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.     

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.     

Axisymmetric thermal boundary layer of a micropolar fluid on a cylinder

The laminar micropolar thermal boundary layer in axial flow along a long, thin circular cylinder is investigated using the theory of micropolar fluids formulated by Eringen. The governing energy equation has been solved numerically by the power series approach. Missing values of the thermal functions are tabulated for a wide range of the material parameters, the transverse curvature parameter, and Prandtl number of the fluid.     

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.     

Nonlinear thermal instability in a horizontal porous layer with an internal heat source and mass flow

Linear and nonlinear stability analyses of Hadley–Prats flow in a horizontal fluid-saturated porous medium with a heat source are performed. The results indicate that, in the linear case, an increase in the horizontal thermal Rayleigh number is stabilizing for both positive and negative values of mass flow. In the nonlinear case, a destabilizing effect is identified at higher mass flow rates. An increase in the heat source has a destabilizing effect. Qualitative changes appear in R_z as the mass flow moves from negative to positive for different internal heat sources.     

Effect of the boundary conditions on convection in a horizontal fluid layer with the Soret contribution

Summary.  In this paper, the phenomenon of natural convection in a horizontal binary fluid layer is studied. The four walls of the cavity are subjected to uniform fluxes of heat. The Soret effect is taken into consideration. The different hydrodynamic boundary conditions applied on the horizontal walls are rigid-rigid, rigid-free and free-free. Based on the parallel flow approach, an analytical solution for the stream function, the temperature and the concentration is established. The numerical results obtained from a finite volume method show a good agreement with those predicted analytically. The system is governed by five control parameters; the aspect ratio of the cavity, A, the Rayleigh number, R _T , the Lewis number, Le, the buoyancy ratio, ϕ, and the lateral heating intensity, α. For given sets of these parameters, the existence of natural and anti-natural flows is discussed. Received March 14, 2002; revised August 5, 2002 Published online: February 10, 2003     

Parameters of wave instability in a boundary layer

The waves developing in a boundary layer during transition from laminar to turbulent flow are investigated experimentally.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 53, No. 4, pp. 624–629, October, 1987.     

Steady convection in a horizontal fluid layer

Summary Steady Rayleigh-Bénard-convection in a rectangular box which is heated from below and cooled from above has been investigated. The onset of convection was calculated using linear Boussinesq equations and a Galerkin method. These calculations have demonstrated the stabilising effect of vertical boundaries. A special differential interferometer served to visualize the flow configurations in gases as well as in silicone oil. The density profiles were measured by means of a laser-differential interferometer with a moving mirror, evaluated quantitatively and compared with previously published results. The test fluids silicone oil (Pr=1780) and nitrogen (Pr=0.71) were chosen to demonstrate the influence of the Pr number both on the onset of convection and on the steady flow pattern at large Ra numbers.

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Stationäre Konvektion in einer horizontalen Flüssigkeitsschicht

Zusammenfassung Es wurde die stationäre Rayleigh-Benard-Konvektion in einem von unten beheizten und an der Oberseite gekühlten rechteckigen Behälter untersucht. Mit Hilfe linearer Boussinesq-Gleichungen und eines Galerkin-Verfahrens wurde das Einsetzen der Konvektion berechnet. Die Rechenergebnisse bestätigen den stabilisierenden Einfluß der vertikalen Berandungen. Ein spezielles Differential-interferometer diente der Sichtbarmachung der Strömungskonfiguration sowohl in Gasen als auch in Silikonöl. Die Dichteprofile wurden mit einem Laser-Differentialinterferometer mit Schwingspiegel gemessen, quantitativ ausgewertet und mit den Ergebnissen anderer Autoren verglichen. Die Versuchsmedien Silikonöl (Pr=1780) und Stickstoff (Pr=0,71) dienten dazu, den Einfluß der Pr-Zahl auf das Einsetzen der Konvektion und auf die stationäre Strömungskonfiguration bei großen Ra-Zahlen zu demonstrieren.

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With 14 Figures     

Unsteady thermal boundary layer flow of a non-newtonian fluid over a flat plate

The transient thermal response of a power law type non-Newtonian, laminar boundary layer flow past a flat plate is investigated. Consideration is given to the case of a step change in surface temperature. The transient heat flux and details of the temperature field are obtained and have been illustrated graphically. The range of Prandtl numbers investigated was 5–1000 while the viscosity index was allowed to vary 0.1–5.0.     

The thermal boundary layer of a non-fourier power-law fluid on a plate with a variable surface temperature

The equation for the thermal boundary layer of a non-Fourier powerlaw fluid on a flat plate with an exponential distribution of surface temperature is reduced to an ordinary equation and solved by the method of finite differences. The effect of the exponent on the temperature profile and on the heat-transfer coefficient is determined. It is demonstrated that the asymptotic solutions of the equation for large are nearly exact.     

