Mathematical modeling and optimal control of malaria

Malaria continues to infect millions and kill hundreds of thousands of people worldwide each year, despite over a century of research and attempts to control and eliminate this infectious disease. Challenges such as the development and spread of drug resistant malaria parasites, insecticide resistance to mosquitoes, climate change, the presence of individuals with subpatent malaria infections which normally are asymptomatic and behavioral plasticity in the mosquito hinder the prospects of malaria control and elimination. In this thesis, mathematical models of malaria transmission and control that address the role of drug resistance, immunity, iron supplementation and anemia, immigration and visitation, and the presence of asymptomatic carriers in malaria transmission are developed. A within-host mathematical model of severe Plasmodium falciparum malaria is also developed. First, a deterministic mathematical model for transmission of antimalarial drug resistance parasites with superinfection is developed and analyzed. The possibility of increase in the risk of superinfection due to iron supplementation and fortification in malaria endemic areas is discussed. The model results calls upon stakeholders to weigh the pros and cons of iron supplementation to individuals living in malaria endemic regions. Second, a deterministic model of transmission of drug resistant malaria parasites, including the inflow of infective immigrants, is presented and analyzed. The optimal control theory is applied to this model to study the impact of various malaria and vector control strategies, such as screening of immigrants, treatment of drug-sensitive infections, treatment of drug-resistant infections, and the use of insecticide-treated bed nets and indoor spraying of mosquitoes. The results of the model emphasize the importance of using a combination of all four controls tools for effective malaria intervention. Next, a two-age-class mathematical model for malaria transmission with asymptomatic carriers is developed and analyzed. In development of this model, four possible control measures are analyzed: the use of long-lasting treated mosquito nets, indoor residual spraying, screening and treatment of symptomatic, and screening and treatment of asymptomatic individuals. The numerical results show that a disease-free equilibrium can be attained if all four control measures are used. A common pitfall for most epidemiological models is the absence of real data; model-based conclusions have to be drawn based on uncertain parameter values. In this thesis, an approach to study the robustness of optimal control solutions under such parameter uncertainty is presented. Numerical analysis of the optimal control problem in the presence of parameter uncertainty demonstrate the robustness of the optimal control approach that: when a comprehensive control strategy is used the main conclusions of the optimal control remain unchanged, even if inevitable variability remains in the control profiles. The results provide a promising framework for the design of cost-effective strategies for disease control with multiple interventions, even under considerable uncertainty of model parameters. Finally, a separate work modeling the within-host Plasmodium falciparum infection in humans is presented. The developed model allows re-infection of already-infected red blood cells. The model hypothesizes that in severe malaria due to parasite quest for survival and rapid multiplication, the Plasmodium falciparum can be absorbed in the already-infected red blood cells which accelerates the rupture rate and consequently cause anemia. Analysis of the model and parameter identifiability using Markov chain Monte Carlo methods is presented.

Multicomponent diffusion during Prato cheese ripening: mathematical modeling using the finite element method

The partial replacement of NaCl by KCl is a promising alternative to produce a cheese with lower sodium content since KCl does not change the final quality of the cheese product. In order to assure proper salt proportions, mathematical models are employed to control the product process and simulate the multicomponent diffusion during the reduced salt cheese ripening period. The generalized Fick's Second Law is widely accepted as the primary mass transfer model within solid foods. The Finite Element Method (FEM) was used to solve the system of differential equations formed. Therefore, a NaCl and KCl multicomponent diffusion was simulated using a 20% (w/w) static brine with 70% NaCl and 30% KCl during Prato cheese (a Brazilian semi-hard cheese) salting and ripening. The theoretical results were compared with experimental data, and indicated that the deviation was 4.43% for NaCl and 4.72% for KCl validating the proposed model for the production of good quality, reduced-sodium cheeses.

