The criticality of the transport system in a slab geometry with partially reflecting boundary conditions

1999 ◽  
Vol 28 (4) ◽  
pp. 419-430
Author(s):  
Wenlong Wang ◽  
Xinshan Yu
Keyword(s):  
Boundary Conditions ◽  
Transport System ◽  
Slab Geometry

scholarly journals Hall instability: origin, properties and asymptotic theory for its tearing mode

2021 ◽  
Vol 87 (4) ◽  
Author(s):  
Leonid Kitchatinov
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Current Velocity ◽  
Necessary Condition ◽  
Perfect Conductor ◽  
Tearing Mode ◽  
Slab Geometry ◽  
Background Magnetic Field ◽  
Type Mode ◽  
Almost All

Hall instability in electron magnetohydrodynamics is interpreted as the shear-Hall instability driven jointly by helicoidal oscillations and shear in the electron current velocity. This explanation suggests an antiparallel orientation of the background magnetic field and vorticity of the current velocity as the necessary condition for Hall instability. The condition is tested and generally confirmed by numerical computations in plane slab geometry. Unstable eigenmodes are localized in the spatial regions of the antiparallel field and vorticity. Computations of the tearing-type mode of the instability are complemented by (and generally agree with) asymptotic analytical estimations for large Hall numbers. The stabilizing effect of perfect conductor boundary conditions is found and explained. For large Hall numbers, the growth rates approach the power-law dependence $\sigma \propto B^\alpha \eta ^{1-\alpha }$ on the magnetic field ( $B$ ) and diffusivity ( $\eta$ ). Almost all computations give the power index $\alpha = 3/4$ with one exception of the tearing-type mode with vacuum boundary conditions for which case $\alpha = 2/3$ .

scholarly journals Tailings Transport System Design Using Probabilistic Methods

2021 ◽  
Author(s):  
Josh Stowe ◽  
Ian Farrell ◽  
Eric Wingeard
Keyword(s):  
Boundary Conditions ◽  
System Design ◽  
Transport System ◽  
Traditional Approach ◽  
Probabilistic Method ◽  
Probabilistic Methods ◽  
Process Conditions ◽  
High Solids ◽  
Solids Concentration ◽  
Maximum Process

AbstractTailings transport system design is generally based on identifying the minimum and maximum process boundary conditions for pump selection and pipeline sizing. The approach is robust and well-proven. However, the approach has the potential to skew selections to operating scenarios that have a very low likelihood of occurring, such as the combination of high solids throughput and low tailings solids concentration. The approach can result in a tailings transport system design that is overly conservative. A probabilistic method-based approach captures the independent variability of design inputs and the combined likelihood of outcomes. This approach identifies the process conditions that have the highest likelihood of occurrence and are most applicable to equipment and pipeline selections. An outline of a probabilistic-based approach to tailings transport system design and the resulting selections is provided in this article. The probabilistic-based system design is compared to the outcomes from the traditional approach. The benefits and challenges to this approach are discussed and recommendations for utilizing this approach for tailings transport system design are provided.

scholarly journals The Pij matrix and flux calculation of one-dimensional neutron transport in the slab geometry of nuclear fuel cell using collision probability method

2018 ◽  
Vol 197 ◽  
pp. 02006 ◽  
Author(s):  
Mohammad Ali Shafii ◽  
Jakaria Usman ◽  
Seni H. J. Tongkukut ◽  
Ade Gafar Abdullah
Keyword(s):  
Fuel Cell ◽  
Boundary Conditions ◽  
Neutron Flux ◽  
Nuclear Fuel ◽  
Neutron Transport ◽  
Collision Probability ◽  
Probability Method ◽  
Neutron Transport Equation ◽  
Slab Geometry ◽  
One Dimensional

Calculation of Pij matrix of one-dimensional neutron transport in the slab geometry of the nuclear fuel cell using Collision Probability (CP) method has been done. Pij matrix is one of important parameters within the distribution of neutron flux in the nuclear fuel cell. The CP method is the most efficient methods to solve the neutron transport equation in the reactor core. The study is focused on neutron interaction with nuclear fuel cell of U-235 and U-238 for homogeneous condition. The parameters to calculate the Pij matrix are the cross section of nuclear fuel, width of the region and number of regions. A lattice of slabs have been constructed using void boundary conditions for model of finite system to calculate the collision probabilities. If the Pij matrix has been calculated then neutron flux can be determined. The results show that total value of Pij matrix using CP method for U-235 and U-238 is less than one, respectively. This is in accordance with the definition of void boundary conditions for finite slab geometry. Along with Pij matrix, neutron flux is also appropriate with the reference.

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