Search results for: Effective diffusion coefficient

Authors: Suparat Niwitpong, Sa-aat Niwitpong

Abstract:

In this paper we proposed the new confidence interval for the normal population mean with known coefficient of variation. In practice, this situation occurs normally in environment and agriculture sciences where we know the standard deviation is proportional to the mean. As a result, the coefficient of variation of is known. We propose the new confidence interval based on the recent work of Khan [3] and this new confidence interval will compare with our previous work, see, e.g. Niwitpong [5]. We derive analytic expressions for the coverage probability and the expected length of each confidence interval. A numerical method will be used to assess the performance of these intervals based on their expected lengths.

Keywords: confidence interval, coverage probability, expected length, known coefficient of variation.

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Authors: Mohammad Amin Safi, Mahmud Ashrafizaadeh, Amir Ali Ashrafizaadeh

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A highly optimized implementation of binary mixture diffusion with no initial bulk velocity on graphics processors is presented. The lattice Boltzmann model is employed for simulating the binary diffusion of oxygen and nitrogen into each other with different initial concentration distributions. Simulations have been performed using the latest proposed lattice Boltzmann model that satisfies both the indifferentiability principle and the H-theorem for multi-component gas mixtures. Contemporary numerical optimization techniques such as memory alignment and increasing the multiprocessor occupancy are exploited along with some novel optimization strategies to enhance the computational performance on graphics processors using the C for CUDA programming language. Speedup of more than two orders of magnitude over single-core processors is achieved on a variety of Graphical Processing Unit (GPU) devices ranging from conventional graphics cards to advanced, high-end GPUs, while the numerical results are in excellent agreement with the available analytical and numerical data in the literature.

Keywords: Lattice Boltzmann model, Graphical processing unit, Binary mixture diffusion, 2D flow simulations, Optimized algorithm.

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Authors: Yilun Shang

Abstract:

In this paper, we deal with the fundamental concepts and properties of ergodicity coefficients in a hierarchical sense by making use of partition. Moreover, we establish a hierarchial Hajnal’s inequality improving some previous results.

Keywords: Stochastic matrix, ergodicity coefficient, partition.

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Authors: Jevgenijs Carkovs

Abstract:

The paper is devoted to stochastic analysis of finite dimensional difference equation with dependent on ergodic Markov chain increments, which are proportional to small parameter ". A point-form solution of this difference equation may be represented as vertexes of a time-dependent continuous broken line given on the segment [0,1] with "-dependent scaling of intervals between vertexes. Tending " to zero one may apply stochastic averaging and diffusion approximation procedures and construct continuous approximation of the initial stochastic iterations as an ordinary or stochastic Ito differential equation. The paper proves that for sufficiently small " these equations may be successfully applied not only to approximate finite number of iterations but also for asymptotic analysis of iterations, when number of iterations tends to infinity.

Keywords: Markov dynamical system, diffusion approximation, equilibrium stochastic stability.

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Authors: Naveed Ahmed, Gunar Matthies

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We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numerical results which shows that the cGP(k) and dG(k)- methods are accurate of order k +1, respectively, in the whole time interval. Moreover, the cGP(k)-method is superconvergent of order 2k and dG(k)-method is of order 2k +1 at the discrete time points. Furthermore, the dependence of the results on the choice of the stabilization parameter are discussed and compared.

Keywords: Convection-diffusion-reaction equations, stabilized finite elements, discontinuous Galerkin, continuous Galerkin-Petrov.

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Authors: Subariah Ibrahim, Mohd Aizaini Maarof

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A generalization of the concepts of Feistel Networks (FN), known as Extended Feistel Network (EFN) is examined. EFN splits the input blocks into n > 2 sub-blocks. Like conventional FN, EFN consists of a series of rounds whereby at least one sub-block is subjected to an F function. The function plays a key role in the diffusion process due to its completeness property. It is also important to note that in EFN the F-function is the most computationally expensive operation in a round. The aim of this paper is to determine a suitable type of EFN for a scalable cipher. This is done by analyzing the threshold number of rounds for different types of EFN to achieve the completeness property as well as the number of F-function required in the network. The work focuses on EFN-Type I, Type II and Type III only. In the analysis it is found that EFN-Type II and Type III diffuses at the same rate and both are faster than Type-I EFN. Since EFN-Type-II uses less F functions as compared to EFN-Type III, therefore Type II is the most suitable EFN for use in a scalable cipher.