Sex chromosome translocation and speciation : a Drosophila genetic model

Although exceptions may be readily identified, two generalizations concerning genetic differences among species may be drawn from the available allozyme and chromosome data. First, structural gene differences among species vary widely. In many cases, species pairs do not differ more than intraspecific populations. This suggests that either very few or no gene substitutions are required to produce barriers to reproduction (Avise 1976). Second, chromosome form and/or number differs among even closely related species (White 1963; 1978; Fredga 1977; Wright 1970). Many of the observed chromosomal differences involve translocational rearrangements; these produce severe fitness depression in heterozygotes and were, thus, long considered unlikely candidates for the fixation required of genetic changes leading to speciation (Wright 1977). Nonetheless, the fact that species differences are frequently translocational argues convincingly for their fixation despite prejudices to the contrary. Haldane's rule states that in the F of interspecific crosses, the heterogametic sex is absent or sterile in the preponderance of cases (Haldane 1932). This rule definitely applies in the genus Dr°sophila (Ehrman 1962). Sex chromosome translocations do not impose a fitness depression as severe as that imposed by autosomal translocations, and X-Y translocations may account for Haldane's rule (Haldane 1932). Consequently a study of the fit ness parameters of an X·yL and a yS chromosome in Drosophila melanogaster populations was initiated by Tracey (1972). Preliminary results suggested that x.yL//YSmales enjoyed a mating advantage with X·yL//X·yL females, that this advantage was frequency dependent, that the translocation produced sexual isolation and that interactions between the yL, yS and a yellow marker contributed to the observed isolation (Tracey and Espinet 1976; Espinet and Tracey 1976). Encouraged by the results of these prelimimary studies, further experiments were performed to clarify the genetic nature of the observed sexual isolation, S the reality of the y frequency dependent fitness .and the behavioural changes, if any, produced by the translocation. The results of this work are reported herein. Although the marker genes used in earlier studies, sparkling poliert an d yellow have both been found to affect activity,but only yellow effects asymmetric sexual isolation. In addition yellow effects isolation through an interaction with the T(X-y) chromosomes, yS also effects isolation, and translocational strains are isolated from those of normal karyotype in the absence of marker gene differences. When yS chromosomes are in competition with y chromosomes on an X.yL background, yS males are at a distinct advantage only when their frequency is less than 97%. The sex chromosome translocation alters the normal courtship pattern by the incorporation of circling between vibration and licking in the male repertoire. Finally a model of speciation base on the fixation of this sex chromosome translocation in a geographically isolated gene pool is proposed.

Planification et dimensionnement des réseaux optiques de longues distances

Le projet de recherche porte sur l'étude des problèmes de conception et de planification d'un réseau optique de longue distance, aussi appelé réseau de coeur (OWAN-Optical Wide Area Network en anglais). Il s'agit d'un réseau qui transporte des flots agrégés en mode commutation de circuits. Un réseau OWAN relie différents sites à l'aide de fibres optiques connectées par des commutateurs/routeurs optiques et/ou électriques. Un réseau OWAN est maillé à l'échelle d'un pays ou d’un continent et permet le transit des données à très haut débit. Dans une première partie du projet de thèse, nous nous intéressons au problème de conception de réseaux optiques agiles. Le problème d'agilité est motivé par la croissance de la demande en bande passante et par la nature dynamique du trafic. Les équipements déployés par les opérateurs de réseaux doivent disposer d'outils de configuration plus performants et plus flexibles pour gérer au mieux la complexité des connexions entre les clients et tenir compte de la nature évolutive du trafic. Souvent, le problème de conception d'un réseau consiste à prévoir la bande passante nécessaire pour écouler un trafic donné. Ici, nous cherchons en plus à choisir la meilleure configuration nodale ayant un niveau d'agilité capable de garantir une affectation optimale des ressources du réseau. Nous étudierons également deux autres types de problèmes auxquels un opérateur de réseau est confronté. Le premier problème est l'affectation de ressources du réseau. Une fois que l'architecture du réseau en termes d'équipements est choisie, la question qui reste est de savoir : comment dimensionner et optimiser cette architecture pour qu'elle rencontre le meilleur niveau possible d'agilité pour satisfaire toute la demande. La définition de la topologie de routage est un problème d'optimisation complexe. Elle consiste à définir un ensemble de chemins optiques logiques, choisir les routes physiques suivies par ces derniers, ainsi que les longueurs d'onde qu'ils utilisent, de manière à optimiser la qualité de la solution obtenue par rapport à un ensemble de métriques pour mesurer la performance du réseau. De plus, nous devons définir la meilleure stratégie de dimensionnement du réseau de façon à ce qu'elle soit adaptée à la nature dynamique du trafic. Le second problème est celui d'optimiser les coûts d'investissement en capital(CAPEX) et d'opération (OPEX) de l'architecture de transport proposée. Dans le cas du type d'architecture de dimensionnement considérée dans cette thèse, le CAPEX inclut les coûts de routage, d'installation et de mise en service de tous les équipements de type réseau installés aux extrémités des connexions et dans les noeuds intermédiaires. Les coûts d'opération OPEX correspondent à tous les frais liés à l'exploitation du réseau de transport. Étant donné la nature symétrique et le nombre exponentiel de variables dans la plupart des formulations mathématiques développées pour ces types de problèmes, nous avons particulièrement exploré des approches de résolution de type génération de colonnes et algorithme glouton qui s'adaptent bien à la résolution des grands problèmes d'optimisation. Une étude comparative de plusieurs stratégies d'allocation de ressources et d'algorithmes de résolution, sur différents jeux de données et de réseaux de transport de type OWAN démontre que le meilleur coût réseau est obtenu dans deux cas : une stratégie de dimensionnement anticipative combinée avec une méthode de résolution de type génération de colonnes dans les cas où nous autorisons/interdisons le dérangement des connexions déjà établies. Aussi, une bonne répartition de l'utilisation des ressources du réseau est observée avec les scénarios utilisant une stratégie de dimensionnement myope combinée à une approche d'allocation de ressources avec une résolution utilisant les techniques de génération de colonnes. Les résultats obtenus à l'issue de ces travaux ont également démontré que des gains considérables sont possibles pour les coûts d'investissement en capital et d'opération. En effet, une répartition intelligente et hétérogène de ressources d’un réseau sur l'ensemble des noeuds permet de réaliser une réduction substantielle des coûts du réseau par rapport à une solution d'allocation de ressources classique qui adopte une architecture homogène utilisant la même configuration nodale dans tous les noeuds. En effet, nous avons démontré qu'il est possible de réduire le nombre de commutateurs photoniques tout en satisfaisant la demande de trafic et en gardant le coût global d'allocation de ressources de réseau inchangé par rapport à l'architecture classique. Cela implique une réduction substantielle des coûts CAPEX et OPEX. Dans nos expériences de calcul, les résultats démontrent que la réduction de coûts peut atteindre jusqu'à 65% dans certaines jeux de données et de réseau.

