Onset Of Stability Research Articles

Effect of noninertial acceleration on heat transfer by Rayleigh–Bénard magnetoconvection: Exploring nonlinear dynamics

AbstractBuoyancy‐driven Rayleigh–Bénard convection in the presence of a magnetic field, rotation, and temperature‐dependent viscosity has applications in the field of crystal growth, space laboratory experiments, and atmospheric convection. It also has potential applications in heat transfer and magnetohydrodynamics, which can occur in planetary and stellar interiors. The present work aims to study the combined effect of magnetic fields and rotation on the onset of Rayleigh–Bénard convection in temperature‐dependent viscosity Newtonian liquids with internal heat sources/sinks. Both linear and weak nonlinear stability analyses of convection are performed in the problem. The minimal representation of the Fourier series for the stream function and the magnetic potential allows us to derive the analytical expression for the thermal Rayleigh number () and the generalized Lorenz model. In linear theory, the critical Rayleigh number and the wave number are tabulated for different values of the Chandrasekhar number (), the Taylor number (), and the thermorheological parameter (), and the onset of stability is analyzed. It is found that the instability manifests at when for stress‐free and isothermal boundaries. In nonlinear theory, the generalized Lorenz model obtained is not amenable to analytical treatment; therefore, the classical fourth‐order Runge–Kutta method is applied to solve the Lorenz model. It is found that the internal Rayleigh number, the thermorheological parameter, and the Taylor number influence the onset of convection and heat transfer coefficient. It is also demonstrated that the joint increase in rotational force and magnetic field strength stabilizes the system strongly, thereby reducing heat transfer. However, increasing the heat source and the variable viscosity parameter have antagonistic influences.

Swirl flow stability: thermodynamic analysis and experiments

The current paper presents a theoretical analysis of swirl flow stability, both inside a tube (vortex tube) and in a free annular swirl flow. The starting concept is the study of the evolution of velocity and temperature fluctuations. Methods of non-equilibrium thermodynamics are used to describe the magnitude of fluctuations and their properties. The important role of the total enthalpy follows from a variational analysis. Moreover, the thermodynamic criterion of the stability is formulated using the total enthalpy, and compared with experiments, numerical results and classical Rayleigh theory support its applicability. It was shown that the solid body vortex is at the margin of stability, which is experimentally observed. Analogously, the potential vortex is by the thermodynamic criterion stable; however, by the Rayleigh criteria it is on the onset of stability. The classical Taylor experiment of flow between two rotating cylinders is analysed from the point of view of this criterion. These results are underlined by swirl tube experiments at the Institute of Aerospace Thermodynamics at Stuttgart University and the annular nozzle experiments performed in the Institute of Thermomechanics CAS in Prague. Both independent experiments confirm the transformation of the initial annular vortex into a stable potential-type vortex. The results of this theory can also be used to explain the exceptional stability of tropical cyclones.

Аналіз та тенденції розвитку ринку праці України

The issue of analyzing the labor market and determining trends in its development in modern conditions is the subject of constant scientific interest and the basis of frequent discussions. It is determined that despite the large number of studies, today these issues are relevant and important and constantly require further analysis and additional research. The article considers the current trends in the development of the labor market. The main indicators of employment are analyzed. It has been determined that current security and energy independence issues will require conceptual state reforms, therefore there is a need for qualified civil servants and administrators, whose knowledge and skills will be useful to overcome post-war crises and the onset of stability in the country, which in turn is not possible without quality education.

Onset of stability and heat transfer by Rayleigh-Bénard magnetoconvection with variable viscosity effect using Ginzburg-Landau model: Effect of thermal/gravity modulation

In modulating the commencement of Rayleigh-Bénard convection, thermal/gravitational modulation refers to its promising uses in various technical and scientific disciplines, including crystal formation, space laboratory research, and atmospheric convection. The aim of the study is to demonstrate the effect of thermal/gravitational modulation on the onset of stability and heat transfer of the Rayleigh-Bénard magnetoconvection with variable viscosity. The disturbance produced by the thermal/gravitational modulation is expanded in terms of the power series of the amplitude of the convection, and a non-autonomous Ginzburg-Landau equation is derived. The numerical solution of the Ginzburg-Landau equation is obtained using the classical Runge-Kutta method, which helps to determine the necessary amplitudes for the quantification of heat transfer. The examination of the data demonstrates that the commencement of convection and heat transfer can be advanced or suppressed by appropriately adjusting the problem’s parameters. The issue also shows how different parameters affect the Nusselt number, which measures the heat transfer coefficient.

