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The article presents the procedure for how to establish a mathematical model of nitrogen oxides formation based on the theory of dimensional analysis. The model is based on selected physical quantities (parameters) measurable during regular operation of a heat generation plant. The objective of using dimensional analysis to describe nitrogen oxides formation is to show that between operating parameters of the combustion equipment and the NOx formation there is a significant correlation.The obtained results, which are further described in this article, have proved this fact. The obtained formula expressing nitrogen oxides formation, based on dimensional analysis, applies universally to any boiler fuelled by coal, gas or biomass. However, it is necessary to find C, m, n constants for the formula by experiment, individually for each type of boiler and used fuel. The experiment is based on on-line measurements of selected operational parameters for a given boiler, combusting a certain type of fuel with its actual moisture content and calorific value. The methodology, described in this article, helps to find relationships between the operational parameters and the formation of NOx emissions for a particular furnace. The developed mathematical model has been validated with boilers fuelled by black coal and biomass. Both the results obtained from direct measurements of NOx in both types of boilers, and the results obtained by calculation using equation based on the dimensional analysis, are in a very good accord. When burning coal, the variation between NOx expression from the model and the on-line measurements ranges between -12.23 % and + 9.92 %, and for burning biomass between -0.54 % and 0.48 %.The intention of the authors is to inform the professional community about the suitability of the dimensional analysis to describe any phenomena for which there is currently no exact mathematical formulation based on differential equations or empirical formulas. Many other examples of dimensional analysis applications in practice may be found in the work of Čarnogurská and Příhoda (2011).
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Mathematical Modelling of the Infusion Test

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EN
The objective of this paper was to improve the well established in clinical practice Marmarou model for intracranial volume-pressure compensation by adding the pulsatile components. It was demonstrated that complicated pulsation and growth in intracranial pressure during infusion test could be successfully modeled by the relatively simple analytical expression derived in this paper. The CSF dynamics were tested in 25 patients with clinical symptoms of hydrocephalus. Basing on the frequency spectrum of the patient's baseline pressure and identified parameters of CSF dynamic, for each patient an "ideal" infusion test curve free from artefacts and slow waves was simulated. The degree of correlation between simulated and real curves obtained from clinical observations gave insight into the adequacy of assumptions of Marmarou model. The proposed method of infusion tests analysis designates more exactly the value of the reference pressure, which is usually treated as a secondary and of uncertain significance. The properly identified value of the reference pressure decides on the degree of pulsation amplitude growth during IT, as well as on the value of elastance coefficient. The artificially generated tests with various pulsation components were also applied to examine the correctness of the used algorithm of identification of the original Marmarou model parameters.
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EN
A physical model of the human-javelin system has been developed together with a mathematical model of javelin flight including its transverse elastic vibrations. Three kinds of parametric identifications were distinguished: geometrical, mass and aerodynamic. Numerical calculations were made for different initial velocities and throwing angles. The results obtained have been presented graphically.
EN
Multilayer clustering based adsorption model (uniBET) is aimed at adsorption phenomena modeling with having regard to surface geometrical and energetical heterogeneities. Facilitation of the uniBET model formulas leads to the LBET class models. A review on uniBET model and the analysis of the multilayer heterogeneous adsorption models for characterization of porous materials of carbonaceous origin are presented.
EN
The modeling of ethylbenzene dehydrogenation in a catalytic membrane reactor has been carried out for porous membrane by means of two-dimensional, non-isothermal stationary mathematical model. A mathematical model of the catalytic membrane reactor was applied, in order to study the effects of transport properties of the porous membrane on process performance. The performed modeling of the heat and mass transfer processes within the porous membrane, allowed us to estimate the efficiency of its use in membrane reactors, in comparison with a dense membrane (with additional oxidation of the hydrogen in shell side). The use of a porous ceramic membrane was found to cause an increase of the ethylbenzene conversion at 600°C, up to 93 %, while the conversion in the case of conventional reactor was 67%. In this work, we defined the key parameter values of porous membrane (pore diameter and thickness) for ethylbenzene dehydrogenation in catalytic membrane reactor, at which the highest conversion of ethylbenzene and styrene selectivity can be reached.
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