17 resultados para mathematical modeling

em Universidade Federal do Rio Grande do Norte(UFRN)


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MACHADO, Antônio V. et al. Estudio del Secado de Anacardo (Anacardium occidentale L.) mediante Secador Solar de Radiación Directa. Información Tecnológica, v. 21, n. 1, p. 31-37, 2010.

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This study proposes to do a study on the mathematical modeling of permeation of films based on chitosan. To conduct the study were obtained membranes with various compositions: a virtually pure membrane-based chitosan; one of chitosan associated with poly (ethylene oxide (PEO). The membranes of pure chitosan were treated with plasma in atmospheres of oxygen, argon and methane. The various types of films were characterized as to its permeation regarding sufamerazina sodium. In the process of mathematical modeling were compared the standard method of obtaining the coefficient of permeation recital straight down the slope of the plot obtained by extinction / time with a the integration process of numerical permeability rate will be calculated from the spectroscopy UV

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Modeling transport of particulate suspensions in porous media is essential for understanding various processes of industrial and scientific interest. During these processes, particles are retained due to mechanisms like size exclusion (straining), adsorption, sedimentation and diffusion. In this thesis, a mathematical model is proposed and analytical solutions are obtained. The obtained analytic solutions for the proposed model, which takes pore and particle size distributions into account, were applied to predict the particle retention, pore blocking and permeability reduction during dead-end microfiltration in membranes. Various scenarios, considering different particle and pore size distributions were studied. The obtained results showed that pore blocking and permeability reduction are highly influenced by the initial pore and particle size distributions. This feature was observed even when different initial pore and particle size distributions with the same average pore size and injected particle size were considered. Finally, a mathematical model for predicting equivalent permeability in porous media during particle retention (and pore blocking) is proposed and the obtained solutions were applied to study permeability decline in different scenarios

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The aim of the present study is to reevaluate the logical thought of the English mathematician George Boole (1815 - 1864). Thus, our research centers on the mathematical analysis of logic in the context of the history of mathematics. In order to do so, we present various biographical considerations about Boole in the light of events that happened in the 19th century and their consequences for mathematical production. We briefly describe Boole's innovations in the areas of differential equations and invariant theory and undertake an analysis of Boole's logic, especially as formulated in the book The Mathematical Analysis of Logic, comparing it not only with the traditional Aristotelian logic, but also with modern symbolic logic. We conclude that Boole, as he intended, expanded logic both in terms of its content and also in terms of its methods and formal elaboration. We further conclude that his purpose was the mathematical modeling of deductive reasoning, which led him to present an innovative formalism for logic and, because the different ways it can be interpreted, a new conception of mathematics

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The main goal of the present study is to propose a methodological approach to the teaching of Geometry and, in particular, to the construction of the concepts of circle (circumference) and ellipse by 7th and 8th grade students. In order to aid the students in the construction of these concepts, we developed a module based on mathematical modeling, and both Urban Geometry (Taxicab Geometry) and Isoperimetric Geometry. Our analysis was based on Jean Piaget's Equilibrium Theory. Emphasizing the use of intuition based on accumulated past experiences, the students were encouraged to come up with a hypothesis, try it out, discuss it with their peers, and derive conclusions. Although the graphs of circles and ellipses assume different shapes in Urban and Isoperimetric Geometry than they do in the standard Euclidian Geometry, their definitions are identical regardless of the metric used. Thus, by comparing the graphs produced in the different metrics, the students were able to consolidate their understanding of these concepts. The intervention took place in a series of small group activities. At the end of the study, the 53 seventh grade and the 55 eighth grade students had a better understanding of the concepts of circle and ellipse

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The present work describes the use of a mathematical tool to solve problems arising from control theory, including the identification, analysis of the phase portrait and stability, as well as the temporal evolution of the plant s current induction motor. The system identification is an area of mathematical modeling that has as its objective the study of techniques which can determine a dynamic model in representing a real system. The tool used in the identification and analysis of nonlinear dynamical system is the Radial Basis Function (RBF). The process or plant that is used has a mathematical model unknown, but belongs to a particular class that contains an internal dynamics that can be modeled.Will be presented as contributions to the analysis of asymptotic stability of the RBF. The identification using radial basis function is demonstrated through computer simulations from a real data set obtained from the plant