Pattern formation revisited within nonequilibrium thermodynamics: Burgers'-type equation.

We revisit the description of reaction-diffusion phenomena within nonequilibrium thermodynamics and investigate the role of a nonstandard splitting of the entropy balance into the entropy production and the divergence of entropy flux. As previously reported by Pavelka et al. (Int J Eng Sci 78:192-217, 2014), a new term is identified following from the kinetic energy of diffusion. This newly appearing term acts as a thermodynamic force driving the reaction kinetics. Using the standard constitutive relations within the linear nonequilibrium thermodynamics, the governing equations for a reaction-diffusion problem in a two-species system are derived. They turn out to be linked to Burgers' equation. It is shown that the onset of stability is not altered, but a non-periodic pattern can emerge. The latter follows from the relation of the governing equation to Burger's equation with a source term. Hence, transients formed by glued and merging parabolic profiles are expected to appear at least in certain parameter regimes. We explore the significance of this effect and observe that for a comparable magnitude of the diffusion and of the new term stemming from the kinetic energy of diffusion, the solution is expected to be linked to the saw-tooth like solution to Burger's equation rather than to the eigenmodes of the Laplacian. We conclude that the reaction-diffusion model proposed by Turing is robust to the addition of this effect of the kinetic energy of diffusion, at least when this new term is sufficiently small. As the governing equations can be rewritten into the classical reaction-diffusion problem but with reaction kinetics outside of the classical law of mass action, the analysis presented in this study suggests that a yet richer behaviour of the classical reaction-diffusion problems can be expected, if nonstandard reaction kinetics are considered.

STABILITY OF VISCOUS FLOW IN A CURVED CHANNEL WITH RADIAL TEMPERATURE GRADIENT

In this paper, the stability of Dean’s problem in the presence of a radial temperature gradient is studied for narrow gap case. The analytical solution of the eigen value problem is obtained by using the Galerkin’s method. The critical values of parameters and Λ are computed, where  is wave number and Λ is a parameter determining the onset of stability from the obtained analytical expressions for the first, second and third approximations. It is found that the difference between the numerical values of critical Λ corresponding to the second and third approximations is very small as compared to the difference between first and second approximations. The critical values of Λ obtained by the third approximation agree very well with the earlier results computed numerically by using the finite difference method. This clearly indicates that for the better result one should obtain the numerical values by taking more terms in approximation. Also, the amplitude of the radial velocity and the cell-patterns are shown on the graphs for different values of the parameter M, which depends on difference of temperatures of outer cylinder to the inner one i.e. on (), where is the temperature of inner cylinder and  is the temperature of outer cylinder.

Role of Counterion Association in Colloidal Stability

A generalized model for colloidal stability has been validated against experimentally measured values of Fuchs stability ratio and critical coagulation concentration (ccc) for electrolytes with mono- or divalent cation, i.e., potassium chloride and magnesium chloride, respectively. Besides the classical DLVO theory, the generalized model accounts for the interplay between colloidal interactions and the association of cations with the particles surface charge groups. The model parameters are either obtained or estimated purely on the basis of independent information available in the literature. For the monovalent salt, the predictions agree well with literature experimental data, forecasting both the ccc values and stability ratios quantitatively. For the divalent salt the predictions for large values of the stability ratio tend to deviate from the experimental data produced in this work, but it is noted that the onset of stability, i.e., the ccc, and small stability ratios are correctly predicted. Moreover, a comparison of the above results with those neglecting the effect of counterion association with the particles surface charge groups indicates that the latter substantially overestimates stability ratios in the presence of high salt concentration in the case of the monovalent salt, and leads to unrealistic large values of the ccc for the divalent salt. Including the association of cations with the particles surface charge groups can explain the relatively low values of experimental ccc for divalent salts compared to the theoretical predictions by the classical DLVO theory neglecting ion association, which is apoint of interest in industrial coagulation processes.

Hydrodynamics of compressible liquids: Influence of the piston effect on convection and internal gravity waves

The onset of stability in strongly compressible liquid with fixed volume is found by linear stability analysis. The results coincide with those at fixed pressure proving thereby that the piston effect does not influence the onset of convection. However, the dynamic phenomenon of internal gravity waves essentially depends on the piston effect.

