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International Review of Chemical Engineering (Rapid Communications) - November 2009 - Papers

 

 

         Special Section on Biofuels and Environment

 

   

 

International Review of Chemical Engineering (Rapid Communications) - Papers

 

go to top   EDITORIAL. Quality comes first!

         by Jordan Hristov

       Vol. 1. n. 6, pp. 474


 

go to top   Benchmarking of the Construct of Dimensionless Correlations Regarding Batch Bubble Columns with Suspended Solids:
Performance of the PRESSURE TRANFORM Approach

         by Jordan Hristov

         Vol. 1. n. 6, pp. 475-483

 

Abstract - Benchmark of dimensionless data correlations pertinent to batch bubble columns (BC) with suspended solids has been performed by the pressure transform approach (PTA). The main efforts have addressed the correct definition of dimensionless groups referring to the fact that solids dynamics and the bubble dynamics have different velocity and length scales. The correct definition of the initial set of variable in the classical dimensional analysis depends mainly on the experience of the investigator while the pressure transform approach (PTA) avoids errors at this initial stage. PTA addresses the physics of the phenomena occurring in complex systems involving many phases and allows straightforward definitions of dimensionless numbers.

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Keywords: Bubble column, Pressure transform, Dimensionless correlation construct.

 


 

go to top   Utilization of Lime-Polyelectrolyte in Industrial Wastewater Treatment for Recycle and Reuse Purposes
         by Mahmood M. Barbooti, Ahmad A. Moosa, Mahdi Sh. Jaafar

         Vol. 1. n. 6, pp. 484-491

 

Abstract - In the present work the combined effect of lime and polyelectrolyte (CPE) on the removal of pollutants of synthetic and real wastewater from textile plant to end up with acceptable water quality for some uses. Laboratory tests were first carried out to establish the optimum values of the operating parameters to apply them at a pilot level. The CPE addition with lime as the main coagulants was advantageous in lowering the amounts of lime significantly. The effects of the settling velocity and the dosage of the coagulants were studied on the efficiency of removal of color, turbidity, COD and TSS. Lime (CaO) solution by 35-40 mg/L with addition of polyelectrolyte (1-1.25mg/L) proved very effective. The results indicated good removal efficiencies for Turbidity 87-90%, TSS 81-85%, TDS 30-32% and color by 40-45%. The best removal efficiencies can be achieved by applying a speed of mixing of (120- 130 rpm) with detention time 2-3 min, for the coagulation step and (30-35 rpm) for 20-25 min for the flocculation step. The results were discussed in terms of the Zeta potential approach. Finally, flow rates at level of 80- 100 L/hr were more efficient to produce high quality treated water, for the mechanical mixing pilot plant.

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Keywords: Wastewater treatment, Lime-Polyelectrolyte combination, Recycle, Reuse.

 


 

go to top   Hydrothermal Recovery of Boron from Liquid Bittern
         by G. El Diwani, Sh. El Rafie, S. Hawash

         Vol. 1. n. 6, pp. 492-500

 

Abstract - Hydrothermal treatment was performed to recover boron as recyclable precipitate (CaBO4 , vitimite, B2 O3 , borax (Na2 B4O7.10 H2O ) from Qaron Lake liquid bittern. This method depends on the high affinity of Calcium hydroxide for boron precipitation at pH= 9.5. Content of boron as borates and boric acid recovery in the precipitates have been determined by XRD-patterns and EMS-photographs. Recovery of boron achieved >73% by the hydrothermal method at 150 ºC and 20 hours treatment that proved to be friendly environmentally compared with the conventional removal techniques. The equilibrium concentration and the adsorption capacity at equilibrium were determined using three different sorption models namely: Freundlich and Langmuir isotherms. The results gained from this study were described by Freundlich isotherm model better than Langmuir isotherm model. The adsorbed boron products affinity carbonate hydroxyl lapatite (CHAP) synthesized by using eggshell waste has been compared for boron recovery and calcium fertilizer production as Brushite (Ca HPO4.2H2O) and Ca2.86 Mg0.14(PO4)2 which are slow release fertilizers.

