Search results for: volume fraction

Authors: A. Hasankhani, H. Saadat, M. M. Zahedi

Abstract:

In this paper some properties of the uniformity topology on a BCI-algebras are discussed.

Keywords: (Fuzzy) ideal, (Fuzzy) subalgebra, Uniformity, clopen sets.

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Authors: Armend Sh. Shabani

Abstract:

Let D ≠ 1 be a positive non-square integer. In this paper are given the proofs for two conjectures related to Pell-s equation x2 -Dy2 = ± 4, proposed by A. Tekcan.

Keywords: Pell's equation, solutions of Pell's equation.

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Authors: Dmitry Yu. Korulkin, Raissa A. Muzychkina

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In review the generalized data about different methods of synthesis of biological activity aminated hydroxyanthraquinones is presented. The basic regularity of a synthesis is analyzed. Action of temperature, pH, solubility, catalysts and other factors on a reaction product yield is revealed.

Keywords: Amination, hydroxyanthraquinones, nucleophilic exchange, physiologically active substances.

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Authors: Ameleh Aghajanloo, Moharam Dolatshahi Pirouz, Masoud Montazeri Namin

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In this paper, a two-dimensional (2D) numerical model for the tidal currents simulation in Persian Gulf is presented. The model is based on the depth averaged equations of shallow water which consider hydrostatic pressure distribution. The continuity equation and two momentum equations including the effects of bed friction, the Coriolis effects and wind stress have been solved. To integrate the 2D equations, the Alternative Direction Implicit (ADI) technique has been used. The base of equations discritization was finite volume method applied on rectangular mesh. To evaluate the model validation, a dam break case study including analytical solution is selected and the comparison is done. After that, the capability of the model in simulation of tidal current in a real field is represented by modeling the current behavior in Persian Gulf. The tidal fluctuations in Hormuz Strait have caused the tidal currents in the area of study. Therefore, the water surface oscillations data at Hengam Island on Hormoz Strait are used as the model input data. The check point of the model is measured water surface elevations at Assaluye port. The comparison between the results and the acceptable agreement of them showed the model ability for modeling marine hydrodynamic.

Keywords: Persian Gulf, Tidal Currents, Shallow Water Equations, Finite Volumes

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Authors: Esam M. Alawadhi, Raed I. Bourisli

Abstract:

Periodic vortex shedding in pulsating flow inside wavy channel and the effect it has on heat transfer are studied using the finite volume method. A sinusoidally-varying component is superimposed on a uniform flow inside a sinusoidal wavy channel and the effects on the Nusselt number is analyzed. It was found that a unique optimum value of the pulsation frequency, represented by the Strouhal number, exists for Reynolds numbers ranging from 125 to 1000. Results suggest that the gain in heat transfer is related to the process of vortex formation, movement about the troughs of the wavy channel, and subsequent ejection/destruction through the converging section. Heat transfer is the highest when the frequencies of the pulsation and vortex formation approach being in-phase. Analysis of Strouhal number effect on Nu over a period of pulsation substantiates the proposed physical mechanism for enhancement. The effect of changing the amplitude of pulsation is also presented over a period of pulsation, showing a monotonic increase in heat transfer with increasing amplitude. The 60% increase in Nusselt number suggests that sinusoidal fluid pulsation can an effective method for enhancing heat transfer in laminar, wavy-channel flows.

Keywords: Vortex shedding, pulsating flow, wavy channel, CFD.

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Authors: Gorana Jelic Mrcelic, Merica Sliskovic

Abstract:

Environmental responsibility includes improvement of environmental performance in order to reduce environmental impact. This paper gives a short review of some important environmental objectives, targets and actions that modern shipping company should follow.

Keywords: Environment, MARPOL, ships, pollutants.

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Authors: Yuan-Kang Shih, Shu-Li Chang, Shin-Shin Kao

Abstract:

Qk n has been shown as an alternative to the hypercube family. For any even integer k ≥ 4 and any integer n ≥ 2, Qk n is a bipartite graph. In this paper, we will prove that given any pair of vertices, w and b, from different partite sets of Qk n, there exist 2n internally disjoint paths between w and b, denoted by {Pi | 0 ≤ i ≤ 2n-1}, such that 2n-1 i=0 Pi covers all vertices of Qk n. The result is optimal since each vertex of Qk n has exactly 2n neighbors.