The effect of thermal relaxation time on a electrohydrodynamic viscoelastic fluid layer heated from below

The problem of the onset of stability in a horizontal layer of a viscoelastic dielectric liquid with one relaxation time heated from below under the action of a vertical ac electric field is analyzed. Linear stability theory is used to derive an eigenvalue system of order eight 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. The critical Rayleigh number and wave number for the onset of instability are presented graphically as functions of the Grashof number for various values of the Prandtl number and one relaxation time. A comparison is made with the results obtained in the absence of an electric field. PACS No.: 47.27.T

The effect of microstructure on the thermal convection in a rectangular box of fluid heated from below

The effect of microstructure on the thermal convection in a rectangular box of fluid heated from below has been investigated by applying the micropolar fluid theory. The influence of lateral walls on the convection process in a rectangular box has been determined. The Galerkin method has been employed to get an approximate solution for the eigenvalue problem. The beam functions which satisfy two boundary conditions on each rigid surface have been used to construct the finite roll (cells with two nonzero velocity components depend on all three spatial variables) trial functions for the Galerkin method. The effect of variations of material parameters at the onset of convection has been presented graphically. It is observed that as the distance between the lateral walls increases the effect of one of the material parameters, characterizing the spin-gradient viscosity, at the onset of stability diminishes. A comparison has been made with the corresponding results for a Newtonian fluid.

Critical sizes for stable multiply charged CO 2 clusters

Because of Coulomb explosion, multiply charged clusters (CO 2) z+ n are observed in mass spectra only if their size n exceeds a critical value which has been determined as n z∗ = 44, 108 and 216 for doubly, triply and quadruply charged clusters, respectively. The onset of stability above n z∗ occurs abruptly

Effects of radiation and convective boundary conditions on the stability of fluid in an inclined slender slot