Étude numérique des origines hémodynamiques des oscillations dans des réseaux de capillaires

En simulant l’écoulement du sang dans un réseau de capillaires (en l’absence de contrôle biologique), il est possible d’observer la présence d’oscillations de certains paramètres comme le débit volumique, la pression et l’hématocrite (volume des globules rouges par rapport au volume du sang total). Ce comportement semble être en concordance avec certaines expériences in vivo. Malgré cet accord, il faut se demander si les fluctuations observées lors des simulations de l’écoulement sont physiques, numériques ou un artefact de modèles irréalistes puisqu’il existe toujours des différences entre des modélisations et des expériences in vivo. Pour répondre à cette question de façon satisfaisante, nous étudierons et analyserons l’écoulement du sang ainsi que la nature des oscillations observées dans quelques réseaux de capillaires utilisant un modèle convectif et un modèle moyenné pour décrire les équations de conservation de masse des globules rouges. Ces modèles tiennent compte de deux effets rhéologiques importants : l’effet Fåhraeus-Lindqvist décrivant la viscosité apparente dans un vaisseau et l’effet de séparation de phase schématisant la distribution des globules rouges aux points de bifurcation. Pour décrire ce dernier effet, deux lois de séparation de phase (les lois de Pries et al. et de Fenton et al.) seront étudiées et comparées. Dans ce mémoire, nous présenterons une description du problème physiologique (rhéologie du sang). Nous montrerons les modèles mathématiques employés (moyenné et convectif) ainsi que les lois de séparation de phase (Pries et al. et Fenton et al.) accompagnés d’une analyse des schémas numériques implémentés. Pour le modèle moyenné, nous employons le schéma numérique explicite traditionnel d’Euler ainsi qu’un nouveau schéma implicite qui permet de résoudre ce problème d’une manière efficace. Ceci est fait en utilisant une méthode de Newton- Krylov avec gradient conjugué préconditionné et la méthode de GMRES pour les itérations intérieures ainsi qu’une méthode quasi-Newton (la méthode de Broyden). Cette méthode inclura le schéma implicite d’Euler et la méthode des trapèzes. Pour le schéma convectif, la méthode explicite de Kiani et al. sera implémentée ainsi qu’une nouvelle approche implicite. La stabilité des deux modèles sera également explorée. À l’aide de trois différentes topologies, nous comparerons les résultats de ces deux modèles mathématiques ainsi que les lois de séparation de phase afin de déterminer dans quelle mesure les oscillations observées peuvent être attribuables au choix des modèles mathématiques ou au choix des méthodes numériques.

