Control of the stirred flow reactor in unstable state control through step changes in the volume of the reaction mixture

1979 ◽  
Vol 44 (1) ◽  
pp. 34-49
Author(s):  
Josef Horák ◽  
František Jiráček ◽  
Zina Sojková
Keyword(s):  
Mathematical Model ◽  
Theoretical Study ◽  
Flow Reactor ◽  
Unstable State ◽  
Theoretical Studies ◽  
State Control ◽  
Ferric Ions ◽  
First Order ◽  
The Mathematical Model ◽  
Oxidation By Hydrogen Peroxide

Possibilities of the control of an adiabatic stirred flow reactor with an exothermic first order reaction in unstable state are studied. The control is studied both on the linearized mathematical model and on the model reaction of oxidation by hydrogen peroxide catalyzed by ferric ions. The control is based on step changes in the volume of the reaction mixture at constant conditions at the reactor inlet. The aim is stabilization of the outlet degree of conversion of the reactant. From the theoretical study on the mathematical model resulted that control of the reactor by step changes of the volume can be a very simple and effective method of control in the unstable steady state. The results of theoretical studies have been verified experimentally.

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. 

Enhancement the Solar Still Performance Using Chimney Exhaust Gases

2021 ◽  
Author(s):  
Hamdy Hassan
Keyword(s):  
Mathematical Model ◽  
Theoretical Study ◽  
Saline Water ◽  
Kutta Method ◽  
Solar Still ◽  
Climate Conditions ◽  
Exhaust Gases ◽  
Runge Kutta Method ◽  
The Impact ◽  
The Mathematical Model

Abstract In this paper, a theoretical study is presented on enhancement of the solar still performance by using the exhaust gases passing inside a chimney under the still basin. The impact of the exhaust gases temperature on the solar still temperature, productivity, and efficiency are considered. The performance of solar still with chimney is compared with that of conventional solar still. The study is carried out under the hot and climate conditions of Upper Egypt. A complete transient mathematical model of the physical model including the solar still regions temperatures, productivity, and heat transfer between the solar still and the exhaust gases are constructed. The mathematical model is solved numerically by using fourth-order Runge-Kutta method and is programmed by using MATLAB. The mathematical model is validated using an experimental work. The results show that the solar still saline water temperature increases and productivity with using and rising the exhaust gases. Furthermore, the impact of using exhaust gases on the still performance in winter is greater than in summer. using chimney exhaust gases at 75 °C and 125 °C enhances the daily freshwater yield of the conventional still by more than three times and about six times in winter, respectively, and about two and half times and more than three times in summer, respectively.

scholarly journals Colpitts Chaotic Oscillator Coupling with a Generalized Memristor

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Ling Lu ◽  
Changdi Li ◽  
Zicheng Zhao ◽  
Bocheng Bao ◽  
Quan Xu
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Fourth Order ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Nonlinear Phenomena ◽  
Unique Equilibrium ◽  
First Order ◽  
The Mathematical Model ◽  
Order Parallel

By introducing a generalized memristor into a fourth-order Colpitts chaotic oscillator, a new memristive Colpitts chaotic oscillator is proposed in this paper. The generalized memristor is equivalent to a diode bridge cascaded with a first-order parallel RC filter. Chaotic attractors of the oscillator are numerically revealed from the mathematical model and experimentally captured from the physical circuit. The dynamics of the memristive Colpitts chaotic oscillator is investigated both theoretically and numerically, from which it can be found that the oscillator has a unique equilibrium point and displays complex nonlinear phenomena.

scholarly journals Water-In-Oil Emulsions through Porous Media and the Effect of Surfactants: Theoretical Approaches

Processes ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 620 ◽  
Author(s):  
Josue F. Perez-Sanchez ◽  
Nancy P. Diaz-Zavala ◽  
Susana Gonzalez-Santana ◽  
Elena F. Izquierdo-Kulich ◽  
Edgardo J. Suarez-Dominguez
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Theoretical Study ◽  
High Viscosity ◽  
Dispersed Phase ◽  
Interaction Energies ◽  
Theoretical Approaches ◽  
Heavy Crude ◽  
Oil Emulsions ◽  
The Mathematical Model

