scholarly journals Mathematical model of unsteady gas to solid particles heat transfer in fluidized bed

2009 ◽  
Vol 13 (1) ◽  
pp. 55-68 ◽  
Author(s):  
Mladen Stojiljkovic ◽  
Branislav Stojanovic ◽  
Jelena Janevski ◽  
Gradimir Ilic
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Computer Program ◽  
Fluidized Bed ◽  
Particle Temperature ◽  
Prediction Method ◽  
Solid Particles ◽  
Gas Temperature ◽  
One Dimensional ◽  
The Mathematical Model

The mathematical model of unsteady one-dimensional gas to particles heat transfer for non-isothermal fluidized bed with periodic heating of solid particles has been described. The method of numerical solution of governing differential equations, the algorithm and the computer program, have been presented. By using mathematical model and computer program, the temperature profiles for interstitial gas, gas in bubbles, and solid particles along the height of fluidized bed in function of time, have been determined. The results obtained on the basis of prediction method are compared to the experimental results of the authors; the satisfactory agreement has been found for interstitial gas temperature and solid particle temperature. On the basis of this comparison, the mathematical model has been verified.

scholarly journals INCORPORATION OF A TWO-FLUX MODEL FOR RADIATIVE HEAT TRANSFER IN A COMPREHENSIVE FLUIDIZED BED SIMULATOR PART I: PRELIMINARY THEORETICAL INVESTIGATIONS

2003 ◽  
Vol 2 (1) ◽  
pp. 64 ◽  
Author(s):  
J. A. Rabi ◽  
M. L. De Souza Santos
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Thermal Radiation ◽  
Fluidized Bed ◽  
Radiative Heat ◽  
Radiation Heat Transfer ◽  
Basic Structure ◽  
Solid Particles ◽  
Particulate Media ◽  
Bubbling Fluidized Bed

Over the last two decades, a comprehensive mathematical model and its corresponding computational program, aimed to simulate steady-state operations of bubbling fluidized bed equipments, has been continuously improved and tested. Despite its success, the simulator has employed a simple approach for radiative heat transfers. In cases of high temperatures, thermal radiation becomes an important energy transfer mode and the original model could lead to deviations above acceptable levels. The purpose of the present work was to improve the model for thermal radiation heat transfer between all solid particles in the bed section by applying a two-flux method to a non-homogeneous polydispersed particulate media in radiative equilibrium. Gases in the emulsion and in the bubbles were assumed transparent to thermal radiation. This first part of the paper presents and discusses the basic structure of the former mathematical model and of the new one.

scholarly journals INCORPORATION OF A TWO-FLUX MODEL FOR RADIATIVE HEAT TRANSFER IN A COMPREHENSIVE FLUIDIZED BED SIMULATOR PART I: PRELIMINARY THEORETICAL INVESTIGATIONS

2003 ◽  
Vol 2 (1) ◽  
Author(s):  
J. A. Rabi ◽  
M. L. De Souza Santos
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Thermal Radiation ◽  
Fluidized Bed ◽  
Radiative Heat ◽  
Radiation Heat Transfer ◽  
Basic Structure ◽  
Solid Particles ◽  
Particulate Media ◽  
Bubbling Fluidized Bed

Over the last two decades, a comprehensive mathematical model and its corresponding computational program, aimed to simulate steady-state operations of bubbling fluidized bed equipments, has been continuously improved and tested. Despite its success, the simulator has employed a simple approach for radiative heat transfers. In cases of high temperatures, thermal radiation becomes an important energy transfer mode and the original model could lead to deviations above acceptable levels. The purpose of the present work was to improve the model for thermal radiation heat transfer between all solid particles in the bed section by applying a two-flux method to a non-homogeneous polydispersed particulate media in radiative equilibrium. Gases in the emulsion and in the bubbles were assumed transparent to thermal radiation. This first part of the paper presents and discusses the basic structure of the former mathematical model and of the new one.

Study of Heat Transfer and Hydrodynamics in a Gas-Solid Fluidized Bed Reactor Experimentally and Numerically

2011 ◽  
Vol 110-116 ◽  
pp. 4187-4197
Author(s):  
Mahdi Hamzehei ◽  
Hassan Rahimzadeh ◽  
Goodarz Ahmadi
Keyword(s):  
Heat Transfer ◽  
Computational Model ◽  
Fluidized Bed ◽  
Particle Temperature ◽  
Fluidized Bed Reactor ◽  
Solid Particles ◽  
Experimental Results ◽  
Heat Conducting ◽  
Momentum Exchange ◽  
Good Agreement

—In this research, the heat transfer and hydrodynamics of a gas–solid fluidized bed reactor were studied experimentally and computationally. A multi-fluid Eulerian computational model incorporating the kinetic theory for solid particles was developed and used to simulate the heat conducting gas–solid flows in a fluidized bed configuration. Momentum exchange coefficients were evaluated using the Syamlal–O’Brien drag functions. Temperature distributions of different phases in the reactor were also computed. Good agreement was found between the model predictions and the experimentally obtained data for the bed expansion ratio as well as the qualitative gas–solid flow patterns. The simulation and experimental results showed that the gas temperature decreases as it moves upward in the reactor, while the solid particle temperature increases. Pressure drop and temperature distribution predicted by the simulations were in good agreement with the experimental measurements at superficial gas velocities higher than the minimum fluidization velocity. Also, the predicted time-average local voidage profiles were in reasonable agreement with the experimental results. The study showed that the computational model was capable of predicting the heat transfer and the hydrodynamic behavior of gas-solid fluidized bed flows with reasonable accuracy.

