scholarly journals Finite amplitude thermal convection with spatially modulated boundary temperatures

1995 ◽  
Vol 449 (1937) ◽  
pp. 459-478 ◽  
Keyword(s):  
Stability Analysis ◽  
Thermal Convection ◽  
Fluid Layer ◽  
Perturbation Technique ◽  
Lower Boundary ◽  
Finite Amplitude ◽  
Resonant Wavelength ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
One Dimensional

Finite amplitude thermal convection in a fluid layer between two horizontal walls with different fixed mean temperatures is considered when spatially modulated temperatures with amplitudes L 1 * and L u * are prescribed at the lower and upper walls, respectively. The nonlinear steady problem is solved by a perturbation technique, and the preferred mode of convection is determined by a stability analysis. In the case of a resonant wavelength excitation, regular or non-regular multi-modal pattern convection can be preferred for some ranges of L 1 * and L u *, provided the wave vectors for such patterns are contained in a certain subset of the wave vectors representing a linear combination of modulated upper and lower boundary temperatures. In the case of non-resonant wavelength excitation, a three (two) dimensional solution in the form of multi-modal (rolls) pattern convection can be preferred, even if the boundary modulations are one (two) or two (one) dimensional, provided the wavelengths of the modulations are not too small. Heat transported by convection can be enhanced by boundary modulations in some ranges of L 1 * and L u *.

Nonlinear thermal convection with finite conducting boundaries

1985 ◽  
Vol 152 ◽  
pp. 113-123 ◽  
Author(s):  
N. Riahi
Keyword(s):  
Stability Analysis ◽  
Prandtl Number ◽  
Thermal Convection ◽  
Perturbation Technique ◽  
Three Dimensional ◽  
Horizontal Layer ◽  
Finite Amplitude ◽  
Two Dimensional ◽  
Convection Pattern ◽  
Square Cells

Finite-amplitude thermal convection in a horizontal layer with finite conducting boundaries is investigated. The nonlinear steady problem is solved by a perturbation technique, and the preferred mode of convection is determined by a stability analysis. Square cells are found to be the preferred form of convection in a semi-infinite three-dimensional region Ω in the (γb,γt, P)-space (γb and γt are the ratios of the thermal conductivities of the lower and upper boundaries to that of the fluid and P is the Prandtl number). Two-dimensional rolls are found to be the preferred convection pattern outside Ω. The dependence on γb, γt and P of the heat transported by convection is computed for the various solutions analysed in the paper.

von Neumann Stability Analysis of a Segregated Pressure-Based Solution Scheme for One-Dimensional and Two-Dimensional Flow Equations

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Santosh Konangi ◽  
Nikhil K. Palakurthi ◽  
Urmila Ghia
Keyword(s):  
Stability Analysis ◽  
Euler Equations ◽  
Two Dimensional ◽  
Von Neumann ◽  
One Dimensional ◽  
Flow Equations ◽  
Solution Scheme ◽  
Von Neumann Stability ◽  
The Stability ◽  
Stability Limits

The goal of this paper is to derive the von Neumann stability conditions for the pressure-based solution scheme, semi-implicit method for pressure-linked equations (SIMPLE). The SIMPLE scheme lies at the heart of a class of computational fluid dynamics (CFD) algorithms built into several commercial and open-source CFD software packages. To the best of the authors' knowledge, no readily usable stability guidelines appear to be available for this popularly employed scheme. The Euler equations are examined, as the inclusion of viscosity in the Navier–Stokes (NS) equation serves to only soften the stability limits. First, the one-dimensional (1D) Euler equations are studied, and their stability properties are delineated. Next, a rigorous stability analysis is carried out for the two-dimensional (2D) Euler equations; the analysis of the 2D equations is considerably more challenging as compared to analysis of the 1D form of equations. The Euler equations are discretized using finite differences on a staggered grid, which is used to achieve equivalence to finite-volume discretization. Error amplification matrices are determined from the stability analysis, stable and unstable regimes are identified, and practical stability limits are predicted in terms of the maximum allowable Courant–Friedrichs–Lewy (CFL) number as a function of Mach number. The predictions are verified using the Riemann problem, and very good agreement is obtained between the analytically predicted and the “experimentally” observed CFL values. The successfully tested stability limits are presented in graphical form, as compared to complicated mathematical expressions often reported in published literature. Since our analysis accounts for the solution scheme along with the full system of flow equations, the conditions reported in this paper offer practical value over the conditions that arise from analysis of simplified 1D model equations.

