DEVELOPMENT OF A MATHEMATICAL MODEL FOR RESEARCHING THE PROCESS OF REDUCTION OF TUNGSTEN HEXAFLUORIDE BY GASEOUS HYDROGEN

В работе рассмотрена математическая модель, описывающая движение течения стационарной, ламинарной, вязкой, несжимаемой смеси газа в трехмерном осесимметричном канале. Математическая модель, описывающая этот процесс, состоит из уравнений Навье – Стокса, уравнения неразрывности и массообмена, которые записаны в безразмерной форме с учетом осесимметричности в цилиндрической системе координат. Решение уравнений осуществляется в физических переменных «скорость – давление» на разнесенной разностной сетке. Показано влияние характерных параметров на распределение концентрации смеси газа гексафторида вольфрама и водорода в канале. Полученная математическая модель позволяет проводить численные исследования по выбору оптимальных условий осуществления процесса восстановления гексафторида вольфрама водородом. The paper considers a mathematical model describing the flow motion of a stationary, laminar, viscous, incompressible gas mixture in a three-dimensional axisymmetric channel. The mathematical model describing this process consists of the Navier-Stokes equations, the continuity and mass transfer equations, which are written in dimensionless form taking into account axisymmetry in a cylindrical coordinate system. The equations are solved in the physical variables "velocity - pressure" on a spaced difference grid. The influence of characteristic parameters on the concentration distribution of a mixture of tungsten hexafluoride gas and hydrogen in the channel is shown. The obtained mathematical model makes it possible to conduct numerical studies on the choice of optimal conditions for the process of reduction of tungsten hexafluoride with hydrogen.

Regulation of Temperature on Multitrays in an Indirect Solar Dryer (ISD) with Energy Storage and Three Airflow Modes

This work presents the regulation of temperature in an indirect multitrays solar dryer with oriented flux under the irradiance fluctuation. The temperature regulator using a negative temperature coefficient (NTC) as a sensor and fans is designed, and a similar device is also used to measure humidity through a sensor. Inlet and outlet dryer temperature and temperature on the three trays have been recorded with the regulation system according to different airflow modes. Irradiance and humidity have also been recorded. The model of outlet temperature with energy storage was given by using heat transfer equations. The results have shown that in the linking airflow mode, the average temperature on the three trays is 51.3 ± 1.5a°C, 52.18 ± 1.4a°C, and 51.9 ± 1.2a°C, respectively, with 52°C as setpoint temperature and NTC fixed on tray number 2. With temperature sensor in the same tray and 51°C as setpoint temperature, the average temperatures on the three trays are 51.86 ± 1.54°C, 51.60 ± 1.16°C, and 50.42 ± 1.13°C, respectively, in mixed mode, whereas in crossing airflow mode, the temperature gradient does not allow regulation on all trays. The regulation is possible when the temperature in the dryer chamber exceeds the set point temperature by more than 5%. The proportional type corrector is suitable for the temperature controller in indirect solar dryers. When the energy source is unstable, humidity which is a variable parameter is used to mark the end of drying instead of time.

Numerical Study of Cylindrical Tropical Woods Pyrolysis Using Python Tool

In this paper, the thermal behavior of large pieces of wood pyrolysis has been modeled. Two mathematical models coupling heat transfer equations to chemical kinetics were used to predict the pyrolytic degradation of a 25 mm radius wood sample, assumed to be dry in the first model and wet in the second, when heated to 973.15 K. The reactions involved in the pyrolysis process are assumed to be endothermic. The diffusion of bounded water during the process is taken into account in the second model, where the heat transfer equation has been coupled to that of the diffusion of moisture. This model, although simple, provides more information on the drying and pyrolysis processes during the heating of wood, which is its originality. It can therefore be advantageously used to calculate the temperature distribution in a pyrolysis bed. The equations of the two models, discretized by an explicit finite difference method, were solved numerically by a program written in Python. The validation of both models against experimental work in the literature is satisfactory. The two models allow examination of the temperature profile in the radial direction of wood samples and highlighting of the effect of temperature on some thermal, physical and physicochemical characteristics.