scholarly journals Adaptation of a Mathematical Model of Generalized Heat Exchange in Furnaces

2020 ◽  
Vol 20 (4) ◽  
pp. 12-22
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Gas Flow ◽  
Calculated Data ◽  
Combustion Products ◽  
Steam Boiler ◽  
Gas Temperature ◽  
Condi Tions ◽  
Proposed Model ◽  
The Mathematical Model

Consideration of the scheme of flows of combustion products in furnaces and flow chambers of combus-tion within the framework of the heat transfer paradigm made it possible to determine the ratio of the genera-lized mechanisms of heat transfer – convection and radiation. The transition from uniform distribution of gas flow velocity to uneven distribution in furnaces with a geometrically peculiar fence has been implemented. This made it possible to take into account the use of recirculation gases, dual-light shades, changes in the shape and size of the cross-section of the furnace, and installation of shade surfaces in a furnace. The condi-tions for the correctness of the mathematical model are considered, and the eigenvalues of the boundary value problem under conditions of an asymmetric temperature field and the function of the gas temperature changing along the height of the furnace are obtained. A comparative analysis of the nature of the change in gas temperature with height according to the proposed model with the calculation for a steam boiler with a capacity of 950 t/h according to the standard method showed a satisfactory agreement of the calculated data with an accuracy of +4.87 %.

Systems Actuated by Shape Memory Alloys: Identification and Modeling

2021 ◽  
Vol 1 (2) ◽  
pp. 12-20
Author(s):  
Najmeh Keshtkar ◽  
Johannes Mersch ◽  
Konrad Katzer ◽  
Felix Lohse ◽  
Lars Natkowski ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Numerical Simulations ◽  
Shape Memory ◽  
Transfer Equation ◽  
Mechanical Parameters ◽  
Heat Transfer Equation ◽  
The Mathematical Model

This paper presents the identification of thermal and mechanical parameters of shape memory alloys by using the heat transfer equation and a constitutive model. The identified parameters are then used to describe the mathematical model of a fiber-elastomer composite embedded with shape memory alloys. To verify the validity of the obtained equations, numerical simulations of the SMA temperature and composite bending are carried out and compared with the experimental results.

scholarly journals SYNTHESIS OF PROGRAM AND FINITE LAWS OF MOTION IN ANALYTICAL MODELS OF CONTROL OF THE FINAL STATE OF BIOMECHANICAL SYSTEMS

2019 ◽  
Vol 19 (1) ◽  
pp. 93-99
Author(s):  
V Zagrevskiy ◽  
O Zagrevskiy
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Center Of Mass ◽  
Material Point ◽  
Object Motion ◽  
Reference Points ◽  
Analytical Models ◽  
Final State ◽  
Finite Control ◽  
The Mathematical Model

Aim. The article deals with developing a computer program to simulate the movement of the object with a given initial and final speed and fixed travel time. Materials and methods. The analysis, as a method of biomechanics, allows us to assess the biomechanical state of the athlete in real sports exercises. The function of motion synthesis is the ability to predict the trajectory and behavior of the biomechanical system at specified reference points of the phase structure of the simulated motion. The article deals with one of the methods of biomechanical synthesis of movements: synthesis of control of the final state of biomechanical systems, based on the reduction of finite control to a given program control after attenuation of the transient component of acceleration. The mathematical description of the object motion is based on the known law of finite control with feedback. Integration of the mathematical model constructed in the form of the differential equation of the second order was carried out by one of the numerical methods of integration: Runge–Kutta method of the fourth order of accuracy. Consideration of the method is based on a mathematical apparatus describing the motion of a material point, which can be represented by a common center of mass of a biomechanical system, a joint, a center of mass of a segment, etc. Results. The mathematical model of the motion of a material point with the given kinematic parameters of motion at the initial and final moments is implemented in a computer program in the Visual Basic 2010 language environment based on the integrated development environment Visual Studio Express 2013. The output provides numerical and visual support for simulation results. Conclusion. It is shown that the developed computer model of the method always implements the goal of motion: to transfer an object from a given initial state by speed to a given final state for a fixed time of movement.

scholarly journals Development of condenser mathematical model for research and development of ways to improve its efficiency

2020 ◽  
Vol 18 (4) ◽  
pp. 578-585
Author(s):  
Madina Shavdinova ◽  
Konstantin Aronson ◽  
Nina Borissova
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Water Temperature ◽  
Steam Turbine ◽  
Cooling Water ◽  
Laboratory Research ◽  
Thermal Engineering ◽  
Linear Regression Method ◽  
Cooling Water Temperature ◽  
The Mathematical Model

