One dimensional vertical infiltration

Soil Research ◽  
1972 ◽  
Vol 10 (2) ◽  
pp. 143 ◽  
Author(s):  
T Talsma ◽  
J Parlange
Keyword(s):  
Hydraulic Conductivity ◽  
Boundary Conditions ◽  
Soil Properties ◽  
Field Data ◽  
Large Time ◽  
Three Dimensional ◽  
Time Interval ◽  
Large Time Interval ◽  
One Dimensional ◽  
Field Soils

Various concise equations have been proposed, and used, to describe the dynamics of one-dimensional, vertical, infiltration into uniform soils. Such equations, even when initial and boundary conditions are satisfied, do not describe infiltration with equal accuracy for all materials, especially when applied over a large time interval. Recently proposed equations appear more reliable and require only two, easily measurable, soil properties, viz., sorptivity and hydraulic conductivity, for application in most practical situations. Numerical, laboratory, and field data are presented. These adequately support the reliability of the solutions. The applicability of the solutions to field soils with systematically varying conductivity is more restricted than the two- or three-dimensional solutions.

Infiltration from semi-circular furrows in the field

Soil Research ◽  
1969 ◽  
Vol 7 (3) ◽  
pp. 277 ◽  
Author(s):  
T Talsma
Keyword(s):  
Hydraulic Conductivity ◽  
Spatial Variability ◽  
Soil Properties ◽  
Qualitative Agreement ◽  
One Dimensional ◽  
Infiltration Rates ◽  
Cumulative Infiltration ◽  
Field Soils ◽  
Gravity Effects ◽  
High Hydraulic Conductivity

Experiments on a number of field soils have provided data to check the applicability of recently proposed theory on infiltration from semi-circular furrows. Although spatial variability of soil properties was rather high, the theoretical solutions adequately described cumulative infiltration. The effect of gravity on flow, which is dependent on furrow radius and the ratio of hydraulic conductivity to sorptivity, is not necessarily greatest in soils of high hydraulic conductivity. In most soils gravity effects were pronounced. Qualitative agreement was found between the observed advance of wet fronts and those the theory predicts. Steeper moisture gradients exist near the furrow than would occur near the surface during one-dimensional flow in the same soil. Some factors of relevance to furrow irrigation, and estimation of final infiltration rates from 'short furrow' tests, are discussed.

Microprocessor Silicon Die Temperature Prediction by Simplified Boundary Conditions

2015 ◽  
Author(s):  
Koji Nishi ◽  
Tomoyuki Hatakeyama ◽  
Shinji Nakagawa ◽  
Masaru Ishizuka
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Thermal Resistance ◽  
Hot Spot ◽  
Three Dimensional ◽  
Thermal Design ◽  
Target Temperature ◽  
One Dimensional ◽  
Thermal Network

The thermal network method has a long history with thermal design of electronic equipment. In particular, a one-dimensional thermal network is useful to know the temperature and heat transfer rate along each heat transfer path. It also saves computation time and/or computation resources to obtain target temperature. However, unlike three-dimensional thermal simulation with fine pitch grids and a three-dimensional thermal network with sufficient numbers of nodes, a traditional one-dimensional thermal network cannot predict the temperature of a microprocessor silicon die hot spot with sufficient accuracy in a three-dimensional domain analysis. Therefore, this paper introduces a one-dimensional thermal network with average temperature nodes. Thermal resistance values need to be obtained to calculate target temperature in a thermal network. For this purpose, thermal resistance calculation methodology with simplified boundary conditions, which calculates thermal resistance values from an analytical solution, is also introduced in this paper. The effectiveness of the methodology is explored with a simple model of the microprocessor system. The calculated result by the methodology is compared to a three-dimensional heat conduction simulation result. It is found that the introduced technique matches the three-dimensional heat conduction simulation result well.

Long-Time Solutions to Heat-Conduction Transients with Time-Dependent Inputs

1980 ◽  
Vol 102 (1) ◽  
pp. 115-120 ◽  
Author(s):  
H. T. Ceylan ◽  
G. E. Myers
Keyword(s):  
Heat Conduction ◽  
Lower Cost ◽  
Piecewise Linear ◽  
Three Dimensional ◽  
Linear Functions ◽  
Time Dependent ◽  
Time Interval ◽  
Piecewise Linear Functions ◽  
One Dimensional ◽  
Long Time

An economical method for obtaining long-time solutions to one, two, or three-dimensional heat-conduction transients with time-dependent forcing functions is presented. The conduction problem is spatially discretized by finite differences or by finite elements to obtain a system of first-order ordinary differential equations. The time-dependent input functions are each approximated by continuous, piecewise-linear functions each having the same uniform time interval. A set of response coefficients is generated by which a long-time solution can be carried out with a considerably lower cost than for conventional methods. A one-dimensional illustrative example is included.