Keywords: container, Hamiltonian, k-ary n-cube, m*-connected.

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Authors: Al-Falahi Amir, Yusoff M. Z, Yusaf T

Abstract:

The aim of this paper is to develop a new two dimensional time accurate Euler solver for shock tube applications. The solver was developed to study the performance of a newly built short-duration hypersonic test facility at Universiti Tenaga Nasional “UNITEN" in Malaysia. The facility has been designed, built, and commissioned for different values of diaphragm pressure ratios in order to get wide range of Mach number. The developed solver uses second order accurate cell-vertex finite volume spatial discretization and forth order accurate Runge-Kutta temporal integration and it is designed to simulate the flow process for similar driver/driven gases (e.g. air-air as working fluids). The solver is validated against analytical solution and experimental measurements in the high speed flow test facility. Further investigations were made on the flow process inside the shock tube by using the solver. The shock wave motion, reflection and interaction were investigated and their influence on the performance of the shock tube was determined. The results provide very good estimates for both shock speed and shock pressure obtained after diaphragm rupture. Also detailed information on the gasdynamic processes over the full length of the facility is available. The agreements obtained have been reasonable.

Keywords: shock tunnel, shock tube, shock wave, CFD.

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Authors: Ayo Afolabi, Rudzani Sigwadi, Ambali Abdulkareem

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All around the world pulp and paper industries are the biggest plant production with the environmental pollution as the biggest challenge facing the pulp manufacturing operations. The concern among these industries is to produce a high volume of papers with the high quality standard and of low cost without affecting the environment. This result obtained from this bleaching study show that the activation of peroxide was an effective method of reducing the total applied charge of chlorine dioxide which is harmful to our environment and also show that softwood and hardwood Kraft pulps responded linearly to the peroxide treatments. During the bleaching process the production plant produce chlorines. Under the trial stages chloride dioxide has been reduced by 3 kg/ton to reduce the brightness from 65% ISO to 60% ISO of pulp and the dosing point returned to the E stage charges by pre-treating Kraft pulps with hydrogen peroxide. The pulp and paper industry has developed elemental chlorine free (ECF) and totally chlorine free (TCF) bleaching, in their quest for being environmental friendly, they have been looking at ways to turn their ECF process into a TCF process while still being competitive. This prompted the research to investigate the capability of the hydrogen peroxide as catalyst to reduce chloride dioxide.

Keywords: bleaching, chloride dioxide, elemental chlorine free (ECF), hydrogen peroxide, totally chlorine free (TCF).

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Authors: D. Sufi Ahmadi, B. Bagheri

Abstract:

Thermal water hammer is a special type of water hammer which rarely occurs in heat exchangers. In biphasic fluids, if steam bubbles are surrounded by condensate, regarding lower condensate temperature than steam, they will suddenly collapse. As a result, the vacuum caused by an extreme change in volume lead to movement of the condensates in all directions and their collision the force produced by this collision leads to a severe stress in the pipe wall. This phenomenon is a special type of water hammer. According to fluid mechanics, this phenomenon is a particular type of transient flows during which abrupt change of fluid leads to sudden pressure change inside the tube. In this paper, the mechanism of abrupt failure of 80 tubes of 481 tubes of a methanol heat exchanger is discussed. Initially, due to excessive temperature differences between heat transfer fluids and simultaneous failure of 80 tubes, thermal shock was presupposed as the reason of failure. Deeper investigation on cross-section of failed tubes showed that failure was, ductile type of failure, so the first hypothesis was rejected. Further analysis and more accurate experiments revealed that failure of tubes caused by thermal water hammer. Finally, the causes of thermal water hammer and various solutions to avoid such mechanism are discussed.

Keywords: Thermal water hammer, Brittle Failure, Condensate thermal shock

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Authors: Songlin Yang, Ying Ge

Abstract:

This paper shows that some properties of the decision rules in the literature do not hold by presenting a counterexample. We give sufficient and necessary conditions under which these properties are valid. These results will be helpful when one tries to choose the right decision rules in the research of rough set theory.

