A Scheme to Assist in the Evaluation of Tenter Frame Dryer Performance

1979 ◽  
Vol 101 (1) ◽  
pp. 80-84 ◽  
Author(s):  
W. F. Beckwith ◽  
J. N. Beard
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Operating Conditions ◽  
Temperature Profiles ◽  
Simulation Studies ◽  
Drying Process ◽  
Optimal Operating

One of the textile industry’s largest consumers of energy is the tenter frame dryer. To assist the industry in operating these dryers efficiently, a mathematical model which simulates the drying process and a scheme to solve for the parameters in the differential equations of the model have been developed and are presented in this paper. Temperature profiles predicted from the model are compared with profiles measured on commercial dryers. Also dryer simulation studies to elucidate optimal operating conditions are discussed.

scholarly journals A mathematical model for the virtual simulator of the power unit electrical part

2022 ◽  
Vol 1216 (1) ◽  
pp. 012009
Author(s):  
P Baran ◽  
Y Varetsky ◽  
V Kidyba ◽  
Y Pryshliak
Keyword(s):  
Mathematical Model ◽  
Power Plant ◽  
Differential Equations ◽  
Power System ◽  
Real Time ◽  
Power Unit ◽  
Operating Conditions ◽  
Auxiliary System ◽  
Algebraic Differential Equations ◽  
Electrical Part

Abstract The mathematical model is developed for a virtual training system (simulator) of the power unit electrical part operators of a thermal (nuclear) power plant. The model is used to simulating the main operating conditions of the power unit electrical part: generator idling, generator synchronization with the power system, excitation shifting from the main unit to the backup one and vice versa, switching in the power unit auxiliary system, and others. Furthermore, it has been implemented modelling some probable emergency conditions within a power plant: incomplete phase switching, damage to standard power unit equipment, synchronous oscillations, asynchronous mode, etc. The model of the power unit electrical part consists of two interacting software units: models of power equipment (turbine, generator with excitation systems, auxiliary system) and models of its control systems, automation, relay protection and signalling. The models are represented by the corresponding algebraic-differential equations that provide real-time mapping power unit processes at the operator’s request. The developed model uses optimal solving algebraic-differential equations to ensure the virtual process behaviour in real-time. In particular, the implicit Euler method is used to solve differential equations, which is stable when simulating processes in significant disturbances, such as accidental disconnection of the unit from the power system, tripping and energizing loads, generator excitation loss, etc.

scholarly journals Hybrid System Converting Solar Energy Into Electric Energy

2021 ◽  
Vol 7 (9) ◽  
pp. 12-26
Author(s):  
Yu. Ismanov ◽  
N. Niyazov ◽  
N. Dzhamankyzov
Keyword(s):  
Mathematical Model ◽  
Temperature Gradient ◽  
Hybrid System ◽  
Thermoelectric Generator ◽  
Thermal Contact Resistance ◽  
Thermal Contact ◽  
Electrical Energy ◽  
Operating Conditions ◽  
Photovoltaic Module ◽  
Optimal Operating

The article discusses a mathematical model of a hybrid system that combines photovoltaic and thermoelectric methods for converting concentrated solar energy into electrical energy. The specified mathematical model makes it possible to determine the temperatures of the photovoltaic module, as well as the temperature of the electrodes of the thermoelectric generator module. Optimal operating conditions have been determined for the hybrid system, taking into account the thermal contact resistance at the hot and cold sides of the thermoelectric generator. The simulation proceeded from the fact that only part of the absorbed solar radiation is converted into electricity due to the photoelectric effect, some part is lost due to radiation and convection from the upper surface of the photovoltaic module into the environment, and the rest is transferred to a thermoelectric generator connected to the lower part. photovoltaic module. A thermoelectric generator converts some of the thermal energy it receives from the photovoltaic module into electricity through the Seebeck effect, but most of it goes to the cooling system. The conversion of heat into electrical energy was based on the well-known Seebeck and Peltier effects. Along with these effects, such effects were taken into account as the formation of Joule heat due to the presence of electric current in the thermoelectric generator, Fourier thermal conductivity, as a consequence of the appearance of a temperature gradient in the transitions of a thermoelectric generator and Thomson heat, which arises both due to the presence of a temperature gradient, and electric current. The resulting model of the hybrid system makes it possible to study the effect of changing the temperature difference between the hot and cold electrodes of the thermoelectric generator and the resistance of the external circuit on the performance of the hybrid system. The model also allows the determination of the optimal operating conditions for the hybrid system, taking into account the thermal contact resistance on the hot and cold sides of the thermoelectric generator.

scholarly journals A mathematical model and simulation of the drying process of thin layers of potatoes in a conveyor-belt dryer

2015 ◽  
Vol 19 (3) ◽  
pp. 1107-1118 ◽  
Author(s):  
Dusko Salemovic ◽  
Aleksandar Dedic ◽  
Nenad Cupric
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Conveyor Belt ◽  
Thin Layers ◽  
Convective Drying ◽  
Drying Process ◽  
Automated Control ◽  
Model And Simulation ◽  
The Mathematical Model