scholarly journals Effect of Vertical Pressure on Horizontal and Vertical Permeability of Soil and Effect of Surcharge Pressure on 3D Consolidation of Soil

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Arpan Laskar ◽  
Sujit Kumar Pal
Keyword(s):  
Soil Properties ◽  
Three Dimensional ◽  
Vertical Pressure ◽  
Soil Layers ◽  
One Dimensional ◽  
Consolidation Theory ◽  
Vertical Permeability ◽  
Homogeneous Soil ◽  
Soil Changes

Permeability and consolidation of soil are known as the most variable soil properties. The values of permeability and consolidation of soil may vary with depth even in case of homogeneous soil layers, and because of that, the determination of appropriate values of permeability and consolidation is a complex and complicated engineering task. In this study, horizontal and vertical permeability apparatus and a 3D (three-dimensional) consolidation apparatus are developed to determine the effects of vertical pressure on horizontal and vertical permeability and the effects of vertical surcharge pressures on three-dimensional consolidation of soil. A series of horizontal and vertical permeability tests of soil under different vertical pressures and a series of 3D consolidation tests under different surcharge pressures are performed. From the study, it is observed that the horizontal and vertical permeability of soil changes with the changes in vertical pressures, and 3D consolidation of soil also changes with the changes in surcharge pressures. The horizontal and vertical permeability values obtained from the newly developed horizontal and vertical permeability apparatus are used in Terzaghi’s one-dimensional consolidation theory to find out the consolidation characteristics of the soil, and it is compared with the results obtained from the newly developed 3D consolidation apparatus.

Surface-directed multi-dimensional wave structures in confined binary mixtures

2015 ◽  
Vol 04 (04) ◽  
pp. 1550023
Author(s):  
Igor B. Krasnyuk
Keyword(s):  
Boundary Conditions ◽  
Binary Mixtures ◽  
Large Time ◽  
Three Dimensional ◽  
Polymer Chains ◽  
Initial Value ◽  
Nonlinear Dynamical ◽  
Wave Patterns ◽  
Dynamical Boundary Conditions ◽  
Cahn Hilliard Equation

In this paper, we consider the process of formation of wave structures in binary mixtures: for example, polymer chains or binary alloys. This process is described by the three-dimensional linear Cahn–Hilliard equation with nonlinear dynamical boundary conditions. The dynamical boundary conditions with “feedback” describe processes of cyclic crystallization and melting, depending on temperature as on a parameter. We describe an initial value boundary problem in cube and in square. It is shown that by action of boundary conditions in cube appears wave structures of relaxation, pre-turbulent and turbulent type. For large time, the wave patterns are in the form of recurrent parallelepiped in volume or parallelogram in plane. Applications to study separation of polymer blends in the square.

scholarly journals SUR LA STABILITÉ POUR L’ÉQUATION MONODIMENSIONNELLE D’UN GAZ VISQUEUX ET CALORIFÈRE AVEC LA FRONTIÈRE VARIABLE

2001 ◽  
Vol 44 (2) ◽  
pp. 295-315
Author(s):  
Rachid Benabidallah
Keyword(s):  
Boundary Conditions ◽  
Positive Constant ◽  
Large Time ◽  
Subject Classification ◽  
Heat Conducting ◽  
Time Behaviour ◽  
Initial Amplitude ◽  
Variable Boundary ◽  
One Dimensional ◽  
Viscous Heat

AbstractWe consider the equation of a one-dimensional viscous heat-conducting compressible gas in the variable domain with the appropriate boundary conditions. We study the large-time behaviour of the solution in the particular case where the displacement of the variable boundary is given by $L(t)=L_0(1+at)^\alpha$ with $0lt\alphalt1$, where $a$ is a positive constant and $L_0$ is the initial amplitude of our domain.AMS 2000 Mathematics subject classification: Primary 35B40; 76N15

Dynamic Analysis of Impact Tools by Using a Method Based on Stress Wave Propagation and Impulse-Momentum Principle

2003 ◽  
Vol 125 (1) ◽  
pp. 131-142 ◽  
Author(s):  
Dante A. Elı´as ◽  
Luciano E. Chiang
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Dynamic Analysis ◽  
Three Dimensional ◽  
Fem Analysis ◽  
Linear Momentum ◽  
Stress Wave Propagation ◽  
One Dimensional ◽  
External Forces ◽  
Initial Strains

We present a numerical method derived from the Impulse-Linear Momentum Principle that can be used in the design of impact tools for rock drilling. This method allows the prediction of energy transmission to rock, the profiles of stress, displacement and velocity, all of which are important in the dynamic analysis of such tools. Using the Impulse-Linear Momentum Principle in an algorithmic manner, multibody interaction is simplified, and also different load and boundary conditions such as external forces, initial strains, and initial body separations can be directly considered. The accuracy of the method has been contrasted theoretically with both one-dimensional and three-dimensional FEM analysis, as well as experimentally.

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