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Keywords: Adsorption, Bittern, Boron, Fertilizer, Hydrothermal.

 


 

go to top   A Case Study Concerning Physicochemical Characteristics and Purification Outputs of Oil Refinery Wastewater Treatment Station (Samir, Sidi Kacem, Morocco)
         by A. Haidar, A. Saad, M. Fadli, A. Chaouch, A. Echchelh

         Vol. 1. n. 6, pp. 501-505

 

Abstract - For the purpose of the physicochemical characterization of oil effluents of S.A.M.I.R oil Refinery, Sidi Kacem, Morocco and to exanimate the performance of its treatment station by the estimation of the purification outputs of its wastewater, we have evaluated for two years (2007-2008) on a monthly basis eleven physicochemical parameters upstream and downstream to this wastewater treatment station (wwts);
With the exception of salinity, chloride and conductivity degree, the wide ranged statistical analysis (ACP) shows that purification operation is well carried for the rest of physicochemical variables, this avoid the contribution of such effluents to a dramatically water pollution if directly rejected in the receiving environment. The important finding of this study is that the main physicochemical characteristics of the treated water are proved compatible with the Moroccan oil refining industry standards.

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Keywords: Oil Refining, Effluents, Physicochemical, Purification, Morocco.

 


 

go to top   Modeling Heat and Mass Transfer in Breaded Chicken Nuggets During Deep Fat Frying
         by Michael Ngadi, Yunfeng Wang

         Vol. 1. n. 6, pp. 506-514

 

Abstract - Simultaneous two-dimensional heat and mass transfer during deep fat frying of coated chicken nuggets was modeled using the moving boundary concept. Appropriate mathematical equations were developed and solved using a finite element method software (COMSOLTM 3.0). Experiments were conducted to validate the model. Chicken nuggets coated with wheat flour based batter and breading were used as samples. The samples were fried in a fryer using oil temperatures at 160, 170 and 180°C. Total frying times ranged from 60 to 300 s. Good agreement between the predicted and observed results was obtained. The techniques could be applied to optimize quality of coated fried chicken nuggets.

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Keywords: Model, Heat and mass transfer, Finite element method, Chicken nugget.

 


 

go to top   Modeling of the Adsorption of Phenol on the Commercial Activated Carbon by Experimental Design
         by S. Meski, F. Aissani, H. Khireddine
         Vol. 1. n. 6, pp. 515-519

 

Abstract - The adsorption of phenol on the commercial activated carbon has been modeled with the factorial design approach. The ability of commercial activated carbon to remove phenol molecules from acidic solutions has been studied for different phenol concentrations by varying the amount of adsorbent (Csus), initial concentration of phenol (C0), contact time and particles size of carbon (dp). Thus, it has seen that a maximum removal of the phenol is obtained under optimums conditions of: carbon dosage of 1g/L, contact time of 2 hours, powdered particle size (0.048 mm) and dilute phenol solution (10 mg/L). The removal efficiency up to Yphenol(97%)) could be achieved. It is believed that the model obtained for adsorption of phenol may well provide a background for detailed mechanism searches and industrial pilot applications.

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Keywords: Activated carbon, Phenol, Modeling, adsorption, Experimental design.

 


 

go to top   An Alternative Analysis of a Mass Transfer Laboratory Experiment
         by Mukhtar Bello, Abdullah A. Shaikh

         Vol. 1. n. 6, pp. 520-524

 

Abstract - This paper reports an alternative experimental and theoretical analysis for an undergraduate experiment on mass transfer in a bubble column. Air for oxygenation of water and nitrogen for de-oxygenation are used to aerate the bubble column. A simple experimental procedure is proposed to determine the volumetric mass transfer coefficient and gas holdup. Comparisons with empirical correlations are satisfactory.

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Keywords: Transport laboratory, Bubble column, Mass transfer coefficient, Gas holdup.

