scholarly journals MATHEMATICAL MODELING OF LEACHING PROCESS OF RED MUD IN ORDER TO OBTAIN THE KINETICS PARAMETERS

2015 ◽  
Vol 14 (2) ◽  
pp. 90 ◽  
Author(s):  
K. L. M. Dos Passos ◽  
B. M. Viegas ◽  
E. N. Macêdo ◽  
J. A. S. Souza ◽  
E. M. Magalhães
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Red Mud ◽  
Mineralogical Composition ◽  
Raw Material ◽  
Data Conversion ◽  
Kinetics Parameters ◽  
Leaching Process ◽  
Iron Leaching ◽  
The Mathematical Model

The use of the waste of the Bayer process, red mud, is due to its chemical and mineralogical composition that shows a material rich in oxides of iron, titanium and aluminum. Some studies conducted show that this waste can be applied as a source of alternative raw material for concentration and subsequent recovery of titanium compounds from an iron leaching process, which is present in higher amounts, about 30% by weight. To obtain a greater understanding about the leaching kinetics, the information of the kinetic data of this process is very important. In this context, the main objective of this work is the development of a mathematical model that is able to fit the experimental data (conversion / extraction iron, titanium and aluminum) of the leaching process by which is possible to obtain the main kinetic parameters such as the activation energy and the velocity of chemical reactions as well as the controlling step of the process. The development of the mathematical model was based on the model of core decreasing. The obtained model system of ordinary differential equations was able to fit the experimental data obtained from the leaching process, enabling the determination of the controlling step, the rate constants and the activation energies of the leaching process.

Application of a Bubble-Induced Turbulence Model to Subcooled Boiling in a Vertical Pipe

1999 ◽  
Author(s):  
Mahmut D. Mat ◽  
Yüksel Kaplan ◽  
Olusegun J. Ilegbusi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Liquid Phase ◽  
Turbulence Model ◽  
Transport Equations ◽  
Subcooled Boiling ◽  
Vertical Pipe ◽  
Void Fractions ◽  
Turbulence Production ◽  
The Mathematical Model

Abstract Subcooled boiling of water in a vertical pipe is numerically investigated. The mathematical model involves solution of transport equations for vapor and liquid phase separately. Turbulence model considers the turbulence production and dissipation by the motion of the bubbles. The radial and axial void fractions, temperature and velocity profiles in the pipe are calculated. The estimated results are compared to experimental data available in the literature. It is found that while present study satisfactorily agrees with experimental data in the literature, it improves the prediction at lower void fractions.

Methods of Mathematical Modeling of the Leaching Process of Cobalt-Containing Solutions

2021 ◽  
Vol 316 ◽  
pp. 661-666
Author(s):  
Nataliya V. Mokrova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Chemical Kinetics ◽  
Group Method ◽  
Data Handling ◽  
Multistage Processes ◽  
Leaching Process ◽  
Proposed Model ◽  
Simulation Results ◽  
The Mathematical Model

Current cobalt processing practices are described. This article discusses the advantages of the group argument accounting method for mathematical modeling of the leaching process of cobalt solutions. Identification of the mathematical model of the cascade of reactors of cobalt-producing is presented. Group method of data handling is allowing: to eliminate the need to calculate quantities of chemical kinetics; to get the opportunity to take into account the results of mixed experiments; to exclude the influence of random interference on the simulation results. The proposed model confirms the capabilities of the group method of data handling for describing multistage processes.

Analytical Study of Hydro-Pneumatic Processes for Gorlov's Power System

1994 ◽  
Vol 208 (1) ◽  
pp. 67-70
Author(s):  
A I Ryazanov
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Power System ◽  
Analytical Study ◽  
Model Tests ◽  
Air Pressure ◽  
Pneumatic Power ◽  
Time Required ◽  
The Mathematical Model

This paper describes the aerohydrodvnamics of processes in chambers of Gorlov's hydro-pneumatic power system. The mathematical model is developed to determine the main parameters of the processes: water and air velocities, air pressure in the chamber, the periods of time required to fill and empty the chambers and the output of energy during the cycle. The results obtained are in agreement with experimental data and model tests.