Experimental studies of iron transformations kinetics and autocatalysis during its physicochemical removal from underground water

The mathematical model of physicochemical iron removal from groundwater was developed. It consists of three interrelated compartments. The results of the experimental research provide information in support of the first two compartments of the mathematical model. The dependencies for the concentrations of the adsorbed ferrous iron and deposited hydroxide concentrations are obtained as a result of the exact solution of the system of the mass transfer equations for two forms of iron in relation to the inlet surface of the bed. An analysis of the experimental data of the dynamics of the deposit accumulation in a small bed sample was made, using a special application that allowed to select the values of the kinetic coefficients and other model parameters based on these dependencies. We evaluated the autocatalytic effect on the dynamics of iron ferrous and ferric forms. The verification of the mathematical model was carried out involving the experimental data obtained under laboratory and industrial conditions.

Mathematical Modeling of Food Processing Operations: A Basic Understanding and Overview

Modeling is the core of food processing supported by many approaches and governed by heat, mass, and momentum transfer equations. The objective of this paper is to mainly discuss and introduce mathematical modeling of some food processes. Food processing is unique from other material processing, as it includes complex multiphase transport and change in material properties during processing. It poses a great challenge in food process engineering. Now a day’s, consumers are taking more precautions before eating something. The way of food processing effectively impacts food quality. Most of the conventional industries use thermal processes like pasteurization, sterilization, and freezing. In recent years the main aim has been to improve these conventional processing technologies. Characterization of temperature distribution is done by mathematical modeling during processing, so this review paper aims to introduce mathematical modeling as a potential tool for the food processing industry. The mathematical models discussed in this article captures the essential features of a complex object or process based on a theoretical understanding of the phenomena and available measurements.

Computational studies of hydrotoparaffin plugs in wells

In Western Siberia and the Far North, complications caused by paraffin plugs in wells are not temporary. They are caused by ongoing factors, such as permafrost zones, a sharp temperature drop along the well, the high gas factor and water in the well products. The paper studies the possibility of using a high-frequency electromagnetic field to remove paraffin plugs inside the well. Mathematical modeling of the problem using a system of heat and mass transfer equations and boundary and initial conditions is described. The phase transition (melting of hydratoparaffin) is denoted by Stefan’s condition which is one of the boundary conditions. The problem does not have an analytical solution, so the numerical implementation of the solution is carried out. Graphs of dependences of melting limits on generator power, and distribution of temperature fields in wells are constructed.

Thermal characteristics of longitudinal fin with Fourier and non-Fourier heat transfer by Fourier sine transforms

The quest for high-performance of heat transfer components on the basis of accommodating shapes, smaller weights, lower costs and little volume has significantly diverted the industries for the enhancement of heat dissipation with variable thermal properties of fins. This manuscript proposes the fractional modeling of Fourier and non-Fourier heat transfer of longitudinal fin via non-singular fractional approach. The configuration of longitudinal fin in terms of one dimension is developed for the mathematical model of parabolic and hyperbolic heat transfer equations. By considering the Fourier and non-Fourier heat transfer from longitudinal fin, the mathematical techniques of Fourier sine and Laplace transforms have been invoked. An analytic approach is tackled for handling the governing equation through special functions for the fractionalized parabolic and hyperbolic heat transfer equations in longitudinal fin. For the sake of comparative analysis of parabolic verses hyperbolic heat conduction of fin temperature, we depicted the distinct graphical illustrations; for instance, 2-dimensional graph, bar chart, contour graphs, heat graph, 3-dimensional graphs and column graphs on for the variants of different rheological impacts of longitudinal fin.

Simulation of shell and tube heat exchanger using COMSOL software

The aim of this paper is to propose a model to simulate the behaviour of water flows in shell and tube heat exchanger. Particularly, the continuity equation, the general heat transfer equations and the energy equation in COMSOL Multiphysics software were implemented in the numerical modelling. Besides, the experiment was also conducted to validate the proposed COMSOL model. The water temperature at locations close to the inlet and outlet of the shell side was respectively predicted at 31.5°C and 34.6°C in the simulation, and it was respectively measured at 31.5°C and 35°C in the experiment. These findings showed that the simulation results had a good agreement with the experiment. Next, this model was extended to simulate the overall heat coefficient and the pressure drops of the water flows in such heat exchanger. The overall heat coefficient was at 736.62 W/m2K. The pressure drops at the inlet/outlet areas of the shell and tubes were at 849.93 Pa and 6255.50 Pa, respectively. Conclusive evidence showed that the proposed model is a reliable method for studying the heat transfer behaviour of the shell and heat exchanger.