Keywords: set, Decision table, Decision rule, coverage factor.

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Authors: Ahmad Mansoor Stanikzai, Yoshitaka Kajita

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This research is a very essential towards transportation planning of Kabul New City. In this research, the travel demand of Kabul metropolitan area (Existing and Kabul New City) are evaluated for three different target years (2015, current, 2025, mid-term, 2040, long-term). The outcome of this study indicates that, though currently the vehicle volume is less the capacity of existing road networks, Kabul city is suffering from daily traffic congestions. This is mainly due to lack of transportation management, the absence of proper policies, improper public transportation system and violation of traffic rules and regulations by inhabitants. On the other hand, the observed result indicates that the current vehicle to capacity ratio (VCR) which is the most used index to judge traffic status in the city is around 0.79. This indicates the inappropriate traffic condition of the city. Moreover, by the growth of population in mid-term (2025) and long-term (2040) and in the case of no development in the road network and transportation system, the VCR value will dramatically increase to 1.40 (2025) and 2.5 (2040). This can be a critical situation for an urban area from an urban transportation perspective. Thus, by introducing high-capacity public transportation system and the development of road network in Kabul New City and integrating these links with the existing city road network, significant improvements were observed in the value of VCR.

Keywords: Afghanistan, Kabul New City, planning, policy, urban transportation.

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Authors: Faheem Ahmed, Fareed Ahmed, Yongheng Guo, Yong Yang

Abstract:

This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations.

Keywords: Nodal Discontinuous Galerkin Method, RKDG, Scalar Wave Equation, LSERK

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Authors: Hasmayadi Abdul Majid, Rohana Musa

Abstract:

This paper presents the development of a 38.5 kS/s 10-bit low power SAR ADC which is realized in MIMOS’s 0.35 µm CMOS process. The design uses a resistive DAC, a dynamic comparator with pre-amplifier and SAR digital logic to create 10 effective bits while consuming less than 7.8 mW with a 3.3 V power supply.

Keywords: Successive Approximation Register Analog-to- Digital Converter, SAR ADC, Resistive DAC.

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Authors: Justyna Rybicka, Ashutosh Tiwari, Shane Enticott

Abstract:

In the age of automation and computation aiding manufacturing, it is clear that manufacturing systems have become more complex than ever before. Although technological advances provide the capability to gain more value with fewer resources, sometimes utilisation of the manufacturing capabilities available to organisations is difficult to achieve. Flexible manufacturing systems (FMS) provide a unique capability to manufacturing organisations where there is a need for product range diversification by providing line efficiency through production flexibility. This is very valuable in trend driven production set-ups or niche volume production requirements. Although FMS provides flexible and efficient facilities, its optimal set-up is key in achieving production performance. As many variables are interlinked due to the flexibility provided by the FMS, analytical calculations are not always sufficient to predict the FMS’ performance. Simulation modelling is capable of capturing the complexity and constraints associated with FMS. This paper demonstrates how discrete event simulation (DES) can address complexity in an FMS to optimise the production line performance. A case study of an automotive FMS is presented. The DES model demonstrates different configuration options depending on prioritising objectives: utilisation and throughput. Additionally, this paper provides insight into understanding the impact of system set-up constraints on the FMS performance and demonstrates the exploration into the optimal production set-up.

Keywords: Automotive, capacity performance, discrete event simulation, flexible manufacturing system.

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Authors: Radouane Elbahjaoui, Hamid El Qarnia

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The present work aims to investigate numerically the thermal and flow characteristics of a rectangular latent heat storage unit (LHSU) during the melting process of a phase change material (PCM). The LHSU consists of a number of vertical and identical plates of PCM separated by rectangular channels. The melting process is initiated when the LHSU is heated by a heat transfer fluid (HTF: water) flowing in channels in a downward or upward direction. The proposed study is motivated by the need to optimize the thermal performance of the LHSU by accelerating the charging process. A mathematical model is developed and a fixed-grid enthalpy formulation is adopted for modeling the melting process coupling with convection-conduction heat transfer. The finite volume method was used for discretization. The obtained numerical results are compared with experimental, analytical and numerical ones found in the literature and reasonable agreement is obtained. Thereafter, the numerical investigations were carried out to highlight the effects of the HTF flow direction and the aspect ratio of the PCM slabs on the heat transfer characteristics and thermal performance enhancement of the LHSU.