Analysis of Conduction-Controlled Rewetting of a Vertical Surface

1975 ◽  
Vol 97 (2) ◽  
pp. 161-165 ◽  
Author(s):  
C. L. Tien ◽  
L. S. Yao
Keyword(s):  
Initial Temperature ◽  
Empirical Relation ◽  
Vertical Surface ◽  
Dimensionless Temperature ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Functional Relationships ◽  
Semi Empirical ◽  
Biot Numbers

The present paper presents a two-dimensional analysis of conduction-controlled rewetting of a vertical surface, whose initial temperature is greater than the rewetting temperature. The physical model consists of an infinitely extended vertical slab with the surface of the dry region adiabatic and the surface of the wet region associated with a constant heat transfer coefficient. The physical problem is characterized by three parameters: the Peclet number or the dimensionless wetting velocity, the Biot number, and a dimensionless temperature. Limiting solutions for large and small Peclet numbers obtained by utilizing the Wiener-Hopf technique and the kernel-substitution method exhibit simple functional relationships among the three dimensionless parameters. A semi- empirical relation has been established for the whole range of Peclet numbers. The solution for large Peclet numbers possesses a functional form different from existing approximate two-dimensional solutions, while the solution for small Peclet numbers reduces to existing one-dimensional solution for small Biot numbers. Discussion of the present findings has been made with respect to previous analyses and experimental observations.

A modified two-dimensional triangular lattice model under honk environment

2020 ◽  
Vol 31 (06) ◽  
pp. 2050089
Author(s):  
Cong Zhai ◽  
Weitiao Wu
Keyword(s):  
Stability Analysis ◽  
Hydrodynamic Model ◽  
High Dimensional ◽  
Two Dimensional ◽  
Lattice Hydrodynamic Model ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The Stability ◽  
Honk Effect ◽  
Real Traffic

The honk effect is not uncommon in the real traffic and may exert great influence on the stability of traffic flow. As opposed to the linear description of the traditional one-dimensional lattice hydrodynamic model, the high-dimensional lattice hydrodynamic model is a gridded analysis of the real traffic environment, which is a generalized form of the one-dimensional lattice model. Meanwhile, the high-dimensional traffic flow exposed to the open-ended environment is more likely to be affected by the honk effect. In this paper, we propose an extension of two-dimensional triangular lattice hydrodynamic model under honk environment. The stability condition is obtained via the linear stability analysis, which shows that the stability region in the phase diagram can be effectively enlarged under the honk effect. Modified Korteweg–de Vries equations are derived through the nonlinear stability analysis method. The kink–antikink solitary wave solution is obtained by solving the equation, which can be used to describe the propagation characteristics of density waves near the critical point. Finally, the simulation example verifies the correctness of the above theoretical analysis.

Subjektive politische Strukturen in der Deutschschweiz

2001 ◽  
Vol 60 (3) ◽  
pp. 192-201 ◽  
Author(s):  
Wolfgang Marx ◽  
Linda Stähli
Keyword(s):  
Political Parties ◽  
Multidimensional Scaling ◽  
Nonmetric Multidimensional Scaling ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
One Dimensional ◽  
Sorting Data ◽  
Association Data

This article attempts to explore, via nonmetric multidimensional scaling (NMDS), the subjective structure of Swiss political parties. Free associations and hierarchical sortings of students are analyzed. The association data is described best by a one-dimensional MINISSA-solution showing the dimension left-right. The sorting data leads to a two-dimensional solution showing the dimension left-right and radicality. Differences and similarities to previous studies in Germany ( Marx & Läge, 1995 ) are discussed.