Keywords: Cryptography, Extended Feistel Network, Diffusion Analysis.

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Authors: B. Sohbi, M. Emtir, M. Elgarni

Abstract:

An interesting method to produce calcium carbonate is based in a gas-liquid reaction between carbon dioxide and aqueous solutions of calcium hydroxide. The design parameters for gas-liquid phase are flow regime, individual mass transfer, gas-liquid specific interfacial area. Most studies on gas-liquid phase were devoted to the experimental determination of some of these parameters, and more specifically, of the mass transfer coefficient, kLa which depends fundamentally on the superficial gas velocity and on the physical properties of absorption phase. The principle investigation was directed to study the effect of the vibration on the mass transfer coefficient kLa in gas-liquid phase during absorption of CO2 in the in aqueous solution of calcium hydroxide. The vibration with a higher frequency increase the mass transfer coefficient kLa, but vibration with lower frequency didn-t improve it, the mass transfer coefficient kLa increase with increase the superficial gas velocity.

Keywords: Environment technology, mass transfer coefficient, absorption, CO2, calcium hydroxide.

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Authors: Morteza Amirabadi, Vahid Fayaz , Fereshteh Felegary, Hossien Hossienkhani

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The most suitable Semiconductor detector, Cadmium Zinc Teloraid , has unique properties because of high Atomic number and wide Brand Gap . It has been tried in this project with different processes such as Lead , Diffusion , Produce and Recombination , effect of Trapping and injection carrier of CdZnTe , to get hole and then present a complete answer of it . Then we should investigate the movement of carrier ( Electron – Hole ) by using above answer.

Keywords: Semiconcuctor detector, Trapping, Recommbination, Diffusion

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Authors: C.K. Hindumathy

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Alcohol and water extracts of Cymbopogon citratus was investigated for anti-bacterial properties and phytochemical constituents. The extract was screened against four gram-negative bacteria Escherichia coli, Klebsiella pneumoniae, Pseudomonas aeruginosa, Proteus vulgaris) and two grampositive bacteria Bacillus subtilis and Staphylococcus aureus at four different concentrations (1:1, 1:5, 1:10 and 1:20) using disc diffusion method. The antibacterial examination was by disc diffusion techniques, while the photochemical constituents were investigated using standard chemical methods. Results showed that the extracts inhibited the growth of standard and local strains of the organisms used. The treatments were significantly different (P = 0.05). The minimum inhibitory concentration of the extracts against the tested microorganisms ranged between 150mg/ml and 50mg/ml. The alcohol extracts were found to be generally more effective than the water extract. The photochemical analysis revealed the presence of alkaloids and phenol but absence of cardiac and cyanogenic glycosides. The presence of alkaloid and phenols were inferred as being responsible for the anti-bacterial properties of the extracts.

Keywords: Cymbopogon citratus; gram negative and grampositive

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Authors: I. Norhuda, A. K. Mohd Omar

Abstract:

Studies on gas solid mass transfer using Supercritical fluid CO2 (SC-CO2) in a packed bed of palm kernels was investigated at operating conditions of temperature 50 °C and 70 °C and pressures ranges from 27.6 MPa, 34.5 MPa, 41.4 MPa and 48.3 MPa. The development of mass transfer models requires knowledge of three properties: the diffusion coefficient of the solute, the viscosity and density of the Supercritical fluids (SCF). Matematical model with respect to the dimensionless number of Sherwood (Sh), Schmidt (Sc) and Reynolds (Re) was developed. It was found that the model developed was found to be in good agreement with the experimental data within the system studied.

Keywords: Mass Transfer, Palm Kernel, Supercritical fluid.

