Study of the one dimensional and transient bioheat transfer equation: Multi-layer solution development and applications

: In this work we derive an analytical solution given by Bessel series to the transient and one-dimensional (1D) bioheat transfer equation in a multi-layer region with spatially dependent heat sources. Each region represents an independent biological tissue characterized by temperature-invariant physiological parameters and a linearly temperature dependent metabolic heat generation. Moreover, 1D Cartesian, cylindrical or spherical coordinates are used to define the geometry and temperature boundary conditions of first, second and third kinds are assumed at the inner and outer surfaces. We present two examples of clinical applications for the developed solution. In the first one, we investigate two different heat source terms to simulate the heating in a tumor and its surrounding tissue, induced during a magnetic fluid hyperthermia technique used for cancer treatment. To obtain an accurate analytical solution, we determine the error associated with the truncated Bessel series that defines the transient solution. In the second application, we explore the potential of this model to study the effect of different environmental conditions in a multi-layered human head model (brain, bone and scalp). The convective heat transfer effect of a large blood vessel located inside the brain is also investigated. The results are further compared with a numerical solution obtained by the Finite Element Method and computed with COMSOL Multi-physics v4.1 (c). (c) 2013 Elsevier Ltd. All rights reserved.

Transfer of cadmium and barium from soil to crops grown in tropical soils

Phytotoxicity and transfer of potentially toxic elements, such as cadmium (Cd) or barium (Ba), depend on the availability of these elements in soils and on the plant species exposed to them. With this study, we aimed to evaluate the effect of Cd and Ba application rates on yields of pea (Pisum sativum L.), sorghum (Sorghum bicolor L.), soybean (Glycine max L.), and maize (Zea mays L.) grown under greenhouse conditions in an Oxisol and an Entisol with contrasting physical and chemical properties, and to correlate the amount taken up by plants with extractants commonly used in routine soil analysis, along with transfer coefficients (Bioconcentration Factor and Transfer Factor) in different parts of the plants. Plants were harvested at flowering stage and measured for yield and Cd or Ba concentrations in leaves, stems, and roots. The amount of Cd accumulated in the plants was satisfactorily evaluated by both DTPA and Mehlich-3 (M-3). Mehlich-3 did not relate to Ba accumulated in plants, suggesting it should not be used to predict Ba availability. The transfer coefficients were specific to soils and plants and are therefore not recommended for direct use in risk assessment models without taking soil properties and group of plants into account.

First day of an oil spill on the open sea: early mass transfers of hydrocarbons to air and water.

During the first hours after release of petroleum at sea, crude oil hydrocarbons partition rapidly into air and water. However, limited information is available about very early evaporation and dissolution processes. We report on the composition of the oil slick during the first day after a permitted, unrestrained 4.3 m(3) oil release conducted on the North Sea. Rapid mass transfers of volatile and soluble hydrocarbons were observed, with >50% of ≤C17 hydrocarbons disappearing within 25 h from this oil slick of <10 km(2) area and <10 μm thickness. For oil sheen, >50% losses of ≤C16 hydrocarbons were observed after 1 h. We developed a mass transfer model to describe the evolution of oil slick chemical composition and water column hydrocarbon concentrations. The model was parametrized based on environmental conditions and hydrocarbon partitioning properties estimated from comprehensive two-dimensional gas chromatography (GC×GC) retention data. The model correctly predicted the observed fractionation of petroleum hydrocarbons in the oil slick resulting from evaporation and dissolution. This is the first report on the broad-spectrum compositional changes in oil during the first day of a spill at the sea surface. Expected outcomes under other environmental conditions are discussed, as well as comparisons to other models.

Salting kinetics and salt diffusivities in farmed Pantanal caiman muscle

The legal Pantanal caiman (Caiman crocodilus yacare) farming, in Brazil, has been stimulated and among meat preservation techniques the salting process is a relatively simple and low-cost method. The objective of this work was to study the sodium chloride diffusion kinetics in farmed caiman muscle during salting. Limited volumes of brine were employed, with salting essays carried at 3, 4 and 5 brine/muscle ratios, at 15%, 20% and 25% w/w brine concentrations, and brine temperatures of 10, 15 and 20ºC. The analytical solution of second Fick's law considering one-dimensional diffusion through an infinite slab in contact with a well-stirred solution of limited volume was used to calculate effective salt diffusion coefficients and to predict the sodium chloride content in the fillets. A good agreement was obtained between the considered analytical model and experimental data. Salt diffusivities in fillets were found to be in the range of 0.47x10-10 to 9.62x10-10 m²/s.

