.     

Scaling approach of the convective drying of a porous medium

We propose a simplified, theoretical approach of the evolution of liquid distribution during the convective drying of a granular packing. In the absence of gravity effects three regimes are distinguished according to the relative importance of surface evaporation, capillarity or evaporation from the interior of the sample. The evolution of the drying rate as a function of the saturation can be inferred from the characteristic velocities associated to each of these effects. We also carried out drying experiments of bead packings saturated with ethanol, at four different velocities of the boundary convection current, and with bead size ranging from 4.5 to 100 μm. The drying curves exhibit different regimes with a scaling as a function of particle radius and current velocity as predicted by the theory. Received 7 June 1999 and Received in final form 25 October 1999     

Effect of a variable magnetic field on the instability of a stratified rotating fluid layer in porous medium

The instability of a stratified rotating fluid layer through porous medium in the presence of an inhomogeneous magnetic field is investigated. For exponentially varying density and magnetic field variations, an eigenvalue solution has been obtained. The dispersion relation is obtained and discussed for both the stable and unstable stratifications separately. It is found, for non-porous medium, that for the stable mode of disturbance, the system is always stable, and for the unstable mode of disturbance, it is stabilized only under a certain condition for the Alfvèn velocity, rotation and the stratification parameter. In the latter case, both rotation and magnetic field are found to have a stabilizing effect on the growth rate. In the presence of porous medium, it is found, for real growth rate n, that the inhomogeneous magnetic field has always a stabilizing effect on the considered system. It is found also, for complex growth rate n, that the system is stable for the stable stratification case, while it is stable or unstable for the unstable case under a certain wavenumbers range depending on the Alfvèn velocity and the stratification parameter. The presence of the magnetic field is found to stabilize a certain wavenumbers band, whereas the system was unstable for all wavenumbers in the absence of the magnetic field. Also, the presence of porous medium is found to hide the stabilizing effect played by rotation on the considered system for non-porous medium, i.e., rotation does not have any significant effect on the stability criterion in this case.     

Rayleigh wave propagation along the boundary of a non-Newtonian fluid-saturated porous medium

The Frenkel-Biot theory is used to study the reflection of elastic waves from the boundary of a non-Newtonian (Maxwell) fluid-saturated porous medium. The velocity and attenuation of a Rayleigh surface wave propagating along the boundary of the medium are determined. Two models of a fluid-saturated porous medium are used for calculation: with pore channels of a fixed diameter and with a lognormal distribution of pore channels in size. The results of calculations show that, when the fluid in the porous medium is characterized by a small Deborah number (i.e., exhibits non-Newtonian properties), the velocity of Rayleigh waves exhibits a considerable frequency dispersion. The results also suggest that, in principle, it is possible to estimate the Deborah number from the measured frequency dispersion of the Rayleigh wave velocity.     

Nonlinear effects of non-Newtonian fluids on natural convection in a porous medium

This paper investigates the rheological effects of non-Newtonian fluids on the natural convection mechanism in a porous medium. A non-Newtonian behavior of power law fluid with a yield stress, saturating a porous medium, in which yield stress is temperature dependent, is considered. The cases of constant temperature boundary and constant heat flux boundary, along the heated vertical cylinder, are analyzed. The approximate similarity solutions in a closed form are shown, from which the velocity and temperature profiles are determined. The numerical solutions for a constant temperature boundary are also shown and discussed.     

Borehole guided waves in a non-Newtonian (Maxwell) fluid-saturated porous medium

<正>The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian (Maxwell) fluid-saturated porous formation with a permeable wall is investigated.The influence of non-Newtonian effects on acoustic guided waves such as Stoneley waves,pseudo-Rayleigh waves,flexural waves,and screw waves propagations in a fluid-filled borehole is demonstrated based on the generalized Biot-Tsiklauri model by calculating their velocity dispersion and attenuation coefficients.The corresponding acoustic waveforms illustrate their properties in time domain.The results are also compared with those based on generalized Biot's theory.The results show that the influence of non-Newtonian effect on acoustic guided wave,especially on the attenuation coefficient of guided wave propagation in borehole is noticeable.     

Thermosolutal instability in porous medium in a partially ionized plasma

The thermosolutal instability in porous medium in a partially ionized plasma in the presence of a uniform vertical magnetic field is considered. The presence of each, magnetic field and stable solute gradient, brings oscillatory modes which were nonexistent in their absence. The collisional effects may also bring in oscillatory modes. The stable solute gradient and magnetic field are found to have stabilizing effect whereas the medium permeability and collisional frequency have destabilizing effect on the thermosolutal instability in porous medium.     