The most complex components in heavy crude oils tend to form aggregates that constitute the dispersed phase in these fluids, showing the high viscosity values that characterize them. Water-in-oil (W/O) emulsions are affected by the presence and concentration of this phase in crude oil. In this paper, a theoretical study based on computational chemistry was carried out to determine the molecular interaction energies between paraffin–asphaltenes–water and four surfactant molecules to predict their effect in W/O emulsions and the theoretical influence on the pressure drop behavior for fluids that move through porous media. The mathematical model determined a typical behavior of the fluid when the parameters of the system are changed (pore size, particle size, dispersed phase fraction in the fluid, and stratified fluid) and the viscosity model determined that two of the surfactant molecules are suitable for applications in the destabilization of W/O emulsions. Therefore, an experimental study must be set to determine the feasibility of the methodology and mathematical model displayed in this work.

The Second Order Optimum Synthesis of a Compound Mechanism With Flexible Member

1992 ◽  
Author(s):  
Caifang Meng ◽  
Zuo Dai ◽  
Jianzhong Cha
Keyword(s):  
Mathematical Model ◽  
Second Order ◽  
Software Environment ◽  
Intelligent Optimization ◽  
Optimization Software ◽  
First Order ◽  
Optimum Synthesis ◽  
Angular Velocities ◽  
The Mathematical Model ◽  
Flexible Member

Abstract An optimum synthesis of a compound mechanism with flexible member (CMFM) is reported in this paper. First, the concepts of the first order optimum synthesis (FOOS) and the second order optimum synthesis (SOOS) are given. Then, the SOOS for the CMFM in a complete period and a half of period are carried out based on the mathematical model established for the SOOS of the CMFM. The results of the SOOS are obtained through the IIO software, an integrated intelligent optimization software environment, and the differences between specified and generated angular velocities are analyzed.

scholarly journals MATHEMATICAL MODEL OF ESTIMATION THE DYNAMIC PARAMETERS OF MACHINE AND TRACTOR UNIT’S ENGINE UNDER UNSTEAD LOAD

2019 ◽  
Vol 14 (2) ◽  
pp. 106-110 ◽  
Author(s):  
Владимир Медведев ◽  
Vladimir Medvedev ◽  
Станислав Синицкий ◽  
Stanislav Sinickiy
Keyword(s):  
Mathematical Model ◽  
Dynamic Characteristics ◽  
Theoretical Basis ◽  
Theoretical Calculations ◽  
Dynamic Performance ◽  
Transition Process ◽  
Theoretical Studies ◽  
The Mathematical Model ◽  
Regulatory Characteristic ◽  
The Ideal

The article provides an analysis of the existing methods and techniques for assessing the dynamic characteristics of engines of mobile machines, and also presents theoretical calculations for estimating the dynamic performance of an machine and tractor unit’s engine under unsteady load. The proposed mathematical model describes the change in the performance of the engine of machine and tractor unit with a linear law of loading and allows you to compare an engine’s operation at unsteady load with the ideal. The quasi-dynamic characteristic was laid as the theoretical basis for study to assess the dynamic performance of machine and tractor unit’s engine under unsteady load. Comparison of the dynamic performance of engines at unsteady load with ideal performance, which have no dynamic losses. It is proposed to apply the “quasi-dynamic” characteristics. The quasidynamic (ideal) characteristic is called - the change in the performance of machine and tractor unit’s engine, in the transition process, occurring in accordance with the change in the frequency of rotation of the crankshaft on the stationary characteristics. The mathematical model for estimating the dynamic performance of an machine and tractor unit’s engine using a correcting branch with an unsteady load is experimental equations for load buildup. Theoretical relationships have been developed for evaluating the dynamic performance of an engine with an unsteady load on the correcting branch of the regulatory characteristic. Using the proposed theoretical dependences, it is possible to carry out theoretical studies of the effect of load on the dynamic performance of an machine and tractor unit’s engine and determine the total dynamic losses.