Ilmavirtausten laskennallinen mallinnus

Diplomityössä tutkitaan kolmea erilaista virtausongelmaa CFD-mallinnuksella. Yhteistä näille ongelmille on virtaavana aineena oleva ilma. Lisäksi tapausten perinteinen mittaus on erittäin vaikeaa tai mahdotonta. Ensimmäinen tutkimusongelma on tarrapaperirainan kuivain, jonka tuotantomäärä halutaan nostaa kaksinkertaiseksi. Tämä vaatii kuivatustehon kaksinkertaistamista, koska rainan viipymäaika kuivausalueella puolittuu. Laskentayhtälöillä ja CFD-mallinnuksella tutkitaan puhallussuihkun nopeuden ja lämpötilan muutoksien vaikutusta rainan pinnan lämmön- ja massansiirtokertoimiin. Tuloksena saadaan varioitujen suureiden sekä massan- ja lämmönsiirtokertoimien välille riippuvuuskäyrät, joiden perusteella kuivain voidaan säätää parhaallamahdollisella tavalla. Toinen ongelma käsittelee suunnitteilla olevan kuparikonvertterin sekundaarihuuvan sieppausasteen optimointia. Ilman parannustoimenpiteitä käännetyn konvertterin päästöistä suurin osa karkaa ohi sekundaarihuuvan. Tilannetta tutkitaan konvertterissa syntyvän konvektiivisen nostevirtauksen eli päästöpluumin sekä erilaisten puhallussuihkuratkaisujen CFD-mallinnuksella. Tuloksena saadaan puhallussuihkuilla päästöpluumia poikkeuttava ilmaverho. Suurin osa nousevasta päästöpluumista indusoituu ilmaverhoon ja kulkeutuu poistokanavaan. Kolmas tutkittava kohde on suunnitteilla oleva kuparielektrolyysihalli, jossa ilmanvaihtoperiaatteena on luonnollinen ilmanvaihto ja mekaaninen happosumun keräysjärjestelmä. Ilmanvaihtosysteemin tehokkuus ja sisäilman virtaukset halutaan selvittää ennen hallin rakentamista. CFD-mallinnuksella ja laskentayhtälöillä tutkitaan lämpötila- ja virtauskentät sekä hallin läpi virtaava ilmamäärä ja ilmanvaihtoaste. Tulo- ja poistoilma-aukkojen mitoitukseen ja sijoitukseen liittyvät suunnitteluarvot varmennetaan sekä löydetään ilmanvaihdon ongelmakohdat. Ongelmakohtia tutkitaan ja niille esitetään parannusehdotukset.

Ion-exchange resins as stationary phase in reactive chromatography

Dynamic behavior of bothisothermal and non-isothermal single-column chromatographic reactors with an ion-exchange resin as the stationary phase was investigated. The reactor performance was interpreted by using results obtained when studying the effect of the resin properties on the equilibrium and kinetic phenomena occurring simultaneously in the reactor. Mathematical models were derived for each phenomenon and combined to simulate the chromatographic reactor. The phenomena studied includes phase equilibria in multicomponent liquid mixture¿ion-exchange resin systems, chemicalequilibrium in the presence of a resin catalyst, diffusion of liquids in gel-type and macroporous resins, and chemical reaction kinetics. Above all, attention was paid to the swelling behavior of the resins and how it affects the kinetic phenomena. Several poly(styrene-co-divinylbenzene) resins with different cross-link densities and internal porosities were used. Esterification of acetic acid with ethanol to produce ethyl acetate and water was used as a model reaction system. Choosing an ion-exchange resin with a low cross-link density is beneficial inthe case of the present reaction system: the amount of ethyl acetate as well the ethyl acetate to water mole ratio in the effluent stream increase with decreasing cross-link density. The enhanced performance of the reactor is mainly attributed to increasing reaction rate, which in turn originates from the phase equilibrium behavior of the system. Also mass transfer considerations favor the use ofresins with low cross-link density. The diffusion coefficients of liquids in the gel-type ion-exchange resins were found to fall rapidly when the extent of swelling became low. Glass transition of the polymer was not found to significantlyretard the diffusion in sulfonated PS¿DVB ion-exchange resins. It was also shown that non-isothermal operation of a chromatographic reactor could be used to significantly enhance the reactor performance. In the case of the exothermic modelreaction system and a near-adiabatic column, a positive thermal wave (higher temperature than in the initial state) was found to travel together with the reactive front. This further increased the conversion of the reactants. Diffusion-induced volume changes of the ion-exchange resins were studied in a flow-through cell. It was shown that describing the swelling and shrinking kinetics of the particles calls for a mass transfer model that explicitly includes the limited expansibility of the polymer network. A good description of the process was obtained by combining the generalized Maxwell-Stefan approach and an activity model that was derived from the thermodynamics of polymer solutions and gels. The swelling pressure in the resin phase was evaluated by using a non-Gaussian expression forthe polymer chain length distribution. Dimensional changes of the resin particles necessitate the use of non-standard mathematical tools for dynamic simulations. A transformed coordinate system, where the mass of the polymer was used as a spatial variable, was applied when simulating the chromatographic reactor columns as well as the swelling and shrinking kinetics of the resin particles. Shrinking of the particles in a column leads to formation of dead volume on top of the resin bed. In ordinary Eulerian coordinates, this results in a moving discontinuity that in turn causes numerical difficulties in the solution of the PDE system. The motion of the discontinuity was eliminated by spanning two calculation grids in the column that overlapped at the top of the resin bed. The reactive and non-reactive phase equilibrium data were correlated with a model derived from thethermodynamics of polymer solution and gels. The thermodynamic approach used inthis work is best suited at high degrees of swelling because the polymer matrixmay be in the glassy state when the extent of swelling is low.

