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.

Studi Perpindahan Panas Material pada Sistem Koordinat Segitiga

2017 ◽  
Vol 1 ◽  
pp. 114
Author(s):  
Imam Basuki ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
The Finite Difference Method ◽  
The Mathematical Model

<p class="Normal1"><strong><em>Abstract: </em></strong><em>Partial Differential Equations (PDP) Laplace equation can be applied to the heat conduction. Heat conduction is a process that if two materials or two-part temperature material is contacted with another it will pass heat transfer. Conduction of heat in a triangle shaped object has a mathematical model in Cartesian coordinates. However, to facilitate the calculation, the mathematical model of heat conduction is transformed into the coordinates of the triangle. PDP numerical solution of Laplace solved using the finite difference method. Simulations performed on a triangle with some angle values α and β</em></p><p class="Normal1"><strong><em> </em></strong></p><p class="Normal1"><strong><em>Keywords:</em></strong><em>  heat transfer, triangle coordinates system.</em></p><p class="Normal1"><em> </em></p><p class="Normal1"><strong>Abstrak</strong> Persamaan Diferensial Parsial (PDP) Laplace  dapat diaplikasikan pada persamaan konduksi panas. Konduksi panas adalah suatu proses yang jika dua materi atau dua bagian materi temperaturnya disentuhkan dengan yang lainnya maka akan terjadilah perpindahan panas. Konduksi panas pada benda berbentuk segitiga mempunyai model matematika dalam koordinat cartesius. Namun untuk memudahkan perhitungan, model matematika konduksi panas tersebut ditransformasikan ke dalam koordinat segitiga. Penyelesaian numerik dari PDP Laplace diselesaikan menggunakan metode beda hingga. Simulasi dilakukan pada segitiga dengan beberapa nilai sudut  dan  </p><p class="Normal1"><strong> </strong></p><p class="Normal1"><strong>Kata kunci :</strong> perpindahan panas, sistem koordinat segitiga.</p>

scholarly journals Numerical Model Of Binary Alloys Solidification Basing On The One Domain Approach And The Simple Macrosegregation Models

2015 ◽  
Vol 60 (3) ◽  
pp. 2431-2435 ◽  
Author(s):  
E. Majchrzak ◽  
B. Mochnacki ◽  
J. Mendakiewicz
Keyword(s):  
Mathematical Model ◽  
Numerical Model ◽  
Finite Difference Method ◽  
Numerical Solutions ◽  
Thermal Capacity ◽  
Thermal Processes ◽  
Domain Method ◽  
The Finite Difference Method ◽  
The One ◽  
The Mathematical Model

AbstractIn the paper the thermal processes proceeding in the domain of solidifying binary alloy are considered. The mathematical model of solidification and cooling processes bases on the one domain method (or fixed domain method). In such a model the parameter called a substitute thermal capacity (STC) appears. At the stage of STC construction the macrosegregation process described by the lever arm rule or the Scheil model is taken into account. In this way one obtains the formulas determining the course of STC resulting from the certain physical considerations and this approach seems to be closer to the real course of thermal processes proceeding in domain of solidifying alloy. In the final part the examples of numerical solutions basing on the finite difference method are presented.

Analysis and Assessment of the Effects of Corrosive Hydrogen Media on the Stress-Strain State of a Spherical Titanium Alloy Shell

2022 ◽  
Vol 1049 ◽  
pp. 85-95
Author(s):  
Violetta Kuznetsova ◽  
Maria Barkova ◽  
Alexandr Zhukov ◽  
Igor Kartsan
Keyword(s):  
Mathematical Model ◽  
Titanium Alloy ◽  
Stress State ◽  
Finite Difference Method ◽  
Diffusion Equation ◽  
Strain State ◽  
Step Method ◽  
Hollow Spherical Shell ◽  
The Finite Difference Method ◽  
Aggressive Effect

We consider the creation of a mathematical model describing the effect of corrosive hydrogen environment on the stress state of a hollow spherical shell made of titanium alloy grade VT1-0, the load is evenly distributed throughout the shell. The solution of the problem in practice was carried out by two-step method of sequential perturbation of parameters using MatLab and Maple programs. To solve the system of solving differential equations the finite difference method was applied. The solution of the diffusion equation of the aggressive hydrogen medium has been considered and the obtained solution has been compared with the results of the classical theory which does not take into account the aggressive effect of the corrosive medium.

