Convective instability of a rotating fluid above a rapidly heated surface

Convection in a rotating fluid above a rapidly heated surface is studied experimentally. Pis’ma Zh. Tekh. Fiz. 23, 1–6 (February 12, 1997)     

Numerical solution of thermal instability of a rotating micropolar fluid layer

In this paper, we have considered the thermal instability of a rotating, heat conducting, micropolar fluid layer heated from below and confined between two rigid boundaries. The onset of thermal instability is governed by a linear eigenvalue problem. The solution of the eigenvalue problem is obtained by using finite difference method and Wilkinson's iteration technique. The effects of rotation and micropolar parameters on the critical Rayleigh number and the wave number at the threshold of instability are discussed in detail.     

Convective instability of a micropolar fluid layer by the method of energy

The convective instability of a micropolar incompressible fluid layer heated from below is treated within the framework of Serrin-Joseph's energy method. In presence of coupling between temperature and micro-rotations, a region of subcritical instability is displayed. The influence of the various micropolar parameters on the onset of convection is also analyzed.     

Hydromagnetic flow past a rotating porous plate in a conducting fluid rotating about a noncoincident parallel axis

Summary The hydromagnetic flow of an incompressible viscous electrically conducting fluid past a porous plate is investigated when the plate rotates with a uniform angular velocity about an axis normal to the plate and the fluid at infinity rotates with the same angular velocity about a non-coincident parallel axis. It is shown that in the presence of a uniform magnetic field parallel to the axis of rotation the boundary layer thickness decreases with an increase in either the suction at the plate or the magnetic parameter M. In the presence of suction at the plate, the velocity component u in the direction normal to the plane containing the axis of rotation of the plate and that of the fluid increases with an increase in M, while the velocity component v in the transverse direction parallel to the plane of the plate decreases with an increase in M. For a fixed value of M, at a given location u increases with an increase in the suction parameter S while v decreases with increasing S. For a fixed value of M, at a given location both u and v decrease with an increase in the blowing parameter S₁. Further, for a fixed value of S₁, at a given position u increases with an increase in M but v decreases with increasing M. It is shown that no torque is exerted by the fluid on the plate, and non-coaxial rotations of the plate and the fluid at infinity have no influence on the torque.The solution of the heat transfer equation reveals that for given values of the suction parameter S, Prandtl number P and Eckert number E, the temperature at a given point in the flow increases with increasing M. On the other hand, for fixed values of M, P and E, the temperature at a given point decreases with increasing S. No steady distribution of temperature exists when there is blowing at the plate.     

Thermal instability of rotating nanofluid layer

In the present paper we have considered thermal instability of rotating nanofluids heated from below. Linear stability analysis has been made to investigate analytically the effect of rotation. The more important effect of Brownian motion and thermophoresis has been included in the model of nanofluid. Galerkin method is used to obtain the analytical expression for both non-oscillatory and oscillatory cases, when boundaries surfaces are free–free. The influence of various nanofluids parameters and rotation on the onset of convection has been analysed. It has been shown that the rotation has a stabilizing effect depending upon the values of various nanofluid parameters. The critical Rayleigh number for the onset of instability is determined numerically and results are depicted graphically. The necessary and sufficient conditions for the existence of over stability are also obtained.     

Thermal relaxation effect on magnetohydrodynamic instability in a rotating micropolar fluid layer heated from below

Summary. The effect of a vertical magnetic field on the onset of convective instability in a conducting micropolar fluid (Oldroyd fluid) layer heated from below confined between two horizontal planes under the simultaneous action of the rotation of the system and a vertical temperature gradient is considered. Linear stability theory and normal mode analysis are used to derive an eigenvalue system of order twelve, and an exact eigenvalue equation for natural instability is obtained. Under somewhat artificial boundary conditions, this equation can be solved exactly to yield the required eigenvalue relationship from which various critical values are determined in detail. The effects of magnetic field, the relaxation time and micropolar parameters on the critical Rayleigh number and critical wave number are discussed and presented graphically. The analysis presented in this paper is more general than any previous investigation.     

Convective instability in a horizontal fluid layer with a permeable barrier under conditions of arbitrary boundary heat conduction

We examine the effect on the convective stability of a plane horizontal fluid layer from the resistance of a permeable barrier positioned in the middle of the layer, and from the heat conduction of a solid block surrounding that layer.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 60, No. 3, pp. 410–414, March, 1991.     

The onset of transient Marangoni convection in a liquid layer subjected to rotation about a vertical axis

In view of the interesting possibilities of controlling surface tension-driven convection, anticipated in space experiments involving fluid interfaces, the problem of the stability of a thin horizontal fluid layer subjected to rotation about a vertical axis, when the thermal (or concentration) gradient is not uniform is examined by linear stability analysis. Attention is focussed on the situation where the critical Marangoni number is greater than that for the case of uniform thermal gradient and the convection is not, in general, maintained. The case of adiabatic boundary condition is examined because it brings out the effect of surface tension at the free surfaces and allows a simple application of the Galerkin technique, which gives useful results. Numerical results are obtained for special cases and some general conclusions about the destabilizing effects of various basic temperature profiles and the stabilizing effect of coriolis force are presented. The results indicate that the most destabilizing temperature gradient is one for which the temperature gradient is a step function of the depth. Increase in Taylor number and the inverted parabolic basic temperature profile suppress the onset of convection.     