 


 

go to top   Modelling and Simulation of Evacuation Processes of Pollutants in the Room
         by Marius-Constantin Popescu, Luminita-Georgeta Popescu, Cristinel Popescu

         Vol. 1. n. 6, pp. 525-546

 

Abstract - This paper presents a method to identify the value of concentration in certain areas of room, where the air is introducing superposition effect of flow convection (natural or artificial) and diffusion and a recirculation its, which acts as a feedback circuit. The result helps to understand how to conduct a recirculation phenomenon, and may form a basis for future adaptive adjustment of the concentration value. Tests on models can provide both information on the verification of calculation methods and solutions that theory currently can not provide. Climate processes occurring in a site are complex and not fully capture the phenomenon of mass transfer of fluid motion and heat. Those basic methods are used hydraulic moulding, which bypass the practical difficulties created by the incompatibility of the conditions of similarity (using areas of forging, hydraulic or geometric distortion).

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Keywords: Identify of concentration, Modelling and Simulation, Pollutants and air conditioning.

 


 

go to top   Studies on Halide-Induced Corrosion on Different Types of Steel
          by G. Bassioni

         Vol. 1. n. 6, pp. 547-551

 

Abstract - A set of different measurements including inorganic anions simultaneously in presence of chloride is conducted on cement-like CaCO3 whereupon competitive adsorption measurements are correlated to zetapotential measurements. The adsorption isotherm of chloride on is obtained and the amount of bound and free chloride is investigated. Mild and stainless steel coupons are exposed to the supernatant solutions after centrifugation of the limestone suspensions and corrosion rates are calculated. The study gives an insight on the role of salinity and pH and the correlation of bound to free chlorides on the corrosion rates of steel in pipes in oil well cementing.

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Keywords:  Mild steel, Stainless steel, Competitive adsorption, Zetapotential, Corrosion rate.

 


 

go to top   Zinc Adsorption and its Thermodynamic Parameters in Cambisols
          by Lúcia H. G. Chaves, Hugo O. C. Guerra, Iêde de B. Chaves

        Vol. 1. n. 6, pp. 552-556

 

Abstract - Zinc can be added to the soils through disposal of city wastes, sewage sludge and a variety of agricultural practices. Its availability to plants, persistency and mobility in soils are mainly determined by the extent of the adsorption by soil particles. Considering the importance of Zinc to the plants and soil contamination, a study was conducted to obtain the quantitative relationship between the Zn in the equilibrium solution and that adsorbed by the Camara Watershed Cambisols, on the Paraiba State and to evaluate the thermodynamic parameters involved in the adsorption process. Adsorption isotherms were elaborated from batch adsorption experiments, with increasing Zn concentrations. . The driving force of reaction was quantified by Gibbs free energy and a separation factor. Isotherms were H and L-type and the experimental results well fitted to Langmuir model. Zinc adsorption was favorable and spontaneous depending on organic carbon content and, mainly, on the cation exchange capacity of the soil. Free energy adsorption was higher at lower zinc equilibrium concentrations.

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Keywords:  Heavy metal, Isotherm, Free energy.

 


 

go to top   The Noisy Behavior of Avalanches in Cohesive Powders
          by M. A. S. Quintanilla, J. M. Valverde, A. Castellanos

        Vol. 1. n. 6, pp. 557- 562

 

Abstract - Experimental measurements on the maximum stable angle of cohesive powders partially filling horizontal rotating drums are presented. The material is first fluidized by high speed rotation. By suddenly stopping the drum the powder is allowed to settle in a reproducibly initialized state. The drum is then slowly rotated until an avalanche occurs and is detected. This process has been automated allowing us to measure a sufficiently large number of events to perform a robust statistical analysis. The highly fluctuating structure of powders in a local scale manifests itself in a broad distribution of the maximum angle of stability. A contributing factor to raise data scattering is cohesiveness, which increases local heterogeneity of density and stresses. Results are analyzed in the light of a numerical model based on the method of Matsukovic.

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Keywords: Cohesive powders, Toner, Avalanches, Drum experiments, Method of Matsukovic.