Numerical and Analytical Solutions for Two-Dimensional Gas Distribution in Gas-Loaded Heat Pipes

1989 ◽  
Vol 111 (3) ◽  
pp. 598-604 ◽  
Author(s):  
P. F. Peterson ◽  
C. L. Tien
Keyword(s):  
Heat Pipes ◽  
Computational Effort ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Gas Distribution ◽  
Dimensional Solution ◽  
Integral Analysis ◽  
One Dimensional ◽  
Wide Range ◽  
Design Calculations

This work presents a two-dimensional axisymmetric diffusion model for the non-condensable gas distribution in gas-loaded heat pipes and thermosyphons. The new model, based on an integral analysis, has major advantages over existing, computationally time consuming, two-dimensional models. It has equal accuracy while using only the computational effort required for the cruder one-dimensional model, and also includes the effects of wall conduction and spatial variation of the condenser heat transfer coefficient. To simplify design calculations further an analytic two-dimensional solution is established, which gives excellent results over a wide range of parameters.

Finite Amplitude Longitudal Convection Rolls in an Inclined Layer

1973 ◽  
Vol 95 (3) ◽  
pp. 407-408 ◽  
Author(s):  
R. M. Clever
Keyword(s):  
Fluid Layer ◽  
Horizontal Layer ◽  
Finite Amplitude ◽  
Two Dimensional ◽  
Governing Equations ◽  
Inclined Layer ◽  
Experimental Heat ◽  
Inclined Fluid Layer ◽  
Longitudinal Coordinate ◽  
Convection Rolls

For the case of a large Prandtl number, buoyancy driven flow in an inclined fluid layer, it is shown that all longitudinal-coordinate-independent solutions of the governing equations are obtainable from a knowledge of the existing results for two-dimensional convection in a horizontal layer, heated from below. The rescaling here yields results which compare favorably with those of existing experimental heat transport values.

Two-Dimensional Analysis of Conduction-Controlled Rewetting With Precursory Cooling

1976 ◽  
Vol 98 (3) ◽  
pp. 407-413 ◽  
Author(s):  
S. S. Dua ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Dimensional Analysis ◽  
Vertical Surface ◽  
Dimensionless Temperature ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
One Dimensional ◽  
The One

This paper presents a two-dimensional analysis of the effect of precursory cooling on conduction-controlled rewetting of a vertical surface, whose initial temperature is higher than the sputtering temperature. Precursory cooling refers to the cooling caused by the droplet-vapor mixture in the region immediately ahead of the wet front, and is described mathematically by two dimensionless constants which characterize its magnitude and the region of influence. The physical model developed to account for precursory cooling consists of an infinitely extended vertical surface with the dry region ahead of the wet front characterized by an exponentially decaying heat flux and the wet region behind the moving film-front associated with a constant heat transfer coefficient. Apart from the two dimensionless constants describing the extent of precursory cooling, the physical problem is characterized by three dimensionless groups: the Peclet number or the dimensionless wetting velocity, the Biot number and a dimensionless temperature. Limiting solutions for large and small Peclet numbers have been obtained utilizing the Wiener-Hopf technique coupled with appropriate kernel substitutions. A semiempirical matching relation is then devised for the entire range of Peclet numbers. Existing experimental data with variable flow rates at atmospheric pressure are very closely correlated by the present model. Finally a comparison is drawn between the one-dimensional limit of the present analysis and the corresponding one-dimensional solution obtained by treating the dry region ahead of the wet front characterized by an exponentially decaying heat transfer coefficient.

Rolls versus squares in thermal convection of fluids with temperature-dependent viscosity

1987 ◽  
Vol 178 ◽  
pp. 491-506 ◽  
Author(s):  
D. R. Jenkins
Keyword(s):  
Thermal Convection ◽  
Fluid Layer ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Temperature Dependent Viscosity ◽  
Weakly Nonlinear ◽  
Expansion Procedure ◽  
The Stability ◽  
Dependent Viscosity

We consider finite-amplitude thermal convection, in a horizontal fluid layer. The viscosity of the fluid is dependent upon its temperature. Using a weakly nonlinear expansion procedure, we examine the stability of two-dimensional roll and three-dimensional square planforms, in order to determine which should be preferred in convection experiments. The analysis shows that the roll planform is preferred for low values of the ratio of the viscosities at the top and bottom boundaries, but the square planform is preferred for larger values of the ratio. At still larger values, subcritical convection is predicted. We also include the effects of boundaries having finite thermal conductivity, which enables favourable comparison to be made with experimental studies. A discrepancy between the present work and a previous study of this problem (Busse & Frick 1985) is discussed.

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