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Authors: H. Dehghan, E. Mahdavi, M. M. Heyhat

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In pressure vessels contain hydrogen, the role of hydrogen will be important because of hydrogen cracking problem. It is difficult to predict what is happened in metallurgical field spite of a lot of studies have been searched. The main role in controlling the mass diffusion as driving force is related to stress. In this study, finite element analysis is implemented to estimate material-s behavior associated with hydrogen embrittlement. For this purpose, one model of a pressure vessel is introduced that it has definite boundary and initial conditions. In fact, finite element is employed to solve the sequentially coupled mass diffusion with stress near a crack front in a pressure vessel. Modeling simulation intergrarnular fracture of AISI 4135 steel due to hydrogen is investigated. So, distribution of hydrogen and stress are obtained and they indicate that their maximum amounts occur near the crack front. This phenomenon is happened exactly the region between elastic and plastic field. Therefore, hydrogen is highly mobile and can diffuse through crystal lattice so that this zone is potential to trap high volume of hydrogen. Consequently, crack growth and fast fracture will be happened.

Keywords: Stress Intensity Factor, Mass Diffusion, FEM, Pressure Vessel

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Authors: Shivalinge Gowda

Abstract:

The total mass attenuation coefficients m/r, of some halides such as, NaCl, KCl, CuCl, NaBr, KBr, RbCl, AgCl, NaI, KI, AgBr, CsI, HgCl₂, CdI₂ and HgI₂ were determined at photon energies 279.2, 320.07, 514.0, 661.6, 1115.5, 1173.2 and 1332.5 keV in a well-collimated narrow beam good geometry set-up using a high resolution, hyper pure germanium detector. The mass attenuation coefficients and the effective atomic cross sections are found to be in good agreement with the XCOM values. From these mass attenuation coefficients, the effective atomic cross sections s_a, of the compounds were determined. These effective atomic cross section s_a data so obtained are then used to compute the effective atomic numbers Z_eff. For this, the interpolation of total attenuation cross-sections of photons of energy E in elements of atomic number Z was performed by using the logarithmic regression analysis of the data measured by the authors and reported earlier for the above said energies along with XCOM data for standard energies. The best-fit coefficients in the photon energy range of 250 to 350 keV, 350 to 500 keV, 500 to 700 keV, 700 to 1000 keV and 1000 to 1500 keV by a piecewise interpolation method were then used to find the Z_eff of the compounds with respect to the effective atomic cross section s_a from the relation obtained by piece wise interpolation method. Using these Z_eff values, the electron densities N_el of halides were also determined. The present Z_eff and N_el values of halides are found to be in good agreement with the values calculated from XCOM data and other available published values.

Keywords: Mass attenuation coefficient, atomic cross-section, effective atomic number, electron density.

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Authors: Sayantan Khanra, Rojers P. Joseph

Abstract:

This study attempts to analyze the impact of demography and service quality on the adoption and diffusion of e-Government services in the context of India. The objective of this paper is to study the users' perception about e-Government services and investigate the key variables that are most salient to the Indian populace. At the completion of this study, a research model that would help to understand the relationship involving the demographic variables and service quality dimensions, and the willingness to adopt e-Government services is expected to be developed. Dedicated authorities, particularly those in developing economies, may use that model or its augmented versions to design and update e-Government services and promote their use among citizens. After all, enhanced public participation is required to improve efficiency, engagement and transparency in the implementation of the aforementioned services.

Keywords: Adoption and diffusion of e-Government services, demographic variables, hierarchical regression analysis, service quality dimensions.

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Authors: L. Torchane

Abstract:

In this work, our goal is to optimize the nitriding treatment at a low-temperature of the steel 32CrMoV13 using gas mixtures of ammonia, nitrogen and hydrogen to improve the mechanical properties of the surface (good wear resistance, friction and corrosion), and of the diffusion layer of the nitrogen (good resistance to fatigue and good tenacity with heart). By limiting our work to the pure iron and to the alloys iron-chromium and iron-chromium-carbon, we have studied the various parameters which manage the nitriding: flow rate and composition of the gaseous phase, the interaction chromium-nitrogen and chromium-carbon by the help of experiments of nitriding realized in the laboratory by thermogravimetry. The acquired knowledge has been applied by the mastery of the growth of the γ' combination layer on the α diffusion layer in the case of the industrial steel 32CrMoV13.

Keywords: Diffusion of nitrogen, Gaseous nitriding, Layer growth kinetic.