Los conceptos de salud financiera, riesgo y epidemiología en los estados financieros de las compañías del sector de extracción de petróleo crudo y gas natural en Colombia

El presente proyecto tiene como objeto identificar cuáles son los conceptos de salud, enfermedad, epidemiología y riesgo aplicables a las empresas del sector de extracción de petróleo y gas natural en Colombia. Dado, el bajo nivel de predicción de los análisis financieros tradicionales y su insuficiencia, en términos de inversión y toma de decisiones a largo plazo, además de no considerar variables como el riesgo y las expectativas de futuro, surge la necesidad de abordar diferentes perspectivas y modelos integradores. Esta apreciación es pertinente dentro del sector de extracción de petróleo y gas natural, debido a la creciente inversión extranjera que ha reportado, US$2.862 millones en el 2010, cifra mayor a diez veces su valor en el año 2003. Así pues, se podrían desarrollar modelos multi-dimensional, con base en los conceptos de salud financiera, epidemiológicos y estadísticos. El termino de salud y su adopción en el sector empresarial, resulta útil y mantiene una coherencia conceptual, evidenciando una presencia de diferentes subsistemas o factores interactuantes e interconectados. Es necesario mencionar también, que un modelo multidimensional (multi-stage) debe tener en cuenta el riesgo y el análisis epidemiológico ha demostrado ser útil al momento de determinarlo e integrarlo en el sistema junto a otros conceptos, como la razón de riesgo y riesgo relativo. Esto se analizará mediante un estudio teórico-conceptual, que complementa un estudio previo, para contribuir al proyecto de finanzas corporativas de la línea de investigación en Gerencia.

salud financiera y riesgo en los estados financieros de la empresa avianca del sector aeronautico

La globalización y la competitividad como realidad de las empresas, implica que los gerentes preparen a sus empresas de la mejor manera para sobrevivir en este mundo tan inestable y cambiante. El primer paso consta de investigar y medir como se encuentra la empresa en cada uno de sus componentes, tales como recurso humano, mercadeo, logística, operación y por último y más importante las finanzas. El conocimiento de salud financiera y de los riesgos asociados a la actividad de las empresas, les permitirá a los gerentes tomar las decisiones correctas para ser rentables y perdurables en el mundo de los negocios inmerso en la globalización y competitividad. Esta apreciación es pertinente en Avianca S.A. esto teniendo en cuenta su progreso y evolución desde su primer vuelo el 5 de diciembre de 1919 comercial, hasta hoy cuando cotiza en la bolsa de Nueva York. Se realizó un análisis de tipo descriptivo, acompañado de la aplicación de ratios y nomenclaturas, dando lugar a establecer la salud financiera y los riesgos, no solo de Avianca sino también del sector aeronáutico. Como resultado se obtuvo que el sector aeronáutico sea financieramente saludable en el corto plazo, pero en el largo plazo su salud financiera se ve comprometida por los riegos asociados al sector y a la actividad desarrollada.

Evolutionary bi-stability in pathogen transmission mode

Many pathogens transmit to new hosts by both infection (horizontal transmission) and transfer to the infected host's offspring (vertical transmission). These two transmission modes require speci®c adap- tations of the pathogen that can be mutually exclusive, resulting in a trade-off between horizontal and vertical transmission. We show that in mathematical models such trade-offs can lead to the simultaneous existence of two evolutionary stable states (evolutionary bi-stability) of allocation of resources to the two modes of transmission. We also show that jumping between evolutionary stable states can be induced by gradual environmental changes. Using quantitative PCR-based estimates of abundance in seed and vege- tative parts, we show that the pathogen of wheat, Phaeosphaeria nodorum, has jumped between two distinct states of transmission mode twice in the past 160 years, which, based on published evidence, we interpret as adaptation to environmental change. The ®nding of evolutionary bi-stability has impli- cations for human, animal and other plant diseases. An ill-judged change in a disease control programme could cause the pathogen to evolve a new, and possibly more damaging, combination of transmission modes. Similarly, environmental changes can shift the balance between transmission modes, with adverse effects on human, animal and plant health.

Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller-Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated.

A study on intelligent building models

Mathematical models devoted to different aspects of building studies and brought about a significant shift in the way we view buildings. From this background a new definition of building has emerged known as intelligent building that requires integration of a variety of computer-based complex systems. Research relevant to intelligent continues to grow at a much faster pace. This paper is a review of different mathematical models described in literature, which make use of different mathematical methodologies, and are intended for intelligent building studies without complex mathematical details. Models are discussed under a wide classification. Mathematical abstract level of the applied models is detailed and integrated with its literature. The goal of this paper is to present a comprehensive account of the achievements and status of mathematical models in intelligent building research. and to suggest future directions in models.