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. 

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 Dynamic methods of spatial calculation of structures based on a plate model

2019 ◽  
Vol 97 ◽  
pp. 04072 ◽  
Author(s):  
Elyor Toshmatov ◽  
Makhamtali Usarov ◽  
Gayratjon Ayubov ◽  
Davronbek Usarov
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Strain State ◽  
Plate Model ◽  
Dynamic Calculation ◽  
Transverse Vibrations ◽  
Dynamic Methods ◽  
The Finite Difference Method ◽  
Spatial Stress

This article was devoted to the development of methods of the dynamic calculation based on the finite difference method of laminar structures in the framework of the bimoment theory, which takes into account the spatial stress-strain state. Were given the solutions of the problem of transverse vibrations of the plate model of structures.

Heat and Mass Transfer Analysis of Fabric in the Tenter Frame

1997 ◽  
Vol 67 (5) ◽  
pp. 311-316 ◽  
Author(s):  
Sang Il Park ◽  
Doo Hyun Baik
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Finite Difference Method ◽  
Moisture Content ◽  
Heat And Mass Transfer ◽  
Initial Moisture Content ◽  
Transfer Coefficients ◽  
Operation Parameters ◽  
The Finite Difference Method ◽  
Experimental Values

A mathematical model is developed for heat and mass transfer analysis of fabric in the tenter frame. Using the model, the calculated transient fabric temperatures in the tenter frame agree well with the experimental values measured by Beard. Variations in temperature and moisture content distribution are solved using the finite-difference method. The effects of operation parameters, such as temperature and humidity in the tenter, initial moisture content of the fabric, and heat and mass transfer coefficients, are examined using the model.

scholarly journals Solution of Fractional Order System of Bagley-Torvik Equation Using Evolutionary Computational Intelligence

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Muhammad Asif Zahoor Raja ◽  
Junaid Ali Khan ◽  
Ijaz Mansoor Qureshi
Keyword(s):  
Genetic Algorithm ◽  
Neural Networks ◽  
Mathematical Model ◽  
Fractional Order ◽  
Computational Intelligence ◽  
Pattern Search ◽  
Fractional Order System ◽  
Order System ◽  
Search Technique ◽  
The Mathematical Model

A stochastic technique has been developed for the solution of fractional order system represented by Bagley-Torvik equation. The mathematical model of the equation was developed with the help of feed-forward artificial neural networks. The training of the networks was made with evolutionary computational intelligence based on genetic algorithm hybrid with pattern search technique. Designed scheme was successfully applied to different forms of the equation. Results are compared with standard approximate analytic, stochastic numerical solvers and exact solutions.

scholarly journals Неупругое растяжение медного однопроволочного проводника при неограниченных местных деформациях и положительной температуре

2021 ◽  
Vol 91 (6) ◽  
pp. 946
Author(s):  
А.И. Недобитков ◽  
Б.М. Абдеев
Keyword(s):  
Mathematical Model ◽  
Electron Microscope ◽  
Nonlinear Problem ◽  
Strain State ◽  
Mechanical Forces ◽  
Neck Formation ◽  
Stress Strain ◽  
Single Wire ◽  
Copper Conductor ◽  
The Mathematical Model

Results of experimental and desktop studies of the single-wire copper conductor deformation under the overcurrent action are given in the article. The conductor was studied using the JSM-6390L reflection electron microscope. A mathematical model of the stress-strain state of the copper bar in tension and under a temperature below 700 °С has been developed on the basis of the classical nonlinear problem of the structural mechanics. The mechanical forces in a single-wire copper conductor, which cause neck formation during overcurrent flow, have been determined. The mathematical model has been simplified to simple analytical dependences providing their use in forensic fire and technical investigations.

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