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Authors: Shiping Zhou, Minggen Cui

Abstract:

This paper investigates the inverse problem of determining the unknown time-dependent leading coefficient in the parabolic equation using the usual conditions of the direct problem and an additional condition. An algorithm is developed for solving numerically the inverse problem using the technique of space decomposition in a reproducing kernel space. The leading coefficients can be solved by a lower triangular linear system. Numerical experiments are presented to show the efficiency of the proposed methods.

Keywords: parabolic equations, coefficient inverse problem, reproducing kernel.

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Authors: M. Sadoughi, R. Ehsani

Abstract:

The aim of the present study is examining the relationship between conceptual organizational culture and the level of tolerance in employees of Islamic Azad University of Shahre Ghods. This research is a correlational and analytic-descriptive one. The samples included 144 individuals. A 24-item standard questionnaire of organizational culture by Cameron and Queen was used in this study. This questionnaire has six criteria and each criterion includes four items that each item indicates one cultural dimension. Reliability coefficient of this questionnaire was normed using Cronbach's alpha of 0.91. Also, the 25-item questionnaire of tolerance by Conor and Davidson was used. This questionnaire is in a five-degree Likert scale form. It has seven criteria and is designed to measure the power of coping with pressure and threat. It has the needed content reliability and its reliability coefficient is normed using Cronbach's alpha of 0.87. Data were analyzed using Pearson correlation coefficient and multivariable regression. The results showed among various dimensions of organizational culture, there is a positive significant relationship between three dimensions (family, adhocracy, bureaucracy) and tolerance, there is a negative significant relationship between dimension of market and tolerance and components of organizational culture have the power of prediction and explaining the tolerance. In this explanation, the component of family is the most effective and the best predictor of tolerance.

Keywords: Adhocracy, bureaucracy, organizational culture, tolerance.

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Authors: Bhausaheb L. Pangarkar, M. G. Sane, Saroj B. Parjane, Rajendra M. Abhang, Mahendra Guddad

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Vacuum membrane distillation (VMD) process can be used for water purification or the desalination of salt water. The process simply consists of a flat sheet hydrophobic micro porous PTFE membrane and diaphragm vacuum pump without a condenser for the water recovery or trap. The feed was used aqueous NaCl solution. The VMD experiments were performed to evaluate the heat and mass transfer coefficient of the boundary layer in a membrane module. The only operating parameters are feed inlet temperature, and feed flow rate were investigated. The permeate flux was strongly affected by the feed inlet temperature, feed flow rate, and boundary layer heat transfer coefficient. Since lowering the temperature polarization coefficient is essential enhance the process performance considerable and maximizing the heat transfer coefficient for maximizes the mass flux of distillate water. In this paper, the results of VMD experiments are used to measure the boundary layer heat transfer coefficient, and the experimental results are used to reevaluate the empirical constants in the Dittus- Boelter equation.

Keywords: Desalination, heat and mass transfer coefficient, temperature polarization, membrane distillation

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Authors: Giho Jeong, Sooin Jeong, Kuisoon Kim

Abstract:

It is very important to determine reference temperature when convective temperature because it should be used to calculate the temperature potential. This paper deals with the development of a new method that can determine heat transfer coefficient and reference free stream temperature simultaneously, based on transient heat transfer experiments with using two narrow band thermo-tropic liquid crystals (TLC's). The method is validated through error analysis in terms of the random uncertainties in the measured temperatures. It is shown how the uncertainties in heat transfer coefficient and free stream temperature can be reduced. The general method described in this paper is applicable to many heat transfer models with unknown free stream temperature.

Keywords: Heat transfer coefficient, Thermo-tropic LiquidCrystal (TLC), Free stream temperature.

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Authors: J. Miao, C. W. Leung, C. S. Cheung, R. C. K. Leung

Abstract:

The present project was conducted with the circumferential-fuel-jets inverse diffusion flame (CIDF) burner burning liquefied petroleum gas (LPG) enriched with 50% of hydrogen fuel (H2). The range of stable operation of the CIDF burner in terms of Reynolds number (from laminar to turbulent flow regions), equivalence ratio and fuel jet velocity of LPG of the 50% H2-LPG mixed fuel was identified. Experiments were also carried out to investigate the flame structures of the LPG flame and LPG enriched H2 flame. Experimental results obtained from these two flames were compared to fully explore the influence of hydrogen addition on flame stability. Flame heights obtained by burning these two kinds of fuels at various equivalence ratios were compared and correlated with the Global Momentum Ratio (GMR).

