scholarly journals About Two-dimensional Mathematical Model of Contaminant Migration in Unsaturated Catalytic Porous Media with Traps

2020 ◽  
pp. 25-28
Author(s):  
Anatolyy Vlasyuk ◽  
Viktor Zhukovskyy ◽  
Nataliia Zhukovska ◽  
Serhiy Kraychuk
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Moisture Transfer ◽  
Physical Problem ◽  
Two Dimensional ◽  
Contaminant Migration ◽  
Nonlinear Case ◽  
The Finite Difference Method ◽  
Saline Solutions ◽  
Assessment Strategies

This paper proposes an approach for the computer simulation of complex physical problem of contaminant migration through unsaturated catalytic porous media to the filter-trap. The corresponding mathematical model in the two-dimensional nonlinear case is presented. The model includes detailed considerations of the moisture transfer of saline solutions under the generalized Darcy’s and Cluta’s laws in different subregions of soil. The numerical solution of the boundary value problem was found by the finite difference method and proposed the algorithm for computer implementation. The proposed algorithm may be used for creating software with effective risk assessment strategies and predicting the cleaning and further useful use of the soil massifs.

scholarly journals Mathematical Modeling of Heat, Mass and Moisture Transfer in Catalytic Porous Media

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Moisture Transfer ◽  
Nonlinear Mathematical Model ◽  
Software Complex ◽  
Ordered Mesoporous Materials ◽  
Ordered Mesoporous ◽  
Finite Differences Method ◽  
New Applications ◽  
Contaminant Distribution

The discovery of ordered mesoporous materials has opened great opportunities for new applications in heterogeneous catalysis e.g. in soil purification processes. The focus of this study is the development of a mathematical model to simulate heat, mass and moisture transfer in soil arrays tacking into account catalytic micro- or nanoparticles. The nonlinear mathematical model of contaminant distribution in unsaturated catalytic porous media to the filter-trap in non-isothermal conditions is presented. The finite differences method was used to find the numerical solution of the corresponding boundary value problem and the analytical solution for mass transfer in catalytic micro- or nanoparticles was presented as well. Numerical experiments and their analysis were conducted using NanoSurface software complex.

scholarly journals Modeling of the Two-Dimensional Thawing of Logs in an Air Environment

2020 ◽  
Author(s):  
Nencho Deliiski ◽  
Ladislav Dzurenda ◽  
Natalia Tumbarkova
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Experimental Studies ◽  
Longitudinal Section ◽  
Nonstationary Temperature ◽  
Two Dimensional ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
The Finite Difference Method

A two-dimensional mathematical model has been created, solved, and verified for the transient nonlinear heat conduction in logs during their thawing in an air environment. For the numerical solution of the model, an explicit form of the finite-difference method in the computing medium of Visual FORTRAN Professional has been used. The chapter presents solutions of the model and its validation towards own experimental studies. During the validation of the model, the inverse task of the heat transfer has been solved for the determination of the logs’ heat transfer coefficients in radial and longitudinal directions. This task has been solved also in regard to the logs’ surface temperature, which depends on the mentioned coefficients. The results from the experimental and simulative investigation of 2D nonstationary temperature distribution in the longitudinal section of poplar logs with a diameter of 0.24 m, length of 0.48 m, and an initial temperature of approximately –30°C during their many hours thawing in an air environment at room temperature are presented, visualized, and analyzed.

scholarly journals Mathematical Modelling of Non-Isothermal Moisture Transfer and Rheological Behavior in Cappilary-Porous Materials with Fractal Structure During Drying

2014 ◽  
Vol 7 (4) ◽  
pp. 111 ◽  
Author(s):  
Yaroslav Sokolowskyi ◽  
Volodymyr Shymanskyi
Keyword(s):  
Mathematical Model ◽  
Finite Difference Method ◽  
Fractional Order ◽  
Rheological Behavior ◽  
Strain State ◽  
Fractal Structure ◽  
Moisture Transfer ◽  
The Finite Difference Method ◽  
Predictor Corrector ◽  
The Mathematical Model

The mathematical model of non-isothermal moisture transfer and rheological behavior of wood during drying with taking into account the fractal structure of this material is regarded in the article. The mathematical tools of integration and differentiation of fractional order for description the mathematical model of this process was used. For finding the numerical solution of this problem the finite-difference method predictor-corrector was used. Results show the practicability of using the mathematical tools of integration and differentiation of fractional order to calculate the temperature and humidity fields and the stress-strain state during drying timber.

Two Dimensional Unsteady State Mathematical Model for dispersion of Chlorine in Water in a Channel

2011 ◽  
Vol 3 (8) ◽  
pp. 503-505
Author(s):  
Jaipal Jaipal ◽  
◽  
Rakesh Chandra Bhadula ◽  
V. N Kala V. N Kala
Keyword(s):  
Mathematical Model ◽  
Two Dimensional ◽  
Unsteady State

Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A. Buikis ◽  
J. Cepitis ◽  
H. Kalis ◽  
A. Reinfelds ◽  
A. Ancitis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Initial Value Problems ◽  
Moisture Transfer ◽  
Bound Water ◽  
Drying Process ◽  
Initial Value ◽  
First Order ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations. 

Two-Dimensional Flow of Polymer Solutions Through Porous Media

1999 ◽  
Vol 2 (3) ◽  
pp. 251-262
Author(s):  
P. Gestoso ◽  
A. J. Muller ◽  
A. E. Saez
Keyword(s):  
Porous Media ◽  
Polymer Solutions ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow
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