 


 

Special Section on Biofuels and Environment - Papers

 

go to top   Preface from the Guest-Editor
          by Victor Haber Perez

          Vol. 1. n. 6, pp.  563


 

go to top   Atmospheric Pollution: Global Warming and a Possible use of Bio-Fuels in a Wide Scale
          by M. S. Sthel, J. R. Tavares, G. R. Lima, G. Mothé, D. U. S. Schramm, M. G. da Silva, M. P. P. Castro

         Vol. 1. n. 6, pp.  564-570

 

Abstract - Atmospheric Pollution is one of the most concerning problems faced by the modern society. The anomalous concentration of certain gaseous species can occasion dangerous environmental consequences, such as the degeneration of air quality, acid rain, photochemical smog, ozone layer depletion, health diseases and the global warming. Transport sector is responsible for a great part of the damaging pollutant emitted by anthropogenic sources, what justifies a serious preoccupation in the monitoring of gases emitted in the exhaust of automotive vehicles. In this paper, we discuss the main impacts of the atmospheric pollution, especially the global warming, on the environment and on the human society. We still analyze how biofuels can help to mitigate the global warming, beyond boosting Brazilian development. Finally, we present experimental data of pollutant gases emitted in the exhaust of diesel, natural gas, gasoline and alcohol powered vehicles. The measurements were made using photoacoustic and electrochemical techniques..

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Keywords: Atmospheric Pollution, Biofuels, Global Warming, Pollutant Detection .

 


 

go to top   Biodiesel Production: Biotechnological Approach
          by John A. Posada, Carlos E. Orrego, Carlos Ariel Cardona

         Vol. 1. n. 6, pp.  571-580

 

Abstract - Fermentation is used to transform raw materials such as sugar, starch or other substrates with living cells to more complex target products such as alcohols, ketones, vitamins, antibiotics, amino acids or often achiral organic molecules. Biodiesel together with glycerol are produced by transesterification process, which can be carried out by two ways, chemically catalyzed or biocatalytically. Where, methanol from non-renewable oil is the most used raw material. Chemical catalysis has several drawbacks as fatty acid alkaline salts (soaps) generation, difficult glycerol recovering, energetically intensive process, using alkaline catalysts or elevated reaction temperatures and high reaction times using catalysis acid. Biocatalytic approach -whole-cell or enzymatic- is located at the interface between fermentation processes and petrol-based chemistry. This work reviews the biodiesel production through biocatalytic process, and analyzes the biotechnological transformation of glycerol (by product of biodiesel production) to ethanol (a potentially important raw material in biodiesel production), and other bioconversion products.

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Keywords: Biodiesel, Biocatalytic process, Glycerol conversion, Ethanol bioproduction.

 


 

go to top   Challenges in Fuel Ethanol Production
          by Carlos A. Cardona, Julián A. Quintero, Óscar J. Sánchez

         Vol. 1. n. 6, pp.  581-597

 

Abstract - Fuel ethanol production still represents many technological challenges, due mainly to the implicit complexity and costs of feedstock and other inputs. However, this process has been implemented at different scales, including the commercial one, through tax exemptions or subsides, which seek to lower production costs. In this article main feedstocks for ethanol production are discussed considering their production, advantages and drawbacks. The importance of conditioning and pretreatment as decisive process steps for conversion of feedstocks into ethanol is highlighted. Main methods for conditioning and pretreatmen are presented as well as the enzymatic procedures for starch hydrolysis. The need of pretreatment of lignocellulosic biomass is analyzed considering the complexity of this type of raw material. Several methods for pretreatment and detoxification of biomass are briefly described. The difficulties related to the enzymatic hydrolysis of cellulose are analyzed considering the enzyme complexes employed and the presence of solid particles in the reaction mixture. Main fermentation and concentration technologies for ethanol production are discussed. Ethanol dehydration technologies, including the most perspective, are disclosed as well. Finally, some environmental aspects of ethanol production are highlighted.

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Keywords: Fuel ethanol, Lignocellulosic biomass, Technologies, Feedstock, Pretreatment.

