Moving Boundary Model for Leaching of Nuclear Waste Glass

1984 ◽  
Vol 44 ◽  
Author(s):  
T. Banba ◽  
T. Murakami ◽  
H. Kimura
Keyword(s):  
Moving Boundary ◽  
Numerical Solutions ◽  
Surface Layers ◽  
Proposed Model ◽  
Film Mass Transfer ◽  
Leaching Experiments ◽  
Trial And Error Method ◽  
Boundary Model ◽  
Fundamental Equations ◽  
Error Method

AbstractThe leaching experiments of Soxhlet type have been carried out[l, 2] and on the basis of the results we developed the mathematical leaching model which used one dimensional diffusion and could treat the growth of surface layers. The model adopted the following assumptions: 1) The velocity of the bulk glass-surfacé layers boundary depends on time alone. 2) Some of the diffusing substances are immobilized in the surface layers by an irreversible first-order reaction. 3) A fictitious film exists at the solution-surface layers interface. The fundamental equations were established based on these assumptions and the numerical solutions were obtained by the Crank-Nicholson implicit method. The values of the diffusion coefficient, the reaction rate and the film mass transfer coefficient were obtained by a trial-and-error method. The applicability of the model was confirmed by the fact that the leaching mechanisms deduced from the calculated results were consistent with those mechanisms deduced from the experimental results. The present study showed the proposed model was valid for calculation of the leach rates of waste glasses when surface layers grew during leaching, and the study also indicated which parameters should be measured experimentally to predict the leach rates.

scholarly journals Nonlinear Moving Boundary Model of Low-Permeability Reservoir

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8445
Author(s):  
Xiarong Jiao ◽  
Shan Jiang ◽  
Hong Liu
Keyword(s):  
Linear Model ◽  
Nonlinear Equations ◽  
Analytical Solutions ◽  
Moving Boundary ◽  
Numerical Solutions ◽  
Outer Boundary ◽  
Low Permeability ◽  
Gas Seepage ◽  
Boundary Model ◽  
Low Permeability Reservoirs

At present, there are two main methods for solving oil and gas seepage equations: analytical and numerical methods. In most cases, it is difficult to find the analytical solution, and the numerical solution process is complex with limited accuracy. Based on the mass conservation equation and the steady-state sequential substitution method, the moving boundary nonlinear equations of radial flow under different outer boundary conditions are derived. The quasi-Newton method is used to solve the nonlinear equations. The solutions of the nonlinear equations with an infinite outer boundary, constant pressure outer boundary and closed outer boundary are compared with the analytical solutions. The calculation results show that it is reliable to solve the oil-gas seepage equation with the moving boundary nonlinear equation. To deal with the difficulty in solving analytical solutions for low-permeability reservoirs and numerical solutions of moving boundaries, a quasi-linear model and a nonlinear moving boundary model were proposed based on the characteristics of low-permeability reservoirs. The production decline curve chart of the quasi-linear model and the recovery factor calculation chart were drawn, and the sweep radius calculation formula was also established. The research results can provide a theoretical reference for the policy-making of development technology in low-permeability reservoirs.

CONTEXTUAL SUBTEXT INFORMATION OF A FOREIGN LANGUAGE TEXT: HERMENEUTIC APPROACH

2020 ◽  
Vol 2020 (30) ◽  
pp. 75-87
Author(s):  
Lidiya Derbenyova
Keyword(s):  
Foreign Language ◽  
Optimal Solution ◽  
Decision Making Process ◽  
Trial And Error ◽  
Transmission Of Information ◽  
Hermeneutic Approach ◽  
Trial And Error Method ◽  
Problems Of Translation ◽  
Error Method ◽  
Language Text

The article focuses on the problems of translation in the field of hermeneutics, understood as a methodology in the activity of an interpreter, the doctrine of the interpretation of texts, as a component of the transmission of information in a communicative aspect. The relevance of the study is caused by the special attention of modern linguistics to the under-researched issues of hermeneutics related to the problems of transmission of foreign language text semantics in translation. The process of translation in the aspect of hermeneutics is regarded as the optimum search and decision-making process, which corresponds to a specific set of functional criteria of translation, which can take many divergent forms. The translator carries out a number of specific translation activities: the choice of linguistic means and means of expression in the translation language, replacement and compensation of nonequivalent units. The search for the optimal solution itself is carried out using the “trial and error” method. The translator always acts as an interpreter. Within the boundaries of a individual utterance, it must be mentally reconstructed as conceptual situations, the mentally linguistic actions of the author, which are verbalized in this text.