This paper presents a mathematical model and numerical analysis of the convective drying process of small particles of potatoes slowly moving through the flow of a drying agent - hot moist air. The drying process was analyzed in the form of a one-dimensional thin layer. The mathematical model of the drying process is a system of two ordinary nonlinear differential equations with constant coefficients and an equation with a transcendent character. The appropriate boundary conditions of the mathematical model were given. The presented model is suitable in the automated control. The presented system of differential equations was solved numerically. The analysis presented here and the obtained results could be useful in predicting the drying kinetics of potatoes and similar natural products in a conveyor-belt dryer.

scholarly journals Design and development of a process-economic mathematical model of a lupine hydrolysis unit

2019 ◽  
Vol 292 ◽  
pp. 01028
Author(s):  
Jiří Pecha ◽  
Lubomír Šánek ◽  
Miloš Jelínek ◽  
Jakub Husár ◽  
Karel Kolomazník
Keyword(s):  
Mathematical Model ◽  
Amino Acids ◽  
Computer Simulation ◽  
Production Process ◽  
Chemical Reaction ◽  
Process Modelling ◽  
Operating Conditions ◽  
Optimal Operating ◽  
Human Diet ◽  
High Level

Lupine is considered as a source of protein with a high level of valuable amino acids, what can have in a human diet significant impact on the prevention of various diseases. This paper deals with the process modelling and computer simulation of the lupine flour hydrolysis, particularly focusing on calculations and comparisons of different process variants. Suggested process-economic mathematical model of the production process is a very effective tool for achieving optimal operating conditions under which the specific costs of preparing the final hydrolyzed product are minimal. Simultaneously, the proposed mathematical model of the production node of the hydrolysis unit includes the key processes for the preparation of the resulting hydrolyzate, i.e. the chemical reaction itself, filtration of the reaction mixture and concentration of the filtrate, which is the final desired product – the lupine hydrolysate.

Paper 3: An Analytical and Experimental Study of Self-Acting Valves in a Reciprocating Air Compressor

1969 ◽  
Vol 184 (18) ◽  
pp. 24-33 ◽  
Author(s):  
J. F. T. MacLaren ◽  
S. V. Kerr
Keyword(s):  
Mathematical Model ◽  
Experimental Study ◽  
Differential Equations ◽  
Digital Computer ◽  
Pressure Difference ◽  
Operating Conditions ◽  
Air Compressor ◽  
Ring Plate ◽  
Discharge Valve ◽  
Compressor Performance

A digital computer is used to solve the differential equations which form a mathematical model of a self-acting valve. The model describes the movement of a suction or a discharge valve, and the pressure difference across the valve. The computer results are compared with experimental records obtained over a range of operating conditions from a single-stage air compressor fitted with spring-loaded ring-plate valves. Subsequently the analysis provides conventional criteria of compressor performance.

scholarly journals Study of the dynamics of the working cell of the automatic mill of the pipe-rolling unit

2018 ◽  
pp. 74-80
Author(s):  
S.R. Rakhmanov ◽  
V.T Vyshinskyi
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Mechanical System ◽  
Equations Of Motion ◽  
Retention Mechanism ◽  
Operating Conditions ◽  
Dynamic Processes ◽  
Real Spectrum ◽  
Pipe Rolling ◽  
Automatic Mill

Purpose. Determining the real spectrum and the level of dynamic loads would make it possible to develop recommendations for improving the TPA-350 automatic mill, with the aim of expanding its technological capabilities, improving the reliability of operation and durability. Metodology. This work was carried out on the basis of the development of a mathematical model of dynamic processes in the mechanical system of an automatic TPA mill, where an attempt was made to identify the features of the functioning of a working stand with a rolled sleeve in the formulation of dynamic problems. Obviously, the proposed approach is more correct and convenient when studying complex dynamic phenomena in the elements of an automatic TPA mill. Findings. The results of the study of the dynamics of the working stand of the automatic mill of the pipe-rolling unit (TPA) are given The basic parameters of the functioning of the working stand, such as the automatic mill TPA 350, are established, and a mathematical model of the basic problem of the dynamics of a mechanical system is developed. The differential equations of motion for the selected model of the working stand and the elastic elements of the bed retention mechanism on the support nodes of the automatic TPA mill have been compiled. The corresponding patterns of oscillations of the working stand were obtained. Some features of the functioning of the working stand are identified by the example of an automatic mill TPA 350. The dynamic parameters of the working stand of the mill, affecting the difference in the thickness of the rolled sleeves, are established. Originality. The interrelation of the working stand dynamics with the operating conditions of an automatic TPA mill on the basis of a simplified mathematical model of dynamic processes is established. A mathematical model of the mechanical system of a working working stand of an automatic TPA mill has been compiled. In the most general form, the mechanical system of a working stand of a mill is described using differential equations describing the behavior of the selected design scheme of a system with two degrees of freedom. Practical value. A scheme has been proposed for modernizing the working stand and the mechanism for holding the working stand of the TPA-350 automatic mill. IL. 4. Biblography: 8 titles.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

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. 

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