Development of a Mathematical Model for Performance Prediction of Planing Catamaran in Calm Water

2019 ◽  
Vol 161 (A2) ◽  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Performance Prediction ◽  
Data Evaluation ◽  
Empirical Equations ◽  
Calm Water ◽  
Semi Empirical ◽  
The Mathematical Model ◽  
Comparison With Experimental Data

In this paper, an attempt has been made to predict the performance of a planing catamaran using a mathematical model. Catamarans subjected to a common hydrodynamic lift, have an extra lift between the two asymmetric half bodies. In order to develop a mathematical model for performance prediction of planing catamarans, existing formulas for hydrodynamic lift calculation must be modified. Existing empirical and semi-empirical equations in the literature have been implemented and compared against available experimental data. Evaluation of lift in comparison with experimental data has been documented. Parameters influencing the interaction between demi-hulls and separation effects have been analyzed. The mathematical model for planing catamarans has been developed based on Savitsky’s method and results have been compared against experimental data. Finally, the effects of variation in hull geometry such as deadrise angle and distance between two half bodies on equilibrium trim angle, resistance and wetted surface have been examined.

scholarly journals Mathematical Model of the Piped Vehicle Motion in Piped Hydraulic Transportation of Tube-Contained Raw Material

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Yongye Li ◽  
Xihuan Sun
Keyword(s):  
Mathematical Model ◽  
Transportation Cost ◽  
Raw Material ◽  
Maximum Relative Error ◽  
Transportation Energy ◽  
Core Components ◽  
Vehicle Motion ◽  
Motion Characteristics ◽  
Experimental Values ◽  
The Mathematical Model

The piped hydraulic transportation of tube-contained raw material is an emerging technique for transporting materials. In this technique, the piped vehicle is one of the core components, and its motion characteristics directly determine the transportation energy consumption and the transportation cost of this technique. To study the motion characteristics of the piped vehicle, the force of the piped vehicle was analyzed from the mechanical perspective in this paper. On the assumption that the piped vehicle moved steadily and it had sufficient stiffness, the mathematical model of the piped vehicle motion was established in the turbulent flow according to the stress characteristics of the piped vehicle and the factors influencing its motion characteristics, and then the mathematical model was tested by experiments. The findings show that the calculated values of the velocities of the piped vehicle were identical to the experimental values with changes in various influencing factors. When the flow discharge, the diameter or length of the piped vehicle increased, or the mass of transported material decreased, the velocity of the piped vehicle increased. The maximum relative error did not exceed 9.47%, which proved that the mathematical model of the piped vehicle motion was rational. The results can provide theoretical basis to improve the structure of the piped vehicle and the piped hydraulic transportation technique of tube-contained raw material.

scholarly journals Belt conveyor failure simulation at the design stage with transverse displacements of the belt

2020 ◽  
Vol 168 ◽  
pp. 00056
Author(s):  
Vitalii Monastyrskyi ◽  
Serhii Monastyrskyi ◽  
Denis Nomerovskyi ◽  
Borys Mostovyi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Fourier Transform ◽  
Adaptive Control ◽  
Design Stage ◽  
Belt Conveyor ◽  
Failure Simulation ◽  
The Fourier Transform ◽  
External Forces ◽  
The Mathematical Model

To find possible conveyor failures at the design stage means to determine a transverse belt displacement and compare the obtained data with the permissible ones. The dynamic problem of the belt movement on the conveyor has been defined. Resistance and external forces, limits of the belt displacement have been determined. The transverse belt displacement can be described by partial differential equations. To solve the problem, the Fourier transform has been used. Change patterns in the transverse belt conveyor displacement dependent on conveyor’s parameters, type of load, and skewing of the idlers along the conveyor have been obtained. The results agree with experimental data. The method of adaptive control of the transverse belt displacement has been described. The essence of this method is to adapt the model of the moving belt in the conveying trough to changed conditions and to reveal the uncertainty of the control with the known parameters of the mathematical model.

scholarly journals Mathematical modelling of trastuzumab-induced immune response in an in vivo murine model of HER2+ breast cancer

2018 ◽  
Vol 36 (3) ◽  
pp. 381-410 ◽  
Author(s):  
Angela M Jarrett ◽  
Meghan J Bloom ◽  
Wesley Godfrey ◽  
Anum K Syed ◽  
David A Ekrut ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Experimental Data ◽  
Mathematical Model ◽  
Immune Response ◽  
Immune System ◽  
Murine Model ◽  
Tumour Growth ◽  
Experimental Approach ◽  
Her2 Breast Cancer ◽  
The Mathematical Model