 


 

go to top   Study of the Correlation between the Chemical Structure of Biodiesel and their Respective Cetane Number
          by Diogo V. Nadai, Paulo C. M. L. Miranda, Carlos E. N. Gatts

         Vol. 1. n. 6, pp.  598-602

 

Abstract - The cetane number (CN) is one of the most important quality indicators of the diesel. Its experimental determination, however, may be a lengthy and expensive task. When it comes to biodiesel, the availability of data in the literature is also scarce. In this work we search for the correlation between the cetane number of single mono-alkyl esters of fatty acids and mixtures of them (biodiesel) with structural characteristics obtained by 1H nuclear magnetic resonance (1H NMR). The correlation was done through the application of three statistical tools: principal component analysis (PCA), hierarchical clustering and non hierarchical clustering.

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Keywords: Alkyl fatty esters, Biodiesel, Cetane number, Clustering, PCA.

 


 

go to top   Current Processes in Brazilian Biodiesel Production
          by Donato A. G. Aranda, Carla C. C. M. da Silva, Chaline Detoni

     Vol. 1. n. 6, pp.  603-608

 

Abstract - Brazilian biodiesel production has experienced a very fast growing. After the first plant in 2005, more than 60 plants are running and producing about 2 million tons/year in less than 4 years of the national biodiesel programm. In addition to regular transesterification plants, there is a commercial esterification plant running with heterogeneous catalysis producing biodiesel from palm fatty acids. A new process denominated hydroesterification is becoming more important since it is able to use any acid fatty material integrating hydrolysis and esterification reactions. In addition to an european standard biodiesel, hydroesterification produces a very pure glycerol during hydrolysis step. Pure glycerol is a multiple application molecule including hydrogen production to be applied with fatty acid reactions producing high valued bioprodcts.

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Keywords: Biodiesel, Transesterification, Esterification, Hydroesterification.

 


 

go to top   Enzymatic Transformation of Palm Oil in Biodiesel using Porcine Pancreatic Lipase Immobilized on Hybrid Matrix
          by Grazielle S. Silva, Patrícia C. M. da Rós, Julio C. Santos, Victor H. Perez, Heizir F. de Castro

     Vol. 1. n. 6, pp.  609-613

 

Abstract - Porcine pancreatic lipase (PPL) immobilized on a hybrid matrix (polysiloxane polyvinyl alcohol, POS-PVA) was used to catalyze the transesterification of the palm oil with different short chain alcohols (ethanol, propanol and butanol) in solvent free system. The commercial biocatalyst, Lipozyme IM20, was used for comparison. The reaction system oil/ butanol showed to be the most suitable substrate to perform the reaction with both enzymatic preparations, attaining similar yields higher than 75%. Lower yields (< 55%) were achieved for the other reaction systems, and the immobilized pancreatic lipase showed better performance than Lipozyme IM20 in all cases. Based on the potential application of PPL immobilized on POS-PVA, further experiments were performed to determine the oil/butanol molar ratio under which the formation of butyl esters and productivity are maximized.

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Keywords: Immobilized lipase, Biodiesel, Palm oil, Transesterification.

 


 

go to top   Lignocellulosic Bioethanol Production: Perspectives and Challenges
          by Boutros Fouad Sarrouh, Rafael Rodrigues Philippini, Silvio Silvério da Silva

     Vol. 1. n. 6, pp.  614-622

 

Abstract - Biofuels produced from different lignocellulosic materials have the potential to be a valuable substitute for gasoline. Many physicochemical structural and compositional factors hinder the hydrolysis of cellulose present in biomass to sugars and other organic compounds that can later be converted to fuels. Different pretreatment techniques can change the physical and chemical structure of the lignocellulosic biomass and improve their hydrolysis rates. Many methods have been shown to result in high sugar yields, above 90% of the theoretical yield. Advances in pretreatment and biological-processing steps clearly provide the greatest opportunity to reduce bioethanol costs, and much more emphasis is needed in these areas. For pretreatment, improved process configurations are needed that reduce chemical costs for hemicellulose hydrolysis and subsequent conditioning for biological processing. In addition, energy requirements for biomass milling and heating must be reduced, and less corrosive environments are desired to reduce the cost of vessels. Future biotechnology-based developments in processing technology will likely include: Improved cellulase and hemicellulase production economics via microbe or plant-based production systems; improved fermentation strains that efficiently utilize both hemicellulose and cellulosic sugars; consolidated bioprocessing microbes which combine the ability to break down cellulosic materials with the ability to efficiently ferment sugars to ethanol.