Thermal instability in a nanofluid layer with a vertical magnetic field

The combined effect of a vertical magnetic field and the boundaries on the onset of convection in an electrically conducting nanofluid layer heated from below is investigated using linear stability theory. The employed model incorporates the effects of Brownian motion and thermophoresis. The boundaries are considered to be either rigid or free. The eigenvalue problem is solved analytically for free–free boundaries and numerically for rigid–rigid and lower-rigid and upper-free boundaries using the Galerkin technique. Numerical results are presented for alumina–water nanofluid.     

Thermal-convective instability in a liquid layer in a system with rotating pivots

The stability of the main stationary liquid motion defined by Dirichlet boundary conditions on lateral surfaces of pivots was considered for a heated layer of a viscous thermal conducting liquid periodically perforated by a set of thin pivots. It was established that at any type of perforation and exceeding the critical Rayleigh number loss of stability is monotonic. In addition, the asymptotics for the critical Rayleigh number were defined at different types of perforation of the liquid layer.     

On the stability of a hot rotating layer of micropolar fluid

The convective stability of a horizontal layer of incompressible micropolar fluid heated from below and rotating about a vertical axis has been investigated on the basis of linear theory, using normal mode analysis. The boundaries are assumed to be free. After introducing the corrections to the basic equations considered by Sastry and Rao [1], it has been found that the rotation has a destabilizing effect which contradicts the earlier assertion presented in [1].Moreover, microinertia, which does not affect the stability of a hot horizontal layer of incompressible micropolar fluid in the absence of rotation [2], is found to have destabilizing effect.     

Convective instability of a free-convection vortex

The stability of free-convection vortex formations obtained in the laboratory is compared with natural tropical cyclones.Nomenclature r radius - density of air - P pressure drop between the center of a vortex and its edge - latitude of the location of a natural tropical cyclone Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 58, No. 3, pp. 416–419, March, 1990.     

Numerical study of the effect of Hall currents on the hydromagnetic thermal instability of a rotating fluid layer between rigid boundaries

In this paper, we have considered the effect of Hall currents on the hydromagnetic thermal instability of a rotating fluid layer confined between rigid boundaries. The eigenvalue problem governing the onset of instability is solved by using finite difference method and Wilkinson's iteration technique. It is seen that, depending upon the rotation of the system, the Hall currents have a profound influence in affecting the onset of instability.     

Stability of the boundary layer on a sphere rotating in still fluid

Summary A theoretical study of the transition of a three-dimensional boundary layer on a sphere rotating in still fluid is carried out by a linear stability analysis. A set of perturbation equations governing the instability of the flow field is derived assuming the perturbations to be consisting of spiral vortices. It is shown that the critical Reynolds numbers obtained in the present analytical study are close to those observed in experiments. It has been found that the streamline-curvature instability appears in the rotating sphere flow. It is also shown that the cross-flow instability is dominant near the poles of a sphere while the streamline-curvature instability overtakes near the equator.     

Thermal instability in a micropolar fluid layer subject to a magnetic field

In the present paper we have considered thermal instability in a heat conducting micropolar fluid layer under the influence of a transverse magnetic field. Assuming the bounding surfaces to be rigid the eigenvalue problem is solved using finite-difference and Wilkinson's iteration techniques. Here it is seen that the instability sets in not only for adverse temperature gradient but also for positive temperature gradient. Both the microtation and the magnetic field are seen to stabilize the fluid layer. However, the stabilizing effect of microrotation becomes less significant when the strength of the magnetic field is large. In the case of heating from below, the critical wave number is seen to be insensitive to increase in the strength of the magnetic field, while it increases significantly when the fluid is heated from above.     

Perturbed motion of a viscous fluid layer on the surface of a rotating cylinder

We investigate the plane flow of a viscous fluid layer plane flow on the surface of a cylinder rotating with a constant angular velocity with account for inertia forces and the acceleration of gravity.Lomonosov Moscow State University, Moscow; Bauman Moscow State Technical University; Belarusian State University, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 6, pp. 689–694, June, 1994.     

Hydrodynamic stability of convective flow of a non-Newtonian fluid in a vertical layer

Steady convective non-Newtonian fluid flow and its stability under small perturbations are investigated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 32, No. 6, pp. 1065–1070, June, 1977.The author is indebted to G. Z. Gershuni for general interest and discussion.     

Electromagneto-hydrodynamic instability in a horizontal viscoelastic fluid layer with one relaxation time

Summary The stability of viscoelastic conducting liquid (Walters's liquid B) heated from below in the presence of a magnetic field is considered. Linear stability theory is used to derive an eigenvalue system of sixth order, and an exact eigenvalue equation for a neutral instability is obtained. Under somewhat artificial boundary conditions, this equation can be solved exactly to yield the required eigenvalue relationship from which various critical values are determined in detail. Critical Rayleigh number and wavenumber for the onset of instability are presented graphically as functions of the Chandrasekhar number at a Prandtl numberP _r=100 and for various values of the one relaxation time and the elastic parameters.     

Pressure loss during fluid flow in a channel rotating perpendicularly to the axis of rotation

Results are presented which were obtained in experiments to determine the hydraulic resistance of a channel during its rotation around an axis perpendicular to the channel axis.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 29, No. 6, pp. 1024–1030, December, 1975.