Keywords: Phase change material, thermal energy storage, latent heat storage unit, melting.

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Authors: Mosses E. Lufuke, Lorna M. Kamau

Abstract:

This paper attempted to assess whether the size of the regional economic bloc has an impact to the flow of trade to a particular country. Two different sized blocs (COMESA and EAC) and one country (Tanzania) have been used as the point of references. Using the results from of the analyses, the paper also was anticipated to establish whether it was rational for Tanzania to withdraw its membership from COMESA (the larger bloc) to join EAC (the small one). Gravity model has been used to estimate the relationship between the variables, from which the bilateral trade flows between Tanzania and the eighteen member countries of the two blocs (COMESA and EAC) was employed for the time between 2000 and 2013. In the model, the dummy variable for regional bloc (bloc) at which the Tanzania trade partner countries belong are also added to the model to understand which trade bloc exhibit higher trade flow with Tanzania. From the findings, it was noted that over the period of study (2000-2013) Tanzania acknowledged more than 257% of trade volume in EAC than in COMESA. Conclusive, it was noted that the flow of trade is explained by many other variables apart from the size of regional bloc; and that the size by itself offer insufficient evidence in causality relationship. The paper therefore remain neutral on such staggered switching decision since more analyses are required to establish the country’s trade flow, especially when if it had been in multiple membership of COMESA and EAC.

Keywords: Economic Bloc, Flow of Trade, Size of Bloc, Switching.

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Authors: J. Modu, J. F. Georgin, L. Briançon, E. Antoinet

Abstract:

Wind turbine gravity foundations are designed to resist overturning failure through gravitational forces resulting from their masses. Owing to the relatively high volume of the cementitious material present, the foundations tend to suffer thermal strains and internal cracking due to high temperatures and temperature gradients depending on factors such as geometry, mix design and level of restraint. This is a result of a fully coupled mechanism commonly known as THMC (Thermo- Hygro - Mechanical - Chemical) coupling whose kinetics peak during the early age of concrete. The focus of this paper is therefore to present and offer a discussion on the temperature and humidity evolutions occurring in mass pours such as wind turbine gravity foundations based on sensor results obtained from the monitoring of an actual wind turbine foundation. To offer prediction of the evolutions, the formulation of a 3D Thermal-Hydro-Chemical (THC) model that is mainly derived from classical fundamental physical laws is also presented and discussed. The THC model can be mathematically fully coupled in Finite Element analyses. In the current study, COMSOL Multi-physics software was used to simulate the 3D THC coupling that occurred in the monitored wind turbine foundation to predict the temperature evolution at five different points within the foundation from time of casting.

Keywords: Early age behavior, reinforced concrete, THC 3D models, wind turbines.

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Authors: David J. Russell SC

Abstract:

Widespread use of asbestos over the last century has left a terrible legacy of lung disease. Doctors knew of the health risks long ago, but almost nothing was done to protect workers and the public. Some aspects of nanotechnology may have risks similar to asbestos.

Keywords: Asbestos, causation, nanotechnology.

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Authors: Omessaad Hamdi, Ammar Bouallegue, Sami Harari

Abstract:

In [4], Kipnis and Shamir have cryptanalised a version of HFE of degree 2. In this paper, we describe the generalization of this attack of HFE of degree more than 2. We are based on Fourier Transformation to acheive partially this attack.

Keywords: Public, cryptosystem, cryptanalisis, HFE.