scholarly journals Research Results on Influence of Hydraulic Hammer Design Parameters

2021 ◽  
Vol 346 ◽  
pp. 03081
Author(s):  
Irina Teterin ◽  
Igor Ugrumov ◽  
Ivan Teterin ◽  
Andrey Korneev
Keyword(s):  
Mathematical Model ◽  
Control Unit ◽  
Type Structure ◽  
Design Model ◽  
Theoretical Research ◽  
Design Parameters ◽  
Theoretical Studies ◽  
Main Design ◽  
Hydraulic Hammer ◽  
The Mathematical Model

The article presents the results of the theoretical research on the influence of the design parameters on the output characterictics of a hydraulic hammer. The hydraulic hammer under the study has a hydraulic percussive mechanism of a permanent pressure-type structure with a spool free control unit. A design model of a hydraulic percussive mechanism with a spool free control unit has been developed. The mathematical model of the hydraulic percussive mechanism of a permanent pressure-type structure with a spool free control unit is presented. The oscillogram resulting from the theoretical studies, which defines the operation of the hydraulic percussive mechanism, is presented. A range of the rational zones for selecting the main design parameters of the hydraulic percussive mechnism is obtained.

Research on the Modeling of Metal Material Properties Based on Logistic Model

2014 ◽  
Vol 875-877 ◽  
pp. 1076-1082
Author(s):  
Shi Yu Zhang ◽  
Xi Ling Li
Keyword(s):  
Mathematical Model ◽  
Statistical Methods ◽  
Material Properties ◽  
Logistic Model ◽  
Theoretical Study ◽  
Metal Material ◽  
Metal Materials ◽  
The Mathematical Model ◽  
Hardenability Curve

The fact that it is difficult to establish the mathematical model of metal materials by theoretical study method means that can be done by statistical methods. Happens to, the logistic model is more suitable for this work. This paper tries to establish the model of steel hardenability curve by transforming logistic model without a large number of specimens.

Generalized Memristor Consisting of Diode Bridge with First Order Parallel RC Filter

2014 ◽  
Vol 24 (11) ◽  
pp. 1450143 ◽  
Author(s):  
Bocheng Bao ◽  
Jingjing Yu ◽  
Fengwei Hu ◽  
Zhong Liu
Keyword(s):  
Mathematical Model ◽  
Hysteresis Loops ◽  
Experimental Measurements ◽  
First Order ◽  
The Mathematical Model ◽  
Pinched Hysteresis ◽  
Order Parallel

A generalized memristor consisting of a memristive diode bridge with a first order parallel RC filter is proposed in this letter. The mathematical model of the circuit is established and its fingerprints are analyzed by the pinched hysteresis loops with different periodic stimuli. The results verified by experimental measurements indicate that the proposed circuit is a simple voltage-controlled generalized memristor.

Theoretical Study on the Wetting Length in Triangle Wetting Region of Rectangular Microgrooves

2011 ◽  
Author(s):  
Tao Wang ◽  
Xuegong Hu ◽  
Chaohong Guo ◽  
Xuelei Nie ◽  
Ningning Xie
Keyword(s):  
Mathematical Model ◽  
Heat Flux ◽  
Theoretical Analysis ◽  
Tilt Angle ◽  
Heat Sink ◽  
Theoretical Study ◽  
Geometric Dimension ◽  
The Mathematical Model ◽  
The Relationship ◽  
Working Liquid

The mathematical model is established in this article to describe the relationship between the wetting length of working liquid in the triangular wetting region of rectangular capillary microgrooves and the geometric dimension, tilt angle, type of working liquid and heat flux when heating the back of microgrooves heat sink. The model supposes that the vapour-liquid interface of meniscus is quadratic parabola but not arc. The predictions from the theoretical analysis are successfully compared with the experimental results.

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