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With water pollution increment at the last years, so many progresses in researches about treatment of contaminated waters have been developed. In wastewaters containing highly toxic organic compounds, which the biological treatment cannot be applied, the Advanced Oxidation Processes (AOP) is an alternative for degradation of nonbiodegradable and toxic organic substances, because theses processes are generation of hydroxyl radical based on, a highly reactivate substance, with ability to degradate practically all classes of organic compounds. In general, the AOP request use of special ultraviolet (UV) lamps into the reactors. These lamps present a high electric power demand, consisting one of the largest problems for the application of these processes in industrial scale. This work involves the development of a new photochemistry reactor composed of 12 low cost black light fluorescent lamps (SYLVANIA, black light, 40 W) as UV radiation source. The studied process was the photo-Fenton system, a combination of ferrous ions, hydrogen peroxide, and UV radiation, it has been employed for the degradation of a synthetic wastewater containing phenol as pollutant model, one of the main pollutants in the petroleum industry. Preliminary experiments were carrier on to estimate operational conditions of the reactor, besides the effects of the intensity of radiation source and lamp distribution into the reactor. Samples were collected during the experiments and analyzed for determining to dissolved organic carbon (DOC) content, using a TOC analyzer Shimadzu 5000A. The High Performance Liquid Chromatography (HPLC) was also used for identification of the cathecol and hydroquinone formed during the degradation process of the phenol. The actinometry indicated 9,06⋅1018 foton⋅s-1 of photons flow, for 12 actived lamps. A factorial experimental design was elaborated which it was possible to evaluate the influence of the reactants concentration (Fe2+ and H2O2) and to determine the most favorable experimental conditions ([Fe2+] = 1,6 mM and [H2O2] = 150,5 mM). It was verified the increase of ferrous ions concentration is favorable to process until reaching a limit when the increase of ferrous ions presents a negative effect. The H2O2 exhibited a positive effect, however, in high concentrations, reaching a maximum ratio degradation. The mathematical modeling of the process was accomplished using the artificial neural network technique

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Environmental sustainability has become one of the topics of greatest interest in industry, mainly due to effluent generation. Phenols are found in many industries effluents, these industries might be refineries, coal processing, pharmaceutical, plastics, paints and paper and pulp industries. Because phenolic compounds are toxic to humans and aquatic organisms, Federal Resolution CONAMA No. 430 of 13.05.2011 limits the maximum content of phenols, in 0.5 mg.L-1, for release in freshwater bodies. In the effluents treatment, the liquid-liquid extraction process is the most economical for the phenol recovery, because consumes little energy, but in most cases implements an organic solvent, and the use of it can cause some environmental problems due to the high toxicity of this compound. Because of this, exists a need for new methodologies, which aims to replace these solvents for biodegradable ones. Some literature studies demonstrate the feasibility of phenolic compounds removing from aqueous effluents, by biodegradable solvents. In this extraction kind called "Cloud Point Extraction" is used a nonionic surfactant as extracting agent of phenolic compounds. In order to optimize the phenol extraction process, this paper studies the mathematical modeling and optimization of extraction parameters and investigates the effect of the independent variables in the process. A 32 full factorial design has been done with operating temperature and surfactant concentration as independent variables and, parameters extraction: Volumetric fraction of coacervate phase, surfactant and residual concentration of phenol in dilute phase after separation phase and phenol extraction efficiency, as dependent variables. To achieve the objectives presented before, the work was carried out in five steps: (i) selection of some literature data, (ii) use of Box-Behnken model to find out mathematical models that describes the process of phenol extraction, (iii) Data analysis were performed using STATISTICA 7.0 and the analysis of variance was used to assess the model significance and prediction (iv) models optimization using the response surface method (v) Mathematical models validation using additional measures, from samples different from the ones used to construct the model. The results showed that the mathematical models found are able to calculate the effect of the surfactant concentration and the operating temperature in each extraction parameter studied, respecting the boundaries used. The models optimization allowed the achievement of consistent and applicable results in a simple and quick way leading to high efficiency in process operation.