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Authors: Xiaochuan Chen, Jianguo Yang, Beizhi Li

Abstract:

Design for cost (DFC) is a method that reduces life cycle cost (LCC) from the angle of designers. Multiple domain features mapping (MDFM) methodology was given in DFC. Using MDFM, we can use design features to estimate the LCC. From the angle of DFC, the design features of family cars were obtained, such as all dimensions, engine power and emission volume. At the conceptual design stage, cars- LCC were estimated using back propagation (BP) artificial neural networks (ANN) method and case-based reasoning (CBR). Hamming space was used to measure the similarity among cases in CBR method. Levenberg-Marquardt (LM) algorithm and genetic algorithm (GA) were used in ANN. The differences of LCC estimation model between CBR and artificial neural networks (ANN) were provided. ANN and CBR separately each method has its shortcomings. By combining ANN and CBR improved results accuracy was obtained. Firstly, using ANN selected some design features that affect LCC. Then using LCC estimation results of ANN could raise the accuracy of LCC estimation in CBR method. Thirdly, using ANN estimate LCC errors and correct errors in CBR-s estimation results if the accuracy is not enough accurate. Finally, economically family cars and sport utility vehicle (SUV) was given as LCC estimation cases using this hybrid approach combining ANN and CBR.

Keywords: case-based reasoning, life cycle cost (LCC), artificialneural networks (ANN), family cars

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Authors: A. Tellaeche, X. P. Burgos-Artizzu, G. Pajares, A. Ribeiro

Abstract:

One important objective in Precision Agriculture is to minimize the volume of herbicides that are applied to the fields through the use of site-specific weed management systems. In order to reach this goal, two major factors need to be considered: 1) the similar spectral signature, shape and texture between weeds and crops; 2) the irregular distribution of the weeds within the crop's field. This paper outlines an automatic computer vision system for the detection and differential spraying of Avena sterilis, a noxious weed growing in cereal crops. The proposed system involves two processes: image segmentation and decision making. Image segmentation combines basic suitable image processing techniques in order to extract cells from the image as the low level units. Each cell is described by two area-based attributes measuring the relations among the crops and the weeds. From these attributes, a hybrid decision making approach determines if a cell must be or not sprayed. The hybrid approach uses the Support Vector Machines and the Fuzzy k-Means methods, combined through the fuzzy aggregation theory. This makes the main finding of this paper. The method performance is compared against other available strategies.

Keywords: Fuzzy k-Means, Precision agriculture, SupportVectors Machines, Weed detection.

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Authors: Niti Kammuang-lue, Kritsada On-ai, Phrut Sakulchangsatjatai, Pradit Terdtoon

Abstract:

The objectives of this paper are to investigate effects of dimensionless numbers on thermal performance of the vertical closed-loop pulsating heat pipe (VCLPHP) and to establish a correlation to predict the thermal performance of the VCLPHP. The CLPHPs were made of long copper capillary tubes with inner diameters of 1.50, 1.78, and 2.16mm and bent into 26 turns. Then, both ends were connected together to form a loop. The evaporator, adiabatic, and condenser sections length were equal to 50 and 150 mm. R123, R141b, acetone, ethanol, and water were chosen as variable working fluids with constant filling ratio of 50% by total volume. Inlet temperature of heating medium and adiabatic section temperature was constantly controlled at 80 and 50^oC, respectively. Thermal performance was represented in a term of Kutateladze number (Ku). It can be concluded that when Prandtl number of liquid working fluid (Pr_l), and Karman number (Ka) increases, thermal performance increases. On contrary, when Bond number (Bo), Jacob number (Ja), and Aspect ratio (L_e/D_i) increases, thermal performance decreases. Moreover, the correlation to predict more precise thermal performance has been successfully established by analyzing on all dimensionless numbers that have effect on the thermal performance of the VCLPHP.

Keywords: Vertical closed-loop pulsating heat pipe, working fluid, thermal performance, dimensionless parameter.

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Authors: Kelong Zheng, Shouming Zhong

Abstract:

A new nonlinear sum-difference inequality in two variables which generalize some existing results and can be used as handy tools in the analysis of certain partial difference equation is discussed. An example to show boundedness of solutions of a difference value problem is also given.

Keywords: Sum-Difference inequality, Nonlinear, Boundedness.

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Authors: Yacine Challal, Hamida Seba

Abstract:

Group key management is an important functional building block for any secure multicast architecture. Thereby, it has been extensively studied in the literature. In this paper we present relevant group key management protocols. Then, we compare them against some pertinent performance criteria.

Keywords: Multicast, Security, Group Key Management.