The condensing unit is one of the most important elements of the steam turbine of a combined heat and power plant. Defects in elements of the condensing unit lead to disturbances in the steam turbine operation, its failures and breakdowns, as well as efficiency losses of the plant. Therefore, the operating personnel need to know the cause of the malfunction and to correct it immediately. There are no diagnostic models of condensers in the Republic of Kazakhstan at the moment. In this regard, a mathematical model of a condenser based on the methodology of Kaluga Turbine Plant (KTP) has been developed. The mathematical model makes it possible to change the input parameters, plot dependency diagrams, and calculate the plant efficiency indicators. The mathematical model of the condenser can be used to research ways for the improvement of the condensing unit efficiency, for diagnostic purposes of the equipment condition, for the energy audit conduction of the plant, and in the training when performing virtual laboratory research. Using static data processing by linear regression method we obtain that the KTP methodology of condenser calculation is fair at cooling water temperature from 20 °C to 24 °C, but at cooling water temperature from 20 °C to 28 °C, the methodology of JSC "All-Russia Thermal Engineering Institute" (JSC "VTI") is used. One of the ways to increase the condenser efficiency has been proposed. It is the heat transfer augmentation with riffling annular grooves on tubes. This method increases the heat transfer coefficient by 2%, reduces the water subcooling of the heating steam by 0.9 °C, and decreases the cooling area by 2%.

Mathematical modeling of the heat-transfer process and solid particles in a fluidized bed

1982 ◽  
Vol 42 (2) ◽  
pp. 169-176
Author(s):  
V. A. Borodulya ◽  
Yu. S. Teplitskii ◽  
Yu. G. Epanov ◽  
Yu. E. Livshits ◽  
I. I. Yanovich
Keyword(s):  
Mathematical Modeling ◽  
Heat Transfer ◽  
Fluidized Bed ◽  
Transfer Process ◽  
Heat Transfer Process ◽  
Solid Particles

Fluidized-Bed Heat Transfer Modeling for the Development of Particle/Supercritical-CO2 Heat Exchanger

2017 ◽  
Author(s):  
Zhiwen Ma ◽  
Janna Martinek
Keyword(s):  
Heat Transfer ◽  
High Temperature ◽  
Heat Exchanger ◽  
Fluidized Bed ◽  
Solid Particles ◽  
Heat Transfer Modeling ◽  
Power Cycle ◽  
Heat Exchanger Design ◽  
Temperature Heat ◽  
The Cost

Concentrating solar power (CSP) technology is moving toward high-temperature and high-performance design. One technology approach is to explore high-temperature heat-transfer fluids and storage, integrated with a high-efficiency power cycle such as the supercritical carbon dioxide (s-CO2) Brayton power cycle. The s-CO2 Brayton power system has great potential to enable the future CSP system to achieve high solar-to-electricity conversion efficiency and to reduce the cost of power generation. Solid particles have been proposed as a possible high-temperature heat-transfer medium that is inexpensive and stable at high temperatures above 1,000°C. The particle/heat exchanger provides a connection between the particles and s-CO2 fluid in the emerging s-CO2 power cycles in order to meet CSP power-cycle performance targets of 50% thermal-to-electric efficiency, and dry cooling at an ambient temperature of 40°C. The development goals for a particle/s-CO2 heat exchanger are to heat s-CO2 to ≥720°C and to use direct thermal storage with low-cost, stable solid particles. This paper presents heat-transfer modeling to inform the particle/s-CO2 heat-exchanger design and assess design tradeoffs. The heat-transfer process was modeled based on a particle/s-CO2 counterflow configuration. Empirical heat-transfer correlations for the fluidized bed and s-CO2 were used in calculating the heat-transfer area and optimizing the tube layout. A 2-D computational fluid-dynamics simulation was applied for particle distribution and fluidization characterization. The operating conditions were studied from the heat-transfer analysis, and cost was estimated from the sizing of the heat exchanger. The paper shows the path in achieving the cost and performance objectives for a heat-exchanger design.

Parametric Study of Temperature Field During the Cooling Stage for Extrusion Blow Molded Part

2005 ◽  
Author(s):  
Zhan-Song Yin ◽  
Hon-Xiong Huang
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Internal Heat ◽  
Mold Material ◽  
Orthogonal Experimental Design ◽  
Ann Model ◽  
Molded Part ◽  
Artificial Neural Network Ann ◽  
The Mathematical Model ◽  
Part Thickness

A mathematical model of the transient heat transfer during the cooling and solidification of extrusion blow molded part was developed. The temperature profiles were obtained by using finite element (FE) code POLYFLOW to solve the mathematical model. The influences of blow mold material, internal heat transfer coefficient, part thickness, and initial parison temperature on cooling were analyzed. An orthogonal experimental design was applied to determine the significance of four process parameters on the time for opening the mold. The calculated results were estimated by analysis of variance (ANVOA). An artificial neural network (ANN) model based on the numerical simulation data was developed to build for predicting the temperature distribution across thickness. The results showed that ANN approach was an effective method for analyzing the cooling of blow molded part.

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