Analytical solutions for sequentially coupled one-dimensional reactive transport problems – Part I: Mathematical derivations

2008 ◽  
Vol 31 (2) ◽  
pp. 203-218 ◽  
Author(s):  
V. Srinivasan ◽  
T.P. Clement
Keyword(s):  
Analytical Solutions ◽  
Reactive Transport ◽  
One Dimensional ◽  
Transport Problems

scholarly journals Analytical solutions for the neutron transport using the spectral methods

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Abdelouahab Kadem
Keyword(s):  
Analytical Solutions ◽  
Spectral Methods ◽  
Chebyshev Polynomials ◽  
Neutron Transport ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Multidimensional Problems ◽  
Dimensional Equation ◽  
Transport Problems

We present a method for solving the two-dimensional equation of transfer. The method can be extended easily to the general linear transport problem. The used technique allows us to reduce the two-dimensional equation to a system of one-dimensional equations. The idea of using the spectral method for searching for solutions to the multidimensional transport problems leads us to a solution for all values of the independant variables, the proposed method reduces the solution of the multidimensional problems into a set of one-dimensional ones that have well-established deterministic solutions. The procedure is based on the development of the angular flux in truncated series of Chebyshev polynomials which will permit us to transform the two-dimensional problem into a set of one-dimensional problems.

Transient convective diffusion to a uniformly accessible surface under aparent slip conditions

1991 ◽  
Vol 56 (2) ◽  
pp. 334-343
Author(s):  
Ondřej Wein
Keyword(s):  
Power Law ◽  
Analytical Solutions ◽  
Convective Diffusion ◽  
Active Surface ◽  
Velocity Profiles ◽  
One Dimensional ◽  
Slip Conditions ◽  
Accessible Surface ◽  
Diffusion Problems

Analytical solutions are given to a class of unsteady one-dimensional convective-diffusion problems assuming power-law velocity profiles close to the transport-active surface.

scholarly journals PROOST: object-oriented approach to multiphase reactive transport modeling in porous media

2015 ◽  
Vol 18 (2) ◽  
pp. 310-328 ◽  
Author(s):  
P. Gamazo ◽  
L. J. Slooten ◽  
J. Carrera ◽  
M. W. Saaltink ◽  
S. Bea ◽  
...  
Keyword(s):  
Reactive Transport ◽  
Chemical Species ◽  
Object Oriented ◽  
Object Oriented Programming ◽  
Transport Modeling ◽  
Reactive Transport Modeling ◽  
Hydrodynamic Processes ◽  
Object Oriented Approach ◽  
Transport Problems ◽  
Oriented Approach

Reactive transport modeling involves solving several nonlinear coupled phenomena, among them, the flow of fluid phases, the transport of chemical species and energy, and chemical reactions. There are different ways to consider this coupling that might be more or less suitable depending on the nature of the problem to be solved. In this paper we acknowledge the importance of flexibility on reactive transport codes and how object-oriented programming can facilitate this feature. We present PROOST, an object-oriented code that allows solving reactive transport problems considering different coupling approaches. The code main classes and their interactions are presented. PROOST performance is illustrated by the resolution of a multiphase reactive transport problem where geochemistry affects hydrodynamic processes.

BATCH DOUGH VISCOSITY INFLUENCE ON FLOW-PRESSURE CHARACTERISTICS OF THE KNEADING MACHINE

2019 ◽  
Author(s):  
В.С. РУБАН ◽  
В.И. АЛЕШИН ◽  
Д.С. БЕЗУГЛЫЙ
Keyword(s):  
Batch Process ◽  
System Of Equations ◽  
Systems Of Equations ◽  
The Finite Element Method ◽  
Dimensional Model ◽  
Symmetric Form ◽  
Pressure Function ◽  
One Dimensional ◽  
Flow Pressure ◽  
Transport Problems

Рассмотрены уравнения баланса и концентрационных потоков, базирующихся на моделях, позволяющих анализировать одноименные модели реологии течения в канале шнека блока замеса тестомесильной машины. Анализ процесса транспортировки и замеса на основе одномерной модели выявил необходимость использования сигмоидальной функции коэффициента напоропроводности от давления. Переход от одномерных задач к многомерным задачам переноса связан с преобразованием систем уравнений к симметричному виду. Полученные системы уравнений после использования теоремы Грина могут быть решены методом конечных элементов. The balance equation and concentration flows based on the models which make it possible to analyze the eponymous models of flow rheology in the block screw channel in a dough mixing machine has been considered. The analysis of the transportation and batch process based on one-dimensional model proved the necessity to apply sigmoidal coefficient of pressure function. The transition from one-dimensional problems to multidimensional transport problems is associated with the transformation of systems of equations to a symmetric form. The resulting system of equations after using Green’s theorem can be solved by the finite element method.

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