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Keywords: Bioethanol, Cellulose, Hemicellulose, Residues.

 


 

go to top   Photopyroelectric Methodology Applied to Thermal Characterization of Biodiesel
          by A. O. Guimarães, F. A. L. Machado, E. B. Zanelato, M. S. Sthel, E. C. da Silva, D. A. G. Aranda
     Vol. 1. n. 6, pp.  623-631

 

Abstract - This paper presents a methodology based on the photopyroelectric (PPE) detection of thermal waves for the thermal characterization of liquid and pasty materials, specially applied to biodiesel. In this technique, the temperature oscillations produced by the absorption of a modulated laser beam are converted in electric signal by a pyroelectric transducer. The main aspects concerning the mathematical approach are described, as well as the experimental arrangements. Two different PPE configurations are presented, the standard (SPPE) and the inverse (IPPE) ones, from which it is possible to determine the thermal diffusivity and effusivity of materials, respectively. Knowing these two properties allows one to determine the thermal conductivity, also an important parameter when dealing with heat transfer. Measurements were performed for reference samples, as water and ethylene glycol, and for some biodiesel sample. The measurements present a good reproducibility, with uncertainties around 1- 2 % for all the properties. The results point to a suitable and accurate method for thermal characterization of such biofuels. The simplicity of the experimental setups and its low cost implementation are additional features of the photopyroelectric technique, which is clearly an interesting option for several kinds of studies, for instance the investigation of phase transitions, or the effects on the thermal properties of fuels when producing diesel/biodiesel mixtures.

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Keywords: Biodiesel, Photopyroelectric, Thermal Diffusivity, Thermal Effusivity, Thermal Conductivity.

 


 

go to top   The Potential of Macaw Palm (Acrocomia aculeate) as Source of Biodiesel in Brazil
          by S. Y. Motoike, K. N. Kuki
   Vol. 1. n. 6, pp.  632-335

 

Abstract - The production of biofuels should be based on the tripod of environmental, social and economic sustainability. The use of raw materials, with high energy density, combined with a production model of low environmental impact, is the key to achieve this goal. The oil palm (Elaeis guineensis) and the macaw palm (Acrocomia aculeata) are the most efficient plant to produce the raw material for biodiesel. Their oil productivity can be superior to 6 tons per hectare per year. The oil palm exploitation model is well defined, and it can be grown in large areas of the Brazilian Amazon region, where soil and climate conditions are suitable for its cultivation. The macaw palm finds its space in the pastures of the northeast, central and southeast regions of Brazil, where it can be grown integrated with the livestock.

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Keywords: Sustainable biofuel production, Agroforestry, Silvopastoral system, Oil palm.

 


 

go to top   Thermal Diffusivity Measurements of Biodiesel Fuel Using Thermal Lens Technique
          by A. M. Rocha, W. C. Silva, L. F. M. Sangiorgio, M. S. Sthel, A. A. C. Andrade, D. A. G. Aranda, M. P. P. Castro
   Vol. 1. n. 6, pp.  336-639

 

Abstract - In this work the Photothermal Technique, Thermal Lens (LT) is used to obtain the thermal diffusivity of different kinds of biodiesel. The absolute values of thermal diffusivity were determined for samples obtained from fish, olive, animal fat, Piqui, Palm, and Pork fat. Thermal diffusivity essentially measures the thermalization time of a given material and it is known to be strongly dependent upon composition as well as processing conditions. Therefore, the use of non-conventional and advantageous methods to measure the biodiesel appears to be relevant.

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Keywords: Thermal Lens, Biodiesel, Thermal diffusivity.