Modelling oil absorption during post-frying cooling - II: solution of the mathematical model, model testing and simulations

The mathematical models that describe the immersion-frying period and the post-frying cooling period of an infinite slab or an infinite cylinder were solved and tested. Results were successfully compared with those found in the literature or obtained experimentally, and were discussed in terms of the hypotheses and simplifications made. The models were used as the basis of a sensitivity analysis. Simulations showed that a decrease in slab thickness and core heat capacity resulted in faster crust development. On the other hand, an increase in oil temperature and boiling heat transfer coefficient between the oil and the surface of the food accelerated crust formation. The model for oil absorption during cooling was analysed using the tested post-frying cooling equation to determine the moment in which a positive pressure driving force, allowing oil suction within the pore, originated. It was found that as crust layer thickness, pore radius and ambient temperature decreased so did the time needed to start the absorption. On the other hand, as the effective convective heat transfer coefficient between the air and the surface of the slab increased the required cooling time decreased. In addition, it was found that the time needed to allow oil absorption during cooling was extremely sensitive to pore radius, indicating the importance of an accurate pore size determination in future studies.

Using transport diagnostics to understand chemistry climate model ozone simulations

We use observations of N2O and mean age to identify realistic transport in models in order to explain their ozone predictions. The results are applied to 15 chemistry climate models (CCMs) participating in the 2010 World Meteorological Organization ozone assessment. Comparison of the observed and simulated N2O, mean age and their compact correlation identifies models with fast or slow circulations and reveals details of model ascent and tropical isolation. This process‐oriented diagnostic is more useful than mean age alone because it identifies models with compensating transport deficiencies that produce fortuitous agreement with mean age. The diagnosed model transport behavior is related to a model’s ability to produce realistic lower stratosphere (LS) O3 profiles. Models with the greatest tropical transport problems compare poorly with O3 observations. Models with the most realistic LS transport agree more closely with LS observations and each other. We incorporate the results of the chemistry evaluations in the Stratospheric Processes and their Role in Climate (SPARC) CCMVal Report to explain the range of CCM predictions for the return‐to‐1980 dates for global (60°S–60°N) and Antarctic column ozone. Antarctic O3 return dates are generally correlated with vortex Cly levels, and vortex Cly is generally correlated with the model’s circulation, although model Cl chemistry and conservation problems also have a significant effect on return date. In both regions, models with good LS transport and chemistry produce a smaller range of predictions for the return‐to‐1980 ozone values. This study suggests that the current range of predicted return dates is unnecessarily broad due to identifiable model deficiencies.

Comparison of non-linear growth models to describe the growth curve in West African Dwarf sheep

The objectives of this study were to compare the goodness of fit of four non-linear growth models, i.e. Brody, Gompertz, Logistic and Von Bertalanffy, in West African Dwarf (WAD) sheep. A total of 5274 monthly weight records from birth up to 180 days of age from 889 lambs, collected during 2001 to 2004 in Betecoucou breeding farm in Benin were used. In the preliminary analysis, the General Linear Model Procedure of the Statistical Analysis Systems Institute was applied to the dataset to identify the significant effects of the sex of lamb (male and female), type of birth (single and twin), season of birth (rainy season and dry season), parity of dam (1, 2 and 3) and year of birth (2001, 2002, 2003 and 2004) on the observed birth weight and monthly weight up to 6 months of age. The models parameters (A, B and k), coefficient of determination (112), mean square error (MSE) were calculated using language of technical computing package Matlab(R), 2006. The mean values of A, B and k were substituted into each model to calculate the corresponding Akaike's Information Criterion (AIC). Among the four growth functions, the Brody model has been selected for its accuracy of fit according to the higher R(2), lower MSE and A/C Finally, the parameters A, B and k were adjusted in Matlab(R) 2006 for the sex of lamb, year of birth, season of birth, birth type and the parity of ewe, providing a specific slope of the Brody growth curve. The results of this study suggest that Brody model can be useful for WAD sheep breeding in Betecoucou farm conditions through growth monitoring.