scholarly journals System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 787
Author(s):  
Olaniyi Iyiola ◽  
Bismark Oduro ◽  
Trevor Zabilowicz ◽  
Bose Iyiola ◽  
Daniel Kenes
Keyword(s):  
Fractional Order ◽  
Recovery Rate ◽  
Death Rate ◽  
Numerical Solutions ◽  
Complex Nature ◽  
Uniqueness Of Solutions ◽  
Fractional Equations ◽  
Effective Contact ◽  
Proposed Model ◽  
Fractional Models

The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalizations and deaths have been observed, with thousands of cases occurring daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to better understand the transmission of the disease. Non-locality in the model has made fractional differential equations appropriate for modeling. Solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate, quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, and recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium (symmetry), and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam–Bashforth–Moulton method developed for the fractional-order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19. Based on the results with different fractional-order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is currently occurring in many countries.

The determination of units in totally real cubic fields

1960 ◽  
Vol 56 (4) ◽  
pp. 318-321 ◽  
Author(s):  
H. J. Godwin
Keyword(s):  
Trial And Error ◽  
Integral Lattice ◽  
Cubic Field ◽  
Cubic Fields ◽  
Trial And Error Method ◽  
Totally Real ◽  
Rational Integral ◽  
Fundamental Units ◽  
Error Method

The determination of a pair of fundamental units in a totally real cubic field involves two operations—finding a pair of independent units (i.e. such that neither is a power of the other) and from these a pair of fundamental units (i.e. a pair ε1; ε2 such that every unit of the field is of the form with rational integral m, n). The first operation may be accomplished by exploring regions of the integral lattice in which two conjugates are small or else by factorizing small primes and comparing different factorizations—a trial-and-error method, but often a quick one. The second operation is accomplished by obtaining inequalities which must be satisfied by a fundamental unit and its conjugates and finding whether or not a unit exists satisfying these inequalities. Recently Billevitch ((1), (2)) has given a method, of the nature of an extension of the first method mentioned above, which involves less work on the second operation but no less on the first.

Dynamic Simulation of an Organic Rankine Cycle (ORC) System Driven by Exhaust

2015 ◽  
Vol 738-739 ◽  
pp. 986-990
Author(s):  
Zhi Gang Wang ◽  
Jia Guang Cheng ◽  
Yan Wang ◽  
Qiang Shen
Keyword(s):  
Low Temperature ◽  
Control Strategy ◽  
Fossil Fuels ◽  
Moving Boundary ◽  
Organic Rankine Cycle ◽  
Rankine Cycle ◽  
Energy Crisis ◽  
Transient Phenomena ◽  
Simulation Results ◽  
Boundary Model

Organic Rankine Cycle (ORC) is one of the most promising technologies for low-temperature energy conversion. In recent years, it has gotten more attention due to the energy crisis and environmental problems caused by the combustion of fossil fuels. In this paper, a moving boundary model is introduced to describe the transient phenomena of evaporator and condenser, which are the important components of ORC. The simulation results are given to illustrate the efficiency and feasibility of the proposed control strategy.

MXene: a promising photocatalyst for water splitting

2016 ◽  
Vol 4 (29) ◽  
pp. 11446-11452 ◽  
Author(s):  
Zhonglu Guo ◽  
Jian Zhou ◽  
Linggang Zhu ◽  
Zhimei Sun
Keyword(s):  
Water Splitting ◽  
Trial And Error ◽  
Hydrogen Fuel ◽  
Photocatalytic Water Splitting ◽  
Arduous Task ◽  
Trial And Error Method ◽  
Error Method

Identifying suitable photocatalysts for photocatalytic water splitting to produce hydrogen fuelviasunlight is an arduous task by the traditional trial-and-error method.