Abstract The goal of this study is to develop an integrated, mathematical–experimental approach for understanding the interactions between the immune system and the effects of trastuzumab on breast cancer that overexpresses the human epidermal growth factor receptor 2 (HER2+). A system of coupled, ordinary differential equations was constructed to describe the temporal changes in tumour growth, along with intratumoural changes in the immune response, vascularity, necrosis and hypoxia. The mathematical model is calibrated with serially acquired experimental data of tumour volume, vascularity, necrosis and hypoxia obtained from either imaging or histology from a murine model of HER2+ breast cancer. Sensitivity analysis shows that model components are sensitive for 12 of 13 parameters, but accounting for uncertainty in the parameter values, model simulations still agree with the experimental data. Given theinitial conditions, the mathematical model predicts an increase in the immune infiltrates over time in the treated animals. Immunofluorescent staining results are presented that validate this prediction by showing an increased co-staining of CD11c and F4/80 (proteins expressed by dendritic cells and/or macrophages) in the total tissue for the treated tumours compared to the controls ($p < 0.03$). We posit that the proposed mathematical–experimental approach can be used to elucidate driving interactions between the trastuzumab-induced responses in the tumour and the immune system that drive the stabilization of vasculature while simultaneously decreasing tumour growth—conclusions revealed by the mathematical model that were not deducible from the experimental data alone.

scholarly journals Wheat Germ Drying with Different Time-Temperature Combinations in a Fluidized Bed Dryer

Processes ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 245 ◽  
Author(s):  
Der-Sheng Chan ◽  
Meng-I Kuo
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Fluidized Bed ◽  
Wheat Germ ◽  
Dynamic Equilibrium ◽  
Cooling Stage ◽  
Fluidized Bed Dryer ◽  
Drying Condition ◽  
Drying Conditions ◽  
The Mathematical Model

The development of an effective drying performance of the fluidized bed dryer (FBD) is crucial to reduce drying costs. The objective of this study was to investigate the drying performance of wheat germ (WG) with different time-temperature combinations in the FBD. The WG was dried at different set temperatures of 80, 100 and 120 °C. The moisture content (MC) and water activity (WA) of WG were measured. A mathematical model was proposed to develop an optimal drying condition. The changes in the MC of WG during drying in the FBD could be divided into the decreased period, the dynamic equilibrium period and the increased period. The product temperature of 45 °C and WA of 0.3 of WG drying could be attained by different time-temperature combinations. The mathematical model, which was developed in conjunction with different time-temperature combinations, could predict the dehydration time and the condensation time of WG for optimization the drying conditions. The WG dehydration at the heating stage and the WG condensation at the cooling stage could also be evaluated by the dehydration flux and the condensation flux, respectively. The optimal drying performance of WG exists in a compromise between promoting dehydration and reducing condensation. Information obtained from the analysis of dehydration flux and condensation flux with experimental data and simulation gave the guidelines for performing an effective drying of WG in the FBD.

Heat Convection from a Horizontal Cylinder Rotating in a Quiescent Fluid

1986 ◽  
Vol 10 (3) ◽  
pp. 141-152
Author(s):  
H.M. Badr ◽  
S.M. Ahmed
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Mathematical Model ◽  
Horizontal Cylinder ◽  
Heat Transfer Process ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
Boussinesq Fluid ◽  
The Mathematical Model ◽  
Quiescent Fluid

The aim of this work is a theoretical investigation to the problem of heat transfer from an isothermal horizontal cylinder rotating in a quiescent fluid. The study is based on the solution of the conservation equations of mass, momentum and energy for two-dimensional flow of a Boussinesq fluid. The effects of the parameters which influence the heat transfer process namely the Reynolds number and Grashof number are considered while the Prandtl number is held constant. Streamline and isotherm patterns are obtained from the mathematical model and the results are compared with previous experimental data. A satisfactory agreement was found.

Nonlinear dynamic analysis of a Stockbridge damper

2019 ◽  
Vol 46 (9) ◽  
pp. 828-835
Author(s):  
Nilson Barbieri ◽  
Marlon Elias Marchi ◽  
Marcos José Mannala ◽  
Renato Barbieri ◽  
Lucas de Sant’Anna Vitor Barbieri ◽  
...  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Nonlinear Dynamic Analysis ◽  
Nonlinear Behavior ◽  
Vibration Data ◽  
Electric Transmission Line ◽  
Good Concordance ◽  
Tip Mass ◽  
The Mathematical Model ◽  
Stockbridge Damper

The purpose of this work is to validate a nonlinear mathematical model (finite element method) for dynamic simulation of Stockbridge dampers of electric transmission line cables. To obtain the mathematical model, a nonlinear cantilever beam with a tip mass was used. The mathematical model incorporates a nonlinear stiffness matrix of the element due to the nonlinear curvature effect of the beam. To validate the mathematical model, the numerical results were compared with experimental data obtained on a machine adapted from cam test. Five different circular cam profiles with eccentricities of 0.25, 0.5, 0.75, 1.25, and 1.5 mm were used. Vibration data were collected through three accelerometers arranged along the sample. A good concordance was found between the numerical and experimental data. The same behavior was observed in tests of another Stockbridge damper excited by a shaker. The nonlinear behavior of the system was evidenced.

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