A Real-Time Mathematical Model for the Two-Dimensional Temperature Field of Petroleum Coke Calcination in Vertical Shaft Calciner

JOM ◽  
2016 ◽  
Vol 68 (8) ◽  
pp. 2149-2159 ◽  
Author(s):  
Jin Xiao ◽  
Jindi Huang ◽  
Qifan Zhong ◽  
Fachuang Li ◽  
Hongliang Zhang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Temperature Field ◽  
Real Time ◽  
Petroleum Coke ◽  
Vertical Shaft ◽  
Two Dimensional

The restoration of temperature distribution in a two-dimensional domain by a tomographic method by using the results of measurements for electric resistance of oriented conductors

2018 ◽  
Author(s):  
В.А. Деревянко ◽  
А.Ф. Латыпов
Keyword(s):  
Mathematical Model ◽  
Temperature Distribution ◽  
Real Time ◽  
Printed Circuit Board ◽  
Circuit Board ◽  
Two Dimensional ◽  
Electronic Unit ◽  
Resistance Thermometer ◽  
Printed Circuit ◽  
Radio Electronic

Рассмотрена возможность использования “термометра сопротивления” для измерения распределения температуры в двумерной области. Создана математическая модель датчика, сводящаяся к решению томографической задачи. Важной особенностью модели является то, что число уравнений в системе линейных алгебраических уравнений (СЛАУ) больше числа переменных. Это позволяет уменьшить ошибки в исходных данных. Создана программа для определения решения СЛАУ с плохо обусловленной матрицей, позволяющая обрабатывать результаты измерений в реальном масштабе времени. Выполнен тестовый расчет. При малом числе ракурсов измерений получена удовлетворительная точность восстановления температуры. Purpose. To ensure a long period of active lifetime of space vehicles, it is necessary to use effective methods and means to control physical processes leading to premature failure of on-board radio electronic equipment both at the stage of ground testing and during active operation of the spacecraft in space. Long-term testing experience for electronic equipment shows that monitoring compliance with necessary temperature conditions of onboard equipment plays the main role in ensuring reliability. Ideally, the thermal control should be performed for all elements of radio electronic units in real time. Method. The possibility of using a “two-dimensional resistance thermometer” for recording the thermal field of a printed circuit board of an electronic unit is considered. The principle of operation of the thermometer is based on the measurement of integral resistances of extended mutually intersecting conductors in a medium with inhomogeneous temperature distribution. The registration of the integral resistances of individual conductors is possible with the help of an automated measuring system by solving the tomographic problem aimed to obtain the temperature distribution on the surface of the printed circuit board. Result. The design of the “two-dimensional temperature sensor” is considered. The sensor is technologically compatible with the design of the printed circuit board of the radio electronic unit. A mathematical model of the sensor is developed. It is reduced to the solution of a tomographic problem. A program for solving a system of linear equations with an ill-conditioned matrix is developed that provides the real-time processing for measurement results. The test calculation is performed. A satisfactory accuracy of the temperature restoration is achieved. Conclusion. A “two-dimensional resistance thermometer” can be used to measure a two-dimensional temperature field for a printed circuit board of a radio electronic unit in real time. The mathematical model allows adapting the thermometer design to a specific radio electronic unit and selecting the required accuracy of the temperature field restoration.

Numerical analysis of temperature field in a thawing embankment in permafrost

1988 ◽  
Vol 25 (1) ◽  
pp. 163-166 ◽  
Author(s):  
Mu Shen
Keyword(s):  
Mathematical Model ◽  
Temperature Field ◽  
Heat Conduction ◽  
Numerical Analysis ◽  
Finite Elements ◽  
Measured Data ◽  
Two Dimensional ◽  
Nonlinear Mathematical Model ◽  
Permafrost Thawing ◽  
Good Agreement

The objective of this paper is to present a numerical analysis by finite elements of a two-dimensional nonlinear mathematical model for heat conduction with phase change in a thawing embankment in permafrost. The calculated results are compared with actual measured data, and good agreement is obtained. All calculations were carried out on a personal computer. Key words: permafrost, thawing, embankment, temperature field, numerical analysis.

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

Temperature field evaluation of a two-dimensional partial heat flow problem through Green's Functions

2019 ◽  
Author(s):  
Guilherme Ramalho Costa ◽  
José Aguiar santos junior ◽  
José Ricardo Ferreira Oliveira ◽  
Jefferson Gomes do Nascimento ◽  
Gilmar Guimaraes
Keyword(s):  
Temperature Field ◽  
Heat Flow ◽  
Green's Functions ◽  
Flow Problem ◽  
Green’S Functions ◽  
Field Evaluation ◽  
Two Dimensional

A Real-Time Mathematical Model for Three-Dimensional Tidal Flow and Water Quality

1991 ◽  
Vol 24 (6) ◽  
pp. 171-177 ◽  
Author(s):  
Zeng Fantang ◽  
Xu Zhencheng ◽  
Chen Xiancheng
Keyword(s):  
Mathematical Model ◽  
Water Quality ◽  
Real Time ◽  
Control Volume ◽  
Tidal Flow ◽  
Three Dimensional ◽  
River Estuary ◽  
Pearl River Estuary ◽  
Practical Application ◽  
The Pearl River

A real-time mathematical model for three-dimensional tidal flow and water quality is presented in this paper. A control-volume-based difference method and a “power interpolation distribution” advocated by Patankar (1984) have been employed, and a concept of “separating the top-layer water” has been developed to solve the movable boundary problem. The model is unconditionally stable and convergent. Practical application of the model is illustrated by an example for the Pearl River Estuary.

CALCULATION OF THE DEPENDENCE OF THE DISTANCE TO THE LOCATED OBJECT FROM THE CORNER POSITION OF THE VEHICLE LINE

2018 ◽  
pp. 14-18
Author(s):  
V. V. Artyushenko ◽  
A. V. Nikulin
Keyword(s):  
Real Time ◽  
Statistical Physics ◽  
Angular Position ◽  
Three Dimensional ◽  
Line Of Sight ◽  
Two Dimensional ◽  
Radar Station ◽  
Flight Mode ◽  
Vector Algebra ◽  
Analytical Expressions

To simulate echoes from the earth’s surface in the low flight mode, it is necessary to reproduce reliably the delayed reflected sounding signal of the radar in real time. For this, it is necessary to be able to calculate accurately and quickly the dependence of the distance to the object being measured from the angular position of the line of sight of the radar station. Obviously, the simplest expressions for calculating the range can be obtained for a segment or a plane. In the text of the article, analytical expressions for the calculation of range for two-dimensional and three-dimensional cases are obtained. Methods of statistical physics, vector algebra, and the theory of the radar of extended objects were used. Since the calculation of the dependence of the range of the object to the target from the angular position of the line of sight is carried out on the analytical expressions found in the paper, the result obtained is accurate, and due to the relative simplicity of the expressions obtained, the calculation does not require much time.

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