Numerical Solutions of the Viscous Flow Equations for a Class of Closed Flows

1965 ◽  
Vol 69 (658) ◽  
pp. 714-718 ◽  
Author(s):  
Ronald D. Mills
Keyword(s):  
Moving Boundary ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Steady Flows ◽  
Flow Equations ◽  
Steady Streaming ◽  
Difference Formula ◽  
Surface Passing

The Navier-Stokes equations are solved iteratively on a small digital computer for the class of flows generated within a rectangular “cavity” by a surface passing over its open end. Solutions are presented for depth/breadth ratios ƛ=0.5 (shallow), 10 (square), 20 (deep) and Reynolds number 100. Flow photographs ore obtained which largely confirm the predicted flows. The theoretical velocity profiles and pressure distributions through the centre of the vortex in the square cavity are calculated.In an appendix an improved finite difference formula is given for the vorticity generated at a moving boundary.Since Thorn began his pioneering work some thirty-five years ago the number of numerical solutions which have been obtained for the equations of incompressible viscous fluid motion remains small (see bibliographies of Thom and Apelt, Fromm). The known solutions are principally for steady streaming flows, although two methods have now been used with success for non-steady flows (Payne jets and Fromm flow past obstacles). By contrast this paper is concerned with the class of closed flows generated in a rectangular region of varying depth/breadth ratio by a surface passing over an open end. This problem has been considered for a number of reasons.

Numerical Multiphysics Modeling of Microdroplet Motion Dynamics in Digital Microfluidic Systems

2010 ◽  
Author(s):  
Ali Ahmadi ◽  
Jonathan F. Holzman ◽  
Homayoun Najjaran ◽  
Mina Hoorfar
Keyword(s):  
Numerical Algorithm ◽  
Moving Boundary ◽  
Microfluidic Systems ◽  
Multiphysics Modeling ◽  
Transient Motion ◽  
Proposed Model ◽  
Digital Microfluidic ◽  
Motion Dynamics

In this paper a novel numerical algorithm is proposed for modeling the transient motion of microdroplets in digital microfluidic systems. The new methodology combines the effects of the electrostatic and hydrodynamic pressures to calculate the actuating and opposing forces and the moving boundary of the microdroplet. The proposed model successfully predicts transient motion of the microdroplet in digital microfluidic systems, which is crucial in the design, control and fabrication of such devices. The results of such an analysis are in agreement with the expected trend.

scholarly journals Measuring the Deformation of a Flat Die by Applying a Laser Beam on a Reflecting Surface

2009 ◽  
Vol 424 ◽  
pp. 197-204 ◽  
Author(s):  
W. Assaad ◽  
H.J.M. Geijselaers ◽  
K.E. Nilsen
Keyword(s):  
Finite Element ◽  
Laser Beam ◽  
Extrusion Process ◽  
Trial And Error ◽  
Element Calculation ◽  
Extrusion Dies ◽  
Cheap Method ◽  
Trial And Error Method ◽  
Reflecting Surface ◽  
Error Method

The design of extrusion dies depends on the experience of the designer. After the die has been manufactured, it is tested during an extrusion process and machined several times until it works properly. The die is designed by a trial and error method which is expensive interms of time consumption and the amount of scrap. Research is going on to replace the trial pressing with finite element simulations that concentrate on material and tool analysis. In order to validate the tool simulations, an experiment is required for measuring the deformation of the die. Measuring the deformation of the die is faced with two main obstacles: high temperature and little free space. To overcome these obstacles a method is tried, which works by applying a laser beam on a reflecting surface. This cheap method is simple, robust and gives good results. This paper describes measuring the deformation of a flat die used to extrude a single U shape profile. In addition, finite element calculation of the die is performed. Finally, a comparison is performed between experimental and numerical results.

Adjustment of a Grazing Incidence Spectrometer for Maximum Resolution

1969 ◽  
Vol 23 (2) ◽  
pp. 128-132 ◽  
Author(s):  
E. Alexander ◽  
B. S. Fraenkel
Keyword(s):  
Grazing Incidence ◽  
Trial And Error ◽  
Routine Method ◽  
Maximum Resolution ◽  
Trial And Error Method ◽  
Error Method

A routine method to adjust a grazing incidence spectrometer for maximum resolution is described. The trial and error method uses as variable, the distance of the slit from the Rowland circle. Examples of resolved doublets are shown.

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