 


 

go to top   Scaling Analysis in Modeling Transport and Reaction Processes: a Systematic Approach to Model Building and the Art of Approximation (Book Review)
          by Jordan Hristov

           Vol. 1. n. 6, pp.  640-641

 

The book of Prof. Krantz has appeared officially in 2007, but I knew about the project several years ago. In 2002, I work extensively on scaling of complex hat transfer in fire as apart of my visiting professorship in Universidad Politechnica de Catalunya, Barcelona, Spain. Browsing the web I have found some files on scaling and dimensional analysis written by Prof. Krantz and his collaborators, now amalgamated in the texts of Chapter 3 and Chapter 4 of the Book. Then, I have contacted Prof. Krantz by e-mail and from the talks I have understood that he has worked on the final stage of the book. Since that time I have expected to get my own copy and fortunately my friend Yuri Sobral ( University of Brasilia, Brazil) have sent it to me in September as a nice gift to my birthday. Now, I am glad to express, not only my fillings with this book in hands but also professional remarks on its contents.
First of all, I have to mention that everybody who passed the courses of transport phenomena and modelling has met the excellent book of Bird, Steward and Lightfood (BSL). This excellent book gives the starting point of thinking with many examples and clear solutions. I especially mention the BSL book, since every body knows that, to some extent, the problems of scaling are missing in its text. Then, the instructor has to put a lot of efforts in the classroom to make clear some the ideas of scaling and dimensionless numbers. Prof. Krantz mentions in the preface that he also has met the amazing BSL book at the beginning of his carrier and this influenced strongly his work for years and the book at issue, too
Krantz did an excellent textbook with a very clever pedagogical approach using problems available in BSL book to exemplify both the scaling and the consequent dimensional analysis. This approach facilitates the explanations since the problems are well-known and the reader is not afraid that the scaling analysis performed is something magic falling from the sky. Following, this pedagogical strategy, Chapter 1 (Introduction) and Chapter 2 (Systematic method for scaling analysis) are devoted to some introductory notes and explanations about the order of magnitude analysis as basic tool in analysis of models based on differential equations. Besides, the choice of scales is also at issue, trying to overcome the impression that this stage of the scaling analysis is an art and based mainly on intuition. To some extent, the latter is true, but the book tries to convert the art into a science arranged systematically as readable texts. Then, after the starting explanations, the core of the book is organized in Chapter 3 (Applications to Fluid dynamics), Chapter 4 (Applications to Heat Transfer) and Chapter 5 (Applications to Mass Transfer). These chapters explain every small step in scaling and relevant dimensional analysis that has to be done. These texts are supported by examples taken mainly from the BSL book but the analyses performed give much more to the students rather then the starting problems. In the context of these notes, the book and especially chapters 3, 4 and 5 should be studied thoroughly not only by students but by instructors and professors, too. It is hard to explain the feelings reading these chapters, where many questions can be answered as well as other ideas how to explain certain problems originate. Very interesting contributions to the teaching problems of scaling are Chapter 6 (Application to mass transfer with chemical reaction) and Chapter 7 (Application to process design). In contrast to the preceding chapters here complex processes are discussed. The main outcome of these chapters is that the reader can clearly understand how the scaling and the consequent order of magnitude analysis have to be used evaluating the contributions of the physical effects and then to reduce adequately the models. In general, this an art that everybody involved in science of modelling develops through serious work for years. The Krantz’s book shows how this art has to be converted into systematic knowledge that has to enter the classroom. The book is accompanied by as series of appendices providing basic equations of transport phenomena, flow in porous media , problems with mixtures and some mathematical references to the Lebnitz rule of differentiation of an integral integration (commonly missing in textbooks, but widely applicable to moving boundary problems ) and the Ostrogradskii Divergence Theorem.
In recommend the book to everybody who intends to study the modelling thoroughly as well as to use and interpret the model outcomes. This is a starting book in scaling that differs from many others devoted to dimensional analysis and containing chapters on scaling. The difference is manly in its carefully written texts taking into account that the main goal is: that the book should teach, gives tools for solving of present and future problems and inspire new ideas. I believe that everybody involved in chemical or mechanical engineering, heat and mass transfer, transport phenomena, mathematical modeling, unit operations, and fluid dynamics, will see the Krantz‘s book on his desk. .

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