Extração supercrítica do óleo de linhaça: construção do extrator, estudo de parâmetros de processo, avaliação química e antioxidante do produto

The aim of the present study was to extract vegetable oil from brown linseed (Linum usitatissimum L.), determine fatty acid levels, the antioxidant capacity of the extracted oil and perform a rapid economic assessment of the SFE process in the manufacture of oil. The experiments were conducted in a test bench extractor capable of operating with carbon dioxide and co-solvents, obeying 23 factorial planning with central point in triplicate, and having process yield as response variable and pressure, temperature and percentage of cosolvent as independent variables. The yield (mass of extracted oil/mass of raw material used) ranged from 2.2% to 28.8%, with the best results obtained at 250 bar and 50ºC, using 5% (v/v) ethanol co-solvent. The influence of the variables on extraction kinetics and on the composition of the linseed oil obtained was investigated. The extraction kinetic curves obtained were based on different mathematical models available in the literature. The Martínez et al. (2003) model and the Simple Single Plate (SSP) model discussed by Gaspar et al. (2003) represented the experimental data with the lowest mean square errors (MSE). A manufacturing cost of US$17.85/kgoil was estimated for the production of linseed oil using TECANALYSIS software and the Rosa and Meireles method (2005). To establish comparisons with SFE, conventional extraction tests were conducted with a Soxhlet device using petroleum ether. These tests obtained mean yields of 35.2% for an extraction time of 5h. All the oil samples were sterilized and characterized in terms of their composition in fatty acids (FA) using gas chromatography. The main fatty acids detected were: palmitic (C16:0), stearic (C18:0), oleic (C18:1), linoleic (C18:2n-6) and α-linolenic (C18:3n-3). The FA contents obtained with Soxhlet dif ered from those obtained with SFE, with higher percentages of saturated and monounsaturated FA with the Soxhlet technique using petroleum ether. With respect to α-linolenic content (main component of linseed oil) in the samples, SFE performed better than Soxhlet extraction, obtaining percentages between 51.18% and 52.71%, whereas with Soxhlet extraction it was 47.84%. The antioxidant activity of the oil was assessed in the β-carotene/linoleic acid system. The percentages of inhibition of the oxidative process reached 22.11% for the SFE oil, but only 6.09% for commercial oil (cold pressing), suggesting that the SFE technique better preserves the phenolic compounds present in the seed, which are likely responsible for the antioxidant nature of the oil. In vitro tests with the sample displaying the best antioxidant response were conducted in rat liver homogenate to investigate the inhibition of spontaneous lipid peroxidation or autooxidation of biological tissue. Linseed oil proved to be more efficient than fish oil (used as standard) in decreasing lipid peroxidation in the liver tissue of Wistar rats, yielding similar results to those obtained with the use of BHT (synthetic antioxidant). Inhibitory capacity may be explained by the presence of phenolic compounds with antioxidant activity in the linseed oil. The results obtained indicate the need for more detailed studies, given the importance of linseed oil as one of the greatest sources of ω3 among vegetable oils

Sistema de secagem solar para frutos tropicais e modelagem da secagem de banana em um secador de coluna estática

In this study were projected, built and tested an electric solar dryer consisting of a solar collector, a drying chamber, an exhaust fan and a fan to promote forced hot air convection. Banana drying experiments were also carried out in a static column dryer to model the drying and to obtain parameters that can be used as a first approximation in the modeling of an electric solar dryer, depending on the similarity of the experimental conditions between the two drying systems. From the banana drying experiments conducted in the static column dryer, we obtained food weight data as a function of aqueous concentration and temperature. Simplified mathematical models of the banana drying were made, based on Fick s and Fourier s second equations, which were tested with the experimental data. We determined and/or modeled parameters such as banana moisture content, density, thin layer drying curves, equilibrium moisture content, molecular diffusivity of the water in banana DAB, external mass transfer coefficient kM, specific heat Cp, thermal conductivity k, latent heat of water evaporation in the food Lfood, time to heat food, and minimum energy and power required to heat the food and evaporate the water. When we considered the shrinkage of radius R of a banana, the calculated values of DAB and kM generally better represent the phenomenon of water diffusion in a solid. The latent heat of water evaporation in the food Lfood calculated by modeling is higher than the latent heat of pure water evaporation Lwater. The values calculated for DAB and KM that best represent the drying were obtained with the analytical model of the present paper. These values had good agreement with those assessed with a numeric model described in the literature, in which convective boundary condition and food shrinkage are considered. Using parameters such as Cp, DAB, k, kM and Lfood, one can elaborate the preliminary dryer project and calculate the economy using only solar energy rather than using solar energy along with electrical energy