Hall effects on thermosolutal instability of a rotating plasma

Summary The thermosolutal instability of a rotating plasma in the presence of a uniform vertical magnetic field is studied to include the effects of Hall current. When the instability sets in as stationary convection for the case of no rotation, the Hall effects are found to be destabilizing. The stable solute gradient and rotation are found to have stabilizing effects. In the presence of rotation the Hall currents are found to be stabilizing forT ₁>M(1+x)². the case of overstability is also considered and it is shown that such solutions exist. The variation of the frequency with respect to the wave number at the neutral state is graphically shown. The authors of this paper have agreed to not receive the proofs for correction.     

Hydromagnetic instability of streaming fluids in porous medium

The instability of the plane interface between two uniform, superposed, electrically conducting and counter-streaming fluids through a porous medium is considered in the presence of a horizontal magnetic field. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbations in the direction of streaming are ignored. For perturbations in all other directions there exists instability for a certain wavenumber range. The instability of this system is postponed by the presence of magnetic field. The magnetic field and surface tension are able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations and the medium porosity reduces the stability range given in terms of a difference between the streaming velocities and the Alfvén velocity.This research forms a part of the research project awarded to the first author (R.C.S.) by the University Grants Commission.     

Effect of variable gravitational field on thermal instability of a rotating fluid layer with magnetic field in porous medium

The effect of variable gravitational field on thermal instability of a rotating fluid layer in the presence of magnetic field in porous medium is investigated. It is found that the system is stable when gravity is decreasing upwards. The principle of exchange of stability is valid in the absence of rotation and magnetic field when gravity increases upwards. In the stationary convection, rotation has stabilizing or destabilizing effect depending upon whether gravity is increasing or decreasing upwards. The medium permeability and magnetic field have stabilizing or destabilizing effect depending upon condition.     

On the conditions of convective instability in the upper layer of liquid solutions

A linear problem of convective instability near the surface of a two-component liquid medium is considered. The specificity of the problem is in the necessity of the simultaneous allowance for the background stratification and the difference in the exchange coefficients for each component, as well for the thermocapillary effect. The allowance for the latter is shown to suggest the existence of a previously unknown region of monotonic instability. The corresponding dimensionless criterion was found, and neutral curves were calculated.     

Three-dimensional absolute and convective instabilities in mixed convection of a viscoelastic fluid through a porous medium

By using the mathematical formalism of absolute and convective instabilities we study the nature of unstable three-dimensional disturbances of viscoelastic flow convection in a porous medium with horizontal through-flow and vertical temperature gradient. Temporal stability analysis reveals that among three-dimensional (3D) modes the pure down-stream transverse rolls are favored for the onset of convection. In addition, by considering a spatiotemporal stability approach we found that all unstable 3D modes are convectively unstable except the transverse rolls which may experience a transition to absolute instability. The combined influence of through-flow and elastic parameters on the absolute instability threshold, wave number and frequency is then determined, and results are compared to those of a Newtonian fluid.     

Modeling diffusion in white matter in the brain: a composite porous medium

We model diffusion in white matter fascicles as a problem of diffusion in an array of identical thick-walled cylindrical tubes immersed in an outer medium and arranged periodically in a regular lattice. The diffusing molecules have different diffusion coefficients and concentrations (or densities) within the tubes' inner core, membrane, myelin sheath, and within the outer medium. For an impermeable myelin sheath, diffusing molecules within the inner core are completely restricted, while molecules in the outer medium are hindered due to the tortuosity of the array of impenetrable tubes.     

MHD natural convective flow through a porous medium in a square cavity filled with liquid gallium

This article contains a computational study of free convective flow through a square enclosure filled with liquid gallium saturated porous medium in the presence of a uniform inclined magnetic field. Lower boundary of enclosure is considered to be heated uniformly, upper horizontal boundary is taken insulated, left wall of the cavity is heated linearly, and right wall is heated linearly or taken cold. Navier–Stokes equations governing the flow problem are first exposed to penalty method to eliminate the pressure terms and then Galerkin FEM is employed to solve reduced equations. Grid independent results are achieved and shown in tabular form for numerous ranges of physical flow parameters. To ensure the accuracy of developed code, computed results are compared with those available in earlier studies through figures. It is found that the strength of streamlines circulation is increased due to increase in Darcy number while imposition of vertical magnetic field instead of horizontal magnetic field causes slow rate of increase in strength of streamlines circulation. Whereas, in the case of linearly heated right wall, the average Nusselt number is an increasing function of the Darcy number, and vertical magnetic field causes higher values for average Nusselt number as compared to horizontal magnetic field along bottom and side walls of cavity. Contrarily, in the case of cold right wall, the horizontal magnetic field results in higher values of average Nusselt number as compared to the vertical magnetic field case, and the average Nusselt number reduces as we move along lower and right boundary while increases along left wall with increase in distance.