Considerações sobre a eletrogeração de peróxido de hidrogênio

This paper presents some results that may be used as previous considerations to a hydrogen peroxide electrogeneration process design. A kinetic study of oxygen dissolution in aqueous solution is carried out and rate constants for oxygen dissolution are calculated. Voltammetric experiments on vitreous carbon cathode shown that the low saturation concentration drives the oxygen reduction process to a mass transfer controlled process which exhibits low values of limiting currents. Results have shown that the hydrogen peroxide formation and its decomposition to water are separated by 400 mV on the vitreous carbon surface. Diffusion coefficients for oxygen and hydrogen peroxide are calculated using data taken from Levich and Tafel plots. In a series of bulk electrolysis experiments hydrogen peroxide was electrogenerated at several potential values, and concentration profiles as a function of the electrical charged passed were obtained. Data shown that, since limiting current plateaus are poorly defined onto reticulated vitreous carbon, cathodic efficiency may be a good criterion for choosing the potential value in which hydrogen peroxide electrogeneration should be carried out.

Heat Transfer in Plate Heat Exchangers

This study illustrates the different types of plate heat exchangers that are commonly used in various domestic and industrial applications. The main purpose of this paper was to devise a methodology that is capable of calculating optimum number of plates in the design of a plate heat exchanger. To obtain the appropriate number of plates, typically several iterations must be made before a final acceptable design is completed, since plate amount depends on many factors such as, flow velocities, physical properties of the streams, flow channel geometry, allowable pressure drop, plate dimensions, and the gap between the plates. The methodology presented here can be used as a general guide for designing a plate heat exchanger. To investigate the effects of relevant parameters on the thermal-hydraulic design of a plate heat exchanger, several experiments were carried out for single-phase and counter flow arrangement with two brazed plate heat exchangers by varying the flow rates and the inlet temperatures of the fluid streams. The actual heat transfer coefficients obtained based on the experiment were nearly close to the calculated values and to improve the design, a correction factor was introduced. Besides, the effect of flow channel velocity on the pressure drop inside the unit is presented.

COMPREENSÃO MATEMÁTICA DA DIFUSÃO NO CONTEXTO ELETROQUÍMICO

The aim of this study was to explain in detail the mathematical methods used to deal with diffusion equations, mainly for students and researchers interested in electrochemistry and related areas. Emphasis was placed on the deduction and resolution of diffusion equations, as well as addressing cartesian, spherical and cylindrical coordinates. Different aspects of mass transfer processes were discussed including the importance of the resolution of Fick's laws equations to understand and derive parameters of the electroactive species (e.g., diffusion coefficients, formal electrode potentials) from the electrochemical techniques. As an example, the resolution of diffusion equations for a reversible reduction process of soluble oxidized species was presented for the chronopotentiometry technique. This study is envisaged to broaden the understanding of these frequently used methods, in which mathematical deductions are not always completely understood.

