Nonlinear interaction of magnetic field and convection in three-​dimensional motion

Three-​dimensional nonlinear convection in a horizontal Boussinesq layer of fluid heated from below is considered in the presence of a vertical magnetic field. The study is based on local nonlinear anal. which is pivoted on the linear theory. The effect of a magnetic field on convective heat transfer and the phys. preferred cell patterns are detd. Finite-​amplitude steady convection persists only for certain range of the Chandrasekhar no. and the hexagonal planform is the preferred cell pattern. The convective heat transport in H is much greater than that in Hg. The analogy between magnetic field and rotation is brought out

On the stability of the flow of stratified rotating superposed fluids

The effect of Coriolis force on the stability of two superposed fluids is examined under the assumption of ideal (incompressible, non-viscous and zero thermal conductivity) flow. The analysis reveals only one type of instability in contrast to two types of instabilities observed by SoNTowSKI, SEIDEL, and AMES (1%9), in the absence of Coriolis force. Thus the effect of Coriolis force on the superposed flow is to make the flow more stable. In particular, the special case of upper strati fled fluid rotating and the lower non-rotating is examined in detail and we find two separate and different types of instabilities. As the velocity of the rotating fluid relative to the non-rotating one increases from zero, there first appears an instability of a selective and relatively weak nature referred to as the initial instability. This is followed, at higher velocities, by a stronger type of instability ealled the gross instability. We found that the effect of Coriolis force is to suppress the region of initial instability in the sense that the instability occurs for large velocity differences. We also found that the Coriolis force has no effect on the critieal wavenumber. These general stability results are applied to a particular problem of the Kelvin-Helmholtz instability with rotation and we find that the results are in agreement with those of CHANDRAsExHAR (1%1). We determine the rate of growth of initial instabilities, which depends on the density stratifleation and the angular velocity of the rotating gas. This growth rate, in the ease of rotation, is greater than that in the absence of rotation, which is in agreement with observations of MUNK (1947)

Effect of non-uniform basic temperature gradient on the onset of Marangoni convection in a fluid with suspended particles

The effect of a non-uniform basic temperature gradient on the onset of convection driven by surface tension in a horizontal layer of a Boussinesq fluid with suspended particles confined between an upper free, constant heat flux boundary and a lower rigid isothermal boundary is considered. The microrotation is assumed to vanish at the boundaries. A linear stability analysis is performed. The Rayleigh-Ritz technique is used to obtain the eigenvalues. The influence of various parameters on the onset of convection has been analyzed. Six different non-uniform basic state temperature profiles are considered and their comparative influence on onset is discussed. It is observed that the fluid layer with suspended particles heated from below is more stable compared to the classical fluid layer without suspended particles. The problem has possible applications in microgravity situations

Effect of Non-uniform Basic Temperature Gradient on Rayleigh¯Benard¯MarangoNi Convection in Ferrofluids

The effect of different basic temperature gradients on the onset of ferroconvection driven by combined surface tension and buoyancy forces is studied. The lower boundary is assumed to be rigid and either conducting or insulating to temperature perturbations while the upper boundary at which the surface tension acts is free insulating and non-deformable. The resulting eigenvalue problem is solved by the Galerkin technique for various basic temperature gradients. The results indicate that the stability of Rayleigh–Benard–Marangoni ferroconvection is significantly affected by basic temperature gradients and the mechanism for suppressing or augmenting the same is discussed in detail. It is shown that the results obtained under the limiting conditions compare well with the existing ones

Effect of non-uniform concentration distribution on double diffusive convection in magnetic fluids

The effect of non-uniform concentration distribution on double diffusive convection in a Boussinesq magnetic fluid layer confined between two rigid boundaries is studied analytically using the Galerkin method. The condition for direct and oscillatory modes for different non-linear basic concentration distributions is established. It is shown that different non-uniform concentration gradients and diffusivity ratio significantly influence the stability of the system when convection is induced by buoyancy force and/or magnetization

Effect of basic temperature gradients on Marangoni convection in ferromagnetic fluids

The effect of different basic temperature gradients on the onset of Marangoni ferroconvection is studied. The resulting eigenvalue problem is solved by Galerkin technique for the lower boundary rigid and either conducting or adiabatic and the upper boundary at which the surface tension acts is free adiabatic. The results indicate that the stability of Marangoni ferroconvection is significantly affected by basic temperature gradients and the mechanism for suppressing or augmenting the same is discussed in detail. It is found that, the results obtained under the limiting conditions compare well with the existing ones

Effect of non-uniform concentration distribution on double diffusive convection in magnetic fluid

427-435<span style="font-size:11.0pt;line-height:115%; font-family:" calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-fareast-font-family:="" "times="" new="" roman";mso-fareast-theme-font:minor-fareast;mso-hansi-theme-font:="" minor-latin;mso-bidi-font-family:arial;mso-ansi-language:en-us;mso-fareast-language:="" en-us;mso-bidi-language:ar-sa"="">The effect of non-uniform concentration distribution on double diffusive convection in a Boussinesq magnetic fluid layer confined between two rigid boundaries is studied analytically using the Galerkin method. The condition for direct and oscillatory modes for different non-linear basic concentration distributions is establislied. It is shown that different non-uniform concentration gradients and diffusivity ratio significantly influence the stability of the system when convection is induced by buoyancy force and/or magnetization.</span

Effect of basic temperature gradients on Marangoni convection in ferromagnetic fluids

95-106<span style="font-size: 15.5pt;mso-bidi-font-size:8.5pt;font-family:" times="" new="" roman","serif""="">The effect of different basic temperature gradients on the onset of Marangoni ferroconvection is studied. The resulting eigenvalue problem is solved by Galerkin technique for the lower boundary rigid and either conducting or adiabatic and the upper boundary at which the surface tension acts is free adiabatic. The results indicate that the stability of Marangoni ferroconvection is significantly affected by basic temperature gradients and the mechanism for suppressing or augmenting the same is discussed in detail. It is found that, the results obtained under the limiting conditions compare well with the existing ones. </span

Effect of non-uniform concentration distribution on double diffusive convection in magnetic fluids

The effect of non-uniform concentration distribution on double diffusive convection in a Boussinesq magnetic fluid layer confined between two rigid boundaries is studied analytically using the Galerkin method. The condition for direct and oscillatory modes for different non-linear basic concentration distributions is established. Different non-uniform concentration gradients and diffusivity ratio significantly influence the stability of the system when convection is induced by buoyancy force and/or magnetization