Influence of thermal radiation on the laminar boundary layer of a nonabsorbing fluid

The influence of thermal radiation on the laminar boundary layer of a nonabsorbing fluid with variable thermophysical properties flowing around a heat emitting surface is investigated under natural and forced convection conditions.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 6, pp. 1008–1014, June, 1971.     

Viscous fluid flow in a horizontal layee due to thermal inhomogeneity of the lower boundary

The nature of the flow induced in a layer by thermal inhomogeneity of one of the boundaries is determined on the basis of a numerical solution of the complete Navier -Stokes equations. It is found that stable stratification effectively suppresses the generated flow.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 1, pp. 90–93, July, 1981.     

The non-linear evolution of modulated waves in a boundary layer

The series of experiments by Schubauer and Skramstad (1948) provided the first experimental evidence of the role that the instability of Tollmien-Schlichting waves played in the transition of a zero pressure-gradient flat plate boundary layer. The initial experiments studied the oscillations in the boundary layer excited by the freestream fluctuations. This was only possible after the background disturbances in the wind tunnel had been reduced to a very low level. The background wind tunnel environment excited a broad band of amplitude modulated disturbance waves that grew as they propagated downstream, eventually leading to the formation of turbulent spots. Further experiments used artificial two-dimensional harmonic excitation to produce regular wavetrains that could be directly compared with linear theory. Unfortunately, two-dimensional harmonic excitation of this type has also been used in many of the subsequent nonlinear transition investigations; the modulation of the disturbance waves, essential in nonlinear studies, has been largely ignored. Gaster and Grant (1975) used a short duration acoustic pulse to excite the boundary layer and found that the modulated wavepacket that was created admitted bursts of high frequency oscillations. These occurred at amplitudes that were insufficient to generate non-linear behaviour in purely periodic wavetrains. Gaster (1980) suggested that the modulation of the wavepacket played an important role in the non-linear region of transition. This investigation used computer generated deterministic white noise to excite the boundary layer on a flat plate through a single buried loudspeaker. This type of excitation produced amplitude modulated T-S waves at some point downstream from the source. By repeatedly exciting the boundary layer with the same white noise sequence it was possible to map the entire flow-field with a single hot-wire probe and so study the evolution of the modulated wavetrains and the eventual development of turbulent spots. The modulated wavetrains were found to grow initially according to linear theory. But downstream, departures from the linear pattern were observed at isolated time instants. The amplitude of the irregular portions of the signal increased rapidly with downstream distance until bursts of oscillations of frequencies five or six times the basic T-S frequency were observed. These regions developed even higher frequency bursts until a turbulent spot could be considered to have formed. Excitation signals of various amplitudes with different phase relations between the spectral components were used in these experiments. It was found that the phases between the Fourier components played an important role in the highly non-linear behaviour that is the precursor to a turbulent spot. Novel signal processing techniques, such as the wavelet transform and Singular Value Decomposition were used to investigate the fine structure and the propagation characteristics of the high frequency disturbances.     

Laminar thermal boundary layer on a continuous accelerated sheet extruded in an ambient fluid

Summary Exact boundary layer similarity solutions are developed for flow, friction and heat transfer on a continuously accelerated sheet extruded in an ambient fluid of a lower temperature.Melt-spinning, polymer and glass industries and the cooling of extruded metallic plates are practical applications of this problem.Results for skin-friction and heat-transfer coefficients are given. Larger acceleration is accompanied by larger skin-friction and heat-transfer coefficients. Rapid cooling of the sheet is accompanied by a larger Nusselt number.Nomenclature sheet width - c dimensionless constant - c _f local skin friction coefficient - F dimensionless transformed stream function - G dimensionless transformed temperature - local heat transfer coefficient - fluid thermal conductivity - length of deformation zone - m exponent of surface speed variation - q exponent of surface temperature variation - T dimensionless temperature - sheet surface temperature - solidification temperature - ambient temperature - sheet thickness - u velocity component along the sheet - u _s sheet surface velocity - wind up velocity - v velocity component normal to the sheet - x dimensionless coordinate along the sheet - y dimensionless coordinate normal to the sheet - Nu Nusselt number, - Pr Prandtl number, - Re Reynolds number, - =Re^–0.5 - dimensionless similarity coordinate - dynamic viscosity - kinematic viscosity - fluid mass density - sheet mass density - wall shear stress - dimensionless stream function With 3 Figures     

Interferometer investigation of convection in a horizontal fluid layer

The temperature field in free convective motion of a non-Newtonian fluid is studied by using an interferometer. A method of constructing the flow pattern by means of the interferograms obtained is developed.     

Oscillatory instability of convective motion in a horizontal layer of gas

Results of an experimental investigation of oscillatory subcritical motion in horizontal layers of gas of different geometrical dimensions when there is loss of stability in steady roll-shaped flow are presented.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 1, pp. 63–68, January, 1976.