Fundamentals of heat transfer

Following over 170+ pages and additional appendixes are formed based on content of Course: Fundamentals of Heat Transfer. Mainly this summarizes relevant parts on Book of Fundamentals of Heat and Mass Transfer (Incropera), but also other references introducing the same concepts are included. Student’s point of view has been consideredwith following highlights: (1) Relevant topics are presented in a nutshell to provide fast digestion of principles of heat transfer. (2) Appendixes include terminology dictionary. (3) Totally 22 illustrating examples are connecting theory to practical applications and quantifying heat transfer to understandable forms as: temperatures, heat transfer rates, heat fluxes, resistances and etc. (4) Most important Learning outcomes are presented for each topic separately. The Book, Fundamentals of Heat and Mass Transfer (Incropera), is certainly recommended for those going beyond basic knowledge of heat transfer. Lecture Notes consists of four primary content-wise objectives: (1) Give understanding to physical mechanisms of heat transfer, (2)Present basic concepts and terminology relevant for conduction, convection and radiation (3) Introduce thermal performance analysis methods for steady state and transient conduction systems. (4) Provide fast-to-digest phenomenological understanding required for basic design of thermal models

Turbulent heat transfer and pressure drop in pinned annular regions

Experiments were performed to determine average heat transfer coefficients and friction factors for turbulent flow through annular ducts with pin fins. The measurements were carried out by means of a double-pipe heat exchanger. The total number of pins attached to the inner wall of the annular region was 560. The working fluids were air, flowing in the annular channel, and water through the inner circular tube. The average heat transfer coefficients of the pinned air-side were obtained from the experimental determination of the overall heat transfer coefficients of the heat exchanger and from the knowledge of the average heat transfer coefficients of the circular pipe (water-side), which could be found in the pertinent literature. To attain fully developed conditions, the heat exchanger was built with additional lengths before and after the test section. The inner circular duct of the heat exchanger and the pin fins were made of brass. Due to the high thermal conductivity of the brass, the small tube thickness and water temperature variation, the surface of the internal tube was practically isothermal. The external tube was made of an industrial plastic which was insulated from the environment by means of a glass wool batt. In this manner, the outer surface of the annular channel can be considered adiabatic. The results are presented in dimensionless forms, in terms of average Nusselt numbers and friction factors as functions of the flow Reynolds number, ranging from 13,000 to 80,000. The pin fin efficiency, which depends on the heat transfer coefficient, is also determined as a function of dimensionless parameters. A comparison of the present results with those for smooth sections (without pins) is also presented. The purpose of such a comparison is to study the influence of the presence of the pins on the pressure drop and heat transfer rate.

Saline distribution during multicomponent salting in pre-cooked quail eggs

The relationship of NaCl with problems of arterial hypertension has led to a reduction in the levels of this salt in food production. KCl has been used as a partial substitute for NaCl since it cannot be completely substituted without affecting the acceptability of the end product. In this study, the diffusion that occurs during quail egg salting in static and stirred brine was simulated. The mathematical model used was based on a generalization of the Fick's 2nd law, and the COMSOL Multiphysics software was used to simulate the diffusion in the NaCl-KCl-water system. The deviations in the simulated data and experimental data were 2.50% for NaCl and 6.98% for KCl in static brine, while in the stirred brine they were 3.48% for NaCl and 4.72% for KCl. The simulation results presented good agreement with the experimental values and validated the predictive capacity of the model.

Efecto de ajuste del flujo dializante (Qd) sobre la eficacia en hemodialisis a pacientes de bajo peso

Introducción: Las guías KDOQI del 2006 utilizan patrón de adecuación de diálisis el Kt/V, donde V es volumen de distribución de la úrea, pacientes de bajo peso tienen menor agua corporal total, menor V, que podrían reducir el requerimiento de Qd sin afectar la eficiencia de la diálisis. Objetivo: Evaluar el efecto sobre la adecuación de hemodiálisis que produce la reducción del Qd en pacientes con peso menor o igual a 60 kg . Metodología: Se incluyeron pacientes con Enfermedad Renal crónica en hemodiálisis de forma regular con peso menor o igual a 60 Kg de la unidad renal, para evaluar dos períodos I y II, se continuaron los parámetros de la terapia, con descenso del Qd para el segundo período . Las variables fueron recolectadas de forma directa por los investigadores de la historia clínica . Los valores así obtenidos serían comparados mediante prueba t para variables relacionadas o pareadas, y significancia estadística de la prueba inferior a 0,05. Resultados: Se incluyeron 61 pacientes, el 60.7% sexo femenino, promedio de edad 57,3 años (DE 14,8). Edad promedio de los hombres 60,1 (DE 13,9) y de las mujeres fue de 55,9 (DE 15,4). No se encontraron diferencias estadísticamente significativas para las variables Kt/V y Hb, con descenso significativo del P. (p 0.015) Conclusiones: Este estudio demuestra que se logra una adecuada terapia con Qd inferiores a los estándares tradicionales, con 400ml /min en pacientes de bajo peso, siempre y cuando se mantengan los demás parámetros de suplencia renal.