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The oil industry, experiencing a great economic and environmental impact, has increasingly invested in researches aiming a more satisfactory treatment of its largest effluent, i.e., produced water. These are mostly discarded at sea, without reuse and after a basic treatment. Such effluent contains a range of organic compounds with high toxicity and are difficult to remove, such as polycyclic aromatic hydrocarbons, salts, heavy metals, etc.. The main objective of this work was to study the solar distillation of produced water pre-treated to remove salts and other contaminants trough of a hybrid system with a pre-heater. This developed apparatus was called solar system, which consists of a solar heater and a conventional distillation solar still. The first device consisted of a water tank, a solar flat plate collector and a thermal reservoir. The solar distillator is of simple effect, with 1m2 of flat area and 20° of inclination. This dissertation was divided in five steps: measurements in the solar system, i.e. temperatures and distillate flow rate and weather data; modeling and simulation of the system; study of vapor-liquid equilibrium of the synthetic wastewater by the aqueous solution of p-xylene; physical and chemical analyses of samples of the feed, distillate and residue, as well as climatology pertinent variables of Natal-RN. The solar system was tested separately, with the supply water, aqueous NaCl and synthetic oil produced water. Temperature measurements were taken every minute of the thermal reservoir, water tank and distillator (liquid and vapor phases). Data of solar radiation and rainfall were obtained from INPE (National Institute for Space Research). The solar pre-heater demonstrated to be effective for the liquid systems tested. The reservoir fluid had an average temperature of 58°C, which enabled the feed to be pre-heated in the distillator. The temperature profile in the solar distillator showed a similar behavior to daily solar radiation, with temperatures near 70°C. The distillation had an average yield of 2.4 L /day, i.e., an efficiency of 27.2%. Mathematical modeling aided the identification of the most important variables and parameters in the solar system. The study of the vapor-liquid equilibrium from Total Organic Carbon (TOC) analysis indicated heteroazeotropia and the vapor phase resulted more concentrated in p-xylene. The physical-chemical analysis of pH, conductivity, Total Dissolved Solids (TDS), chlorides, cations (including heavy metals) and anions, the effluent distillate showed satisfactory results, which presents a potential for reuse. The climatological study indicates the region of Natal-RN as favorable to the operation of solar systems, but the use of auxiliary heating during periods of higher rainfall and cloud cover is also recommended

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This work aims to study the drying of cashew-nut pulp with different lay-out of dryers using conventional and solar energy. It concerns with the use of exceeding of the regional raw material and the suitable knowledge for the applicability of the drying systems as pathway for food conservation. Besides, it used renewable sources as solar energy to dry these agroindustrial products. Runs were carried out using a conventional tray-dryer with temperature, air velocity control and cashew slice thickness of 55°C, 65°C, 75°C; 3.0; 4.5, 6.0 m s-1; 1.0; 1.5 and 2.0 cm, respectively, in order to compare the studied systems. To evaluate the conventional tray-dryer, it was used a diffusional model of 2nd Fick´s law, where the drying curves were quite well fitted to an infinite flat plate design. For the drying runs where the room temperature had no control, it was developed a phenomenological-mathematical model for the solar dryer with indirect radiation under natural and forced convection based on material and energy balances of the system. Besides, it was carried out assays in the in natura as well as dehydrated, statistic analysis of the experimental drying data, sensorial analysis of the final dry product and a simplified economical analysis of the systems studied

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Urban centers in Pitimbu Watershed use significant groundwater sources for public supply. Therefore, studies in Dunas Barreiras aquifer are relevant to expand knowledge about it and help manage water resources in the region. An essential tool for this management is the numerical modeling of groundwater flow. In this work, we developed a groundwater flow model for Pitimbu Watershed, using the Visual Modflow, version 2.7.1., which uses finite difference method for solving the govern equation of the dynamics of groundwater flow. We carried out the numerical simulation of steady-state model for the entire region of the basin. The model was built in the geographical, geomorphological and hydrogeological study of the area, which defined the boundary conditions and the parameters required for the numerical calculation. Owing to unavailability of current data based on monitoring of the aquifer it was not possible to calibrate the model. However, the simulation results showed that the overall water balance approached zero, therefore satisfying the equation for the three-dimensional behavior of the head water in steady state. Variations in aquifer recharge data were made to verify the impact of this contribution on the water balance of the system, especially in the scenario in which recharge due to drains and sinks was removed. According to the results generated by Visual Modflow occurred significantly hydraulic head lowering, ranging from 16,4 to 82 feet of drawdown. With the results obtained, it can be said that modeling is performed as a valid tool for the management of water resources in Pitimbu River Basin, and to support new studies