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Authors: Kambiz Tahvildari, Shakila ila Motamedi

Abstract:

Presently and in line with the United Nations (EPA), human thinking system has shifted towards clean fuels so as to maintain a cleaner environment and to save our planet earth. One of the most successful studies in order to achieve new energies includes the use of animal wastes and their organic residues, and the result of these researches has been represented in the form of very simple and cheap methods called biogas technology. Biogas technology has developed a lot in the recent decades; its reason is the high cost of fossil fuels and the greater attention of countries to the environmental pollutions due to the consumption of this kind of fuels. IRAN is ready for the optimized application of renewable energies, having much enriched resources of this kind of energies; so a special place could be considered for it when making programs. The purpose of biogas technology is the recovery of energy and finally the protection of the environment, which is much appropriate for the third world farmers with respect to their technical abilities and economic potentials. Studies show that the production and consumption of biogas is appropriate and economic in IRAN, because of the high amount of waste in the agriculture sector, the significant amount of animal and human excrement production, the great volume of garbage produced and the most important the specific social, climatic and agricultural conditions in IRAN, in order to proceed towards the reduction of pollution due to the use of fossil fuels.

Keywords: Agriculture, Biogas, Energy, Environment.

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Authors: Miloš Matúš, Peter Križan, Ľubomír Šooš, Juraj Beniak

Abstract:

The moisture content of densified biomass is a limiting parameter influencing the quality of this solid biofuel. It influences its calorific value, density, mechanical strength and dimensional stability as well as affecting its production process. This paper deals with experimental research into the effect of moisture content of the densified material on the final quality of biofuel in the form of logs (briquettes or pellets). Experiments based on the singleaxis densification of the spruce sawdust were carried out with a hydraulic piston press (piston and die), where the densified logs were produced at room temperature. The effect of moisture content on the qualitative properties of the logs, including density, change of moisture, expansion and physical changes, and compressive and impact resistance were studied. The results show the moisture ranges required for producing good-quality logs. The experiments were evaluated and the moisture content of the tested material was optimized to achieve the optimum value for the best quality of the solid biofuel. The dense logs also have high-energy content per unit volume. The research results could be used to develop and optimize industrial technologies and machinery for biomass densification to achieve high quality solid biofuel.

Keywords: Biomass, briquettes, densification, fuel quality, moisture content, density.

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Authors: M. Jusoh, R. Mohd Yunus, M. A. Abu Hassan

Abstract:

Freeze concentration freezes or crystallises the water molecules out as ice crystals and leaves behind a highly concentrated solution. In conventional suspension freeze concentration where ice crystals formed as a suspension in the mother liquor, separation of ice is difficult. The size of the ice crystals is still very limited which will require usage of scraped surface heat exchangers, which is very expensive and accounted for approximately 30% of the capital cost. This research is conducted using a newer method of freeze concentration, which is progressive freeze concentration. Ice crystals were formed as a layer on the designed heat exchanger surface. In this particular research, a helical structured copper crystallisation chamber was designed and fabricated. The effect of two operating conditions on the performance of the newly designed crystallisation chamber was investigated, which are circulation flowrate and coolant temperature. The performance of the design was evaluated by the effective partition constant, K, calculated from the volume and concentration of the solid and liquid phase. The system was also monitored by a data acquisition tool in order to see the temperature profile throughout the process. On completing the experimental work, it was found that higher flowrate resulted in a lower K, which translated into high efficiency. The efficiency is the highest at 1000 ml/min. It was also found that the process gives the highest efficiency at a coolant temperature of -6 °C.

Keywords: Freeze concentration, progressive freeze concentration, freeze wastewater treatment, ice crystals.

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Authors: Rado Flajs, Miran Saje

Abstract:

We present a simple nonconforming approximation of the linear two–point boundary value problem which violates patch test requirements. Nevertheless the solutions, obtained from these type of approximations, converge to the exact solution.

Keywords: Generalized patch test, Irons' patch test, nonconforming finite element, convergence.

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Authors: Bahadir O. Guler, Serkan Kader, Murat Besenk

Abstract:

In this paper we examine some properties of suborbital graphs for the congruence subgroup r 0 (N) . Then we give necessary and sufficient conditions for graphs to have triangels.

Keywords: Congruence subgroup, Imprimitive action, Modulargroup, Suborbital graphs.

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