The neutral stability of an absorbing, emitting, scattering, nongray viscous fluid contained inside an inclined slender slot and subjected to convective boundary conditions is examined for inclination from 0¬į to 180¬į. The modified P-1 approximation (Eddington approximation) is employed for the radiation part of the problem. The effects of the Biot numbers h 1 and H 2 at the lower and upper surfaces, the conduction-to-radiation parameter, N, optical thickness ŌĄ 0 , single scattering albedo ŌČ, the wall emissivities őĶ 1 and őĶ 2 , the nongrayness factor ő∑ and the inclination angle őī on the onset of stability in gases are determined for both the longitudinal and transverse vortex rolls. The results show that radiation besides its stabilizing effect significantly shifts the transition angle for cross over from the transverse to the longitudinal rolls towards horizontal. Pour une inclinaison variant entre 0¬į et 180¬į, on √©tudie la stabilit√© neutre d'un fluide visqueux absorbant √©missif, diffusant et non-gris contenu dans une cavit√© allong√©e et soumise √† des conditions aux limites de convection. L'approximation modifi√©e P-1 (approximation d'Eddington) est utilis√©e. On d√©termine √† la fois pour les rouleaux tourbillonnaires longitudinaux et transverses, les effets des nombres de Biot H 1 , et H 2 sur les surfaces, du param√®tre conduction-rayonnement N, de l'√©paisseur optique ŌĄ 0 , de l'albedo de diffusion ŌČ, des √©missivit√®s őĶ 1 , et őĶ 2 , du facteur ő∑ et de l'angle d'inclinaison őī, sur les conditions de stabilit√© dans les gaz. Les r√©sultats montrent que le rayonnement, outre son effet stabilisant, d√©place nettement l'angle correspondant au basculement des tourbillons. Es wird die neutrale Stabilit√§t eines absorbierenden, emittierenden, streuenden, nicht-grauen viskosen Fluides untersucht, welches sich innerhalb eines geneigten Spalts befindet und konvektiven Randbedingungen ausgesetzt ist. Die Neigung betr√§gt 0¬į bis 180¬į. Zur L√∂sung des Strahlungsproblems wird die modifizierte P-1 Approximation (Eddington Approximation) eingesetzt. Die Einfl√ľsse der Biot-Zahlen H 1 und H 2 f√ľr die untere und obere Grenzfl√§che, des Verh√§ltnisses von Leitung zu Strahlung N, der optischen Dicke ŌĄ 0 , des Reflexionswinkels ŌČ der einfachen Streuung, der Emissivit√§ten őĶ 1 , und őĺ 2 der Wand, des Faktors ő∑ f√ľr die Abweichung vom grauen Strahler und des Neigungswinkels őī auf das Einsetzen der Stabilit√§t in Gasen werden f√ľr longitudinale und transfersale Wirbelrollen bestimmt. Die Ergebnisse zeigen, daő≤ die Strahlung neben ihrer stabilisierenden Wirkung vor allem den √úbergangswinkel f√ľr den Umschlag von transversalen zu longitudinalen Wirbelrollen in Richtung der Horizontalen verschiebt. –ėcc–Ľe–īye—āc—Ź –Ĺe–Ļ—āpa–Ľ—Ć–Ĺa—Ź yc—āo–Ļ—á–ł–≤oc—ā—Ć –Ņo–≥–Ľo—Ča—é—Če–Ļ, o—āpa–∂a—é—Če–Ļ –ł pacce–ł–≤a—é—Če–Ļ –Ĺecepo–Ļ –≤—Ź–∑–ļo–Ļ –∂–ł–ī–ļoc—ā–ł –≤ y–∑–ļo–ľ –∑a–∑ope –Ĺa–ļ–Ľo–Ĺ–Ĺo–≥o –ļa–Ĺa–Ľa –≤ –ī–ła–Ņa–∑o–Ĺe y–≥–Ľo–≤ o—ā 0 –īo 180¬į –Ņp–ł –≥pa–Ĺ–ł—á–Ĺ—č—á yc–Ľo–≤–ł—Ź—á —āpe—ā—Će–≥o po–īa. –üpo—Üecc –ł–∑–Ľy—áe–Ĺ–ł—Ź y—á–ł—ā—č–≤a–Ľc—Ź c –Ņo–ľo—Č—Ć—é –ľo–ī–ł—Ą–ł—Ü–łpo–≤a–Ĺ–Ĺo–≥o P-I –Ņp–ł–Ī–Ľ–ł–∂e–Ĺ–ł—Ź (–Ņp–ł–Ī–Ľ–ł–∂e–Ĺ–łe –≠–ī–ī–ł–Ĺ–≥—āo–Ĺa). O–Ņpe–īe–Ľ—Ź–Ľoc—Ć –≤–Ľ–ł—Ź–Ĺ–łe —á–łce–Ľ –Ď–ło, H 1 –ł H 2 , –ī–Ľ—Ź –Ĺ–ł–∂–Ĺe–Ļ –ł –≤ep—á–Ĺe–Ļ –Ņo–≤ep—á–Ĺoc—āe–Ļ, –Ľy—á–łc—āo-–ļo–Ĺ–īy–ļ—ā–ł–≤–Ĺo–≥o –Ņapa–ľe—āpa N, o–Ņ—ā–ł—áec–ļo–Ļ —āo–Ľ—Č–ł–Ĺ—č ŌĄ 0 , e–ī–ł–Ĺ–ł—á–Ĺo–≥o –ļo—ć—Ą—Ą–ł—Ü–łe–Ĺ—āa –ī–ł—Ą—Ąy–∑–Ĺo-pacce–ł–≤a—é—Če–≥o o—āpa–∂e–Ĺ–ł—Ź co, –ļo—ć—Ą—Ą–ł—Ü–łe–Ĺ—āo–≤ –ł–∑–Ľy—áe–Ĺ–ł—Ź c—āe–Ĺo–ļ sP 1 –ł őĶ 2 , –ļo—ć—Ą—Ą–ł—Ü–łe–Ĺ—āa –Ĺecepo–≥o –ł–∑–Ľy—áe–Ĺ–ł—Ź ő∑ –ł y–≥–Ľa –Ĺa–ļ–Ľo–Ĺa őī –Ĺa –≤o–∑–Ĺ–ł–ļ–Ĺo–≤e–Ĺ–łe yc—āo–Ļ—á–ł–≤oc—ā–ł –≤ –≥a–∑a—á –ļa–ļ –ī–Ľ—Ź –Ņpo–īo–Ľ—Ć–Ĺ—č—á, —āa–ļ –ł –Ņo–Ņepe—á–Ĺ—č—á –≤–ł—ápe–≤—č—á –≤a–Ľo–≤. Pe–∑y–Ľ—Ć—āa—ā—č c–≤–ł–īe—āe–Ľ—Ćc—ā–≤y—é—ā o —āo–ľ, —á—āo –Ņo–ľ–ł–ľo c—āa–Ī–ł–Ľ–ł–∑–łpy—é—Če–≥o –≤o–∑–īe–Ļc—ā–≤–ł—Ź –ł–∑–Ľy—áe–Ĺ–łe cy—Čec—ā–≤e–Ĺ–Ĺo c–ľe—Čae—ā –ļ –≥op–ł–∑o–Ĺ—āa–Ľ–ł y–≥o–Ľ, –Ņp–ł –ļo—āopo–ľ –Ņpo–łc—áo–ī–ł—ā –Ņepe—áo–ī –Ņo–Ņepe—á–Ĺ—č—á –≤a–Ľo–≤ –≤ –Ņpo–īo–Ľ—Ć–Ĺ—če.