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This paper discusses aspects related to the mathematical language and its understanding, in particular, by students of final years of elementary school. Accordingly, we aimed to develop a proposal for teaching, substantiated by mathematical modeling activities and reading, which takes advantage of the student of elementary school a better understanding of mathematical language for the content of proportion. We also aim to build / propose parameters for the assessment of reading proficiency of the language of the student in analyzing and modeling process, its ability to develop/improve/enhance this proficiency. For this purpose, we develop a qualitative research, with procedures for an action research whose analysis of the data is configured as Content Analysis. We refer to epistemological and didactic, in the studies: Piaget (1975, 1990), Vygotsky (1991, 2001), Bakhtin (2006), Freire (1974, 1994), Bicudo and Garnica (2006), Smole and Diniz (2001), Barbosa (2001), Burak (1992), Biembengut (2004), Bassanezi (2002), Carrasco (2006), Becker (2010), Zuin and Reyes (2010), among others. We understand that to acquire new knowledge one must learn to read and reading to learn it, this process is essential for the development of reading proficiency of a person. Modeling, in turn, is a process which enables contact with different forms of reading providing elements favorable to the development here mentioned. The evaluation parameters we use to analyze the level of reading proficiency of mathematical language proved to be effective and therefore a valuable tool that allows the teacher an efficient evaluation and whose results can guide you better in the planning and execution of their practice

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Actually, Brazil is one of the larger fruit producer worldwide, with most of its production being consumed in nature way or either as juice or pulp. It is important to highlig ht in the fruit productive chain there are a lot lose due mainly to climate reasons, as well as storage, transportation, season, market, etc. It is known that in the pulp and fruit processing industy a yield of 50% (in mass) is usually obtained, with the other part discarded as waste. However, since most this waste has a high nutrient content it can be used to generate added - value products. In this case, drying plays an important role as an alternative process in order to improve these wastes generated by the fruit industry. However, despite the advantage of using this technique in order to improve such wastes, issues as a higher power demand as well as the thermal efficiency limitation should be addressed. Therefore, the control of the main variables in t his drying process is quite important in order to obtain operational conditions to produce a final product with the target specification as well as with a lower power cost. M athematical models can be applied to this process as a tool in order to optimize t he best conditions. The main aim of this work was to evaluate the drying behaviour of a guava industrial pulp waste using a batch system with a convective - tray dryer both experimentally and using mathematical modeling. In the experimental study , the dryin g carried out using a group of trays as well as the power consume were assayed as response to the effects of operational conditions (temperature, drying air flow rate and solid mass). Obtained results allowed observing the most significant variables in the process. On the other hand, the phenomenological mathematical model was validated and allowed to follow the moisture profile as well as the temperature in the solid and gas phases in every tray. Simulation results showed the most favorable procedure to o btain the minimum processing time as well as the lower power demand.

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A type of macro drainage solution widely used in urban areas with predomi-nance of closed catchments (basins without outlet) is the implementation of detention and infiltration reservoirs (DIR). This type of solution has the main function of storing surface runoff and to promote soil infiltration and, consequently, aquifer recharge. The practice is to avoid floods in the drainage basin low-lying areas. The catchment waterproofing reduces the distributed groundwater recharge in urban areas, as is the case of Natal city, RN. However, the advantage of DIR is to concentrate the runoff and to promote aquifer recharge to an amount that can surpass the distributed natu-ral recharge. In this paper, we proposed studying a small urban drainage catchment, named Experimental Mirassol Watershed (EMW) in Natal, RN, whose outlet is a DIR. The rainfall-runoff transformation processes, water accumulation in DIR and the pro-cess of infiltration and percolation in the soil profile until the free aquifer were mod-eled and, from rainfall event observations, water levels in DIR and free aquifer water level measurements, and also, parameter values determination, it is was enabled to calibrate and modeling these combined processes. The mathematical modeling was carried out from two numerical models. We used the rainfall-runoff model developed by RIGHETTO (2014), and besides, we developed a one-dimensional model to simu-late the soil infiltration, percolation, redistribution soil water and groundwater in a combined system to the reservoir water balance. Continuous simulation was run over a period of eighteen months in time intervals of one minute. The drainage basin was discretized in blocks units as well as street reaches and the soil profile in vertical cells of 2 cm deep to a total depth of 30 m. The generated hydrographs were transformed into inlet volumes to the DIR and then, it was carried out water balance in these time intervals, considering infiltration and percolation of water in the soil profile. As a re-sult, we get to evaluate the storage water process in DIR as well as the infiltration of water, redistribution into the soil and the groundwater aquifer recharge, in continuous temporal simulation. We found that the DIR has good performance to storage excess water drainage and to contribute to the local aquifer recharge process (Aquifer Dunas / Barreiras).

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MACHADO, Antônio V. et al. Estudio del Secado de Anacardo (Anacardium occidentale L.) mediante Secador Solar de Radiación Directa. Información Tecnológica, v. 21, n. 1, p. 31-37, 2010.