Avaliação e modelagem da absorção de H2S do gás natural em coluna de leito estagnado

Natural gas, although basically composed by light hydrocarbons, also presents contaminant gases in its composition, such as CO2 (carbon dioxide) and H2S (hydrogen sulfide). The H2S, which commonly occurs in oil and gas exploration and production activities, causes damages in oil and natural gas pipelines. Consequently, the removal of hydrogen sulfide gas will result in an important reduction in operating costs. Also, it is essential to consider the better quality of the oil to be processed in the refinery, thus resulting in benefits in economic, environmental and social areas. All this facts demonstrate the need for the development and improvement in hydrogen sulfide scavengers. Currently, the oil industry uses several processes for hydrogen sulfide removal from natural gas. However, these processes produce amine derivatives which can cause damage in distillation towers, can cause clogging of pipelines by formation of insoluble precipitates, and also produce residues with great environmental impact. Therefore, it is of great importance the obtaining of a stable system, in inorganic or organic reaction media, able to remove hydrogen sulfide without formation of by-products that can affect the quality and cost of natural gas processing, transport, and distribution steps. Seeking the study, evaluation and modeling of mass transfer and kinetics of hydrogen removal, in this study it was used an absorption column packed with Raschig rings, where the natural gas, with H2S as contaminant, passed through an aqueous solution of inorganic compounds as stagnant liquid, being this contaminant gas absorbed by the liquid phase. This absorption column was coupled with a H2S detection system, with interface with a computer. The data and the model equations were solved by the least squares method, modified by Levemberg-Marquardt. In this study, in addition to the water, it were used the following solutions: sodium hydroxide, potassium permanganate, ferric chloride, copper sulfate, zinc chloride, potassium chromate, and manganese sulfate, all at low concentrations (»10 ppm). These solutions were used looking for the evaluation of the interference between absorption physical and chemical parameters, or even to get a better mass transfer coefficient, as in mixing reactors and absorption columns operating in counterflow. In this context, the evaluation of H2S removal arises as a valuable procedure for the treatment of natural gas and destination of process by-products. The study of the obtained absorption curves makes possible to determine the mass transfer predominant stage in the involved processes, the mass transfer volumetric coefficients, and the equilibrium concentrations. It was also performed a kinetic study. The obtained results showed that the H2S removal kinetics is greater for NaOH. Considering that the study was performed at low concentrations of chemical reagents, it was possible to check the effect of secondary reactions in the other chemicals, especially in the case of KMnO4, which shows that your by-product, MnO2, acts in H2S absorption process. In addition, CuSO4 and FeCl3 also demonstrated to have good efficiency in H2S removal

Kinetics of osmotic dehydration and air-drying of pumpkins (Cucurbita moschata)

Kinetics of osmotic dehydration (OD) and effects of sucrose impregnation on thermal air-drying of pumpkin slices were investigated. A simplified model based on the solution of Fick's Law was used to estimate effective diffusion coefficients during OD and air-drying. In order to take into account shrinkage, average and variable thicknesses were considered. Pumpkin slices were dehydrated in sucrose solutions (40%, 50% and 60%, w/w, 27 degrees C. The effective water diffusion coefficients were higher than the sucrose, and low diffusivity dependence with solution concentration was observed. Samples non-treated and pre-treated in 60% osmotic solutions during one hour were dried in a hot-air-dryer at 50 and 70 degrees C (2 m/s) until equilibrium was achieved. Pre-treatment enhanced mass transfer during air-drying. Great volume reduction was observed in pre and non-treated dried samples. Using variable thickness in the model diminished the relative deviations between predicted and experimental OD and drying data. (C) 2007 Elsevier Ltd. All rights reserved.