4 resultados para Matrius (Matemàtica) -- Problemes, exercicis, etc.
em Universidade Federal do Rio Grande do Norte(UFRN)
Resumo:
Discrepancies between classical model predictions and experimental data for deep bed filtration have been reported by various authors. In order to understand these discrepancies, an analytic continuum model for deep bed filtration is proposed. In this model, a filter coefficient is attributed to each distinct retention mechanism (straining, diffusion, gravity interception, etc.). It was shown that these coefficients generally cannot be merged into an effective filter coefficient, as considered in the classical model. Furthermore, the derived analytic solutions for the proposed model were applied for fitting experimental data, and a very good agreement between experimental data and proposed model predictions were obtained. Comparison of the obtained results with empirical correlations allowed identifying the dominant retention mechanisms. In addition, it was shown that the larger the ratio of particle to pore sizes, the more intensive the straining mechanism and the larger the discrepancies between experimental data and classical model predictions. The classical model and proposed model were compared via statistical analysis. The obtained p values allow concluding that the proposed model should be preferred especially when straining plays an important role. In addition, deep bed filtration with finite retention capacity was studied. This work also involves the study of filtration of particles through porous media with a finite capacity of filtration. It was observed, in this case, that is necessary to consider changes in the boundary conditions through time evolution. It was obtained a solution for such a model using different functions of filtration coefficients. Besides that, it was shown how to build a solution for any filtration coefficient. It was seen that, even considering the same filtration coefficient, the classic model and the one here propposed, show different predictions for the concentration of particles retained in the porous media and for the suspended particles at the exit of the media
Resumo:
This work presents a proposal to build a Mathematics Teaching Laboratory (MTL) whose main theme is the study, construction and use of instruments for navigation and location of mathematical content in an interdisciplinary way approach, and develop a notebook of activities focused on navigational instruments. For this it was necessary a literature review to understand the different conceptions of MTL and its pedagogical implications. The methodology used was literature research, construction and handling of instruments, and pedagogical experimentation. Lorenzato (2006) highlights the importance of an environment and suitable for a professional who can do a good job instruments. The implementation of an LEM can find some obstacles. The lack of support from other teachers or the management, the lack of a suitable place to store the materials produced, the lack of time in the workload of the teacher to prepare the lab activity, etc. Even in unfavorable or adverse conditions, according Lorenzato (2006), its implementation will benefit teachers and students. The lack of teacher training in their initial and continuing education, to use materials, and the lack of manuals with lab activities are also mentioned as factors that keep teachers from MTL. With propóposito assist the teacher of elementary or middle school in building a theme MTL prepared and we are providing a notebook of activities that provides a didactic sequence involving History and Mathematics. The book consists of four accompanied by suggestions for teachers activities, however the teacher has full autonomy to adapt the activities to the reality of your school. Among the instruments of navigation presented in this study chose to build the quadrant due to its simplicity, low cost of material and great teaching potential that this instrument has. But a theme lab is always being built and rebuilt as it is a research environment
Resumo:
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.
Resumo:
Discrepancies between classical model predictions and experimental data for deep bed filtration have been reported by various authors. In order to understand these discrepancies, an analytic continuum model for deep bed filtration is proposed. In this model, a filter coefficient is attributed to each distinct retention mechanism (straining, diffusion, gravity interception, etc.). It was shown that these coefficients generally cannot be merged into an effective filter coefficient, as considered in the classical model. Furthermore, the derived analytic solutions for the proposed model were applied for fitting experimental data, and a very good agreement between experimental data and proposed model predictions were obtained. Comparison of the obtained results with empirical correlations allowed identifying the dominant retention mechanisms. In addition, it was shown that the larger the ratio of particle to pore sizes, the more intensive the straining mechanism and the larger the discrepancies between experimental data and classical model predictions. The classical model and proposed model were compared via statistical analysis. The obtained p values allow concluding that the proposed model should be preferred especially when straining plays an important role. In addition, deep bed filtration with finite retention capacity was studied. This work also involves the study of filtration of particles through porous media with a finite capacity of filtration. It was observed, in this case, that is necessary to consider changes in the boundary conditions through time evolution. It was obtained a solution for such a model using different functions of filtration coefficients. Besides that, it was shown how to build a solution for any filtration coefficient. It was seen that, even considering the same filtration coefficient, the classic model and the one here propposed, show different predictions for the concentration of particles retained in the porous media and for the suspended particles at the exit of the media