Keywords: Flame stability, hydrogen enriched LPG, inverse diffusion flame.

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Authors: A. R. Shahani, E. Mahdavi, M. Amidpour

Abstract:

Hydrogen diffusion is the main problem for corrosion fatigue in corrosive environment. In order to analyze the phenomenon, it is needed to understand their behaviors specially the hydrogen behavior during the diffusion. So, Hydrogen embrittlement and prediction its behavior as a main corrosive part of the fractions, needed to solve combinations of different equations mathematically. The main point to obtain the equation, having knowledge about the source of causing diffusion and running the atoms into materials, called driving force. This is produced by either gradient of electrical or chemical potential. In this work, we consider the gradient of chemical potential to obtain the property equation. In diffusion of atoms, some of them may be trapped but, it could be ignorable in some conditions. According to the phenomenon of hydrogen embrittlement, the thermodynamic and chemical properties of hydrogen are considered to justify and relate them to fracture mechanics. It is very important to get a stress intensity factor by using fugacity as a property of hydrogen or other gases. Although, the diffusive behavior and embrittlement event are common and the same for other gases but, for making it more clear, we describe it for hydrogen. This considering on the definite gas and describing it helps us to understand better the importance of this relation.

Keywords: Hydrogen embrittlement, Fracture mechanics, Thermodynamic, Stress intensity factor.

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Authors: Y. Galerkin, A. Rekstin, K. Soldatova

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Universal modeling method well proven for industrial compressors was applied for design of the high flow rate supersonic stage. Results were checked by ANSYS CFX and NUMECA Fine Turbo calculations. The impeller appeared to be very effective at transonic flow velocities. Stator elements efficiency is acceptable at design Mach numbers too. Their loss coefficient versus inlet flow angle performances correlates well with Universal modeling prediction. The impeller demonstrates ability of satisfactory operation at design flow rate. Supersonic flow behavior in the impeller inducer at the shroud blade to blade surface Φ des deserves additional study.

Keywords: Centrifugal compressor stage, supersonic impeller, inlet flow angle, loss coefficient, return channel, shock wave, vane diffuser.

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Authors: Nopparat Pochai, Rujira Deepana

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Water pollution assessment problems arise frequently in environmental science. In this research, a finite difference method for solving the one-dimensional steady convection-diffusion equation with variable coefficients is proposed; it is then used to optimize water treatment costs.

Keywords: Finite difference, One-dimensional, Steady state, Waterpollution control, Optimization, Convection-diffusion equation.

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Authors: Manpreet Singh, Parvinder Singh Sandhu, Basant Raj Singh

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Hybridization refers to the crossing breeding of two plants. Coefficient of Parentage (COP) is used by the plant breeders to determine the genetic diversity across various varieties so as to incorporate the useful characters of the two varieties to develop a new crop variety with particular useful characters. Genetic Diversity is the prerequisite for any cultivar development program. Genetic Diversity depends upon the pedigree information of the varieties based on particular levels. Pedigree refers to the parents of a particular variety at various levels. This paper discusses the searching and analyses of different possible pairs of varieties selected on the basis of morphological characters, Climatic conditions and Nutrients so as to obtain the most optimal pair that can produce the required crossbreed variety. An algorithm was developed to determine the coefficient of parentage (COP) between the selected wheat varieties. Dummy values were used wherever actual data was not available.

Keywords: Coefficient of Parentage, Morphological characters, Pedigree, Genetic Diversity.

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Authors: Un-Hwan Park, Jun-Hyeok Heo, In-Sung Lee, Tae-Hyeon Oh, Dae-Gyu Park

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Automotive interior material consisting of several material layers has the sound-absorbing function. It is difficult to predict sound absorbing coefficient because of several material layers. So, many experimental tunings are required to achieve the target of sound absorption. Therefore, while the car interior materials are developed, so much time and money is spent. In this study, we present a method to predict the sound absorbing performance of the material with multi-layer using physical properties of each material. The properties are predicted by Foam-X software using the sound absorption coefficient data measured by impedance tube. Then, we will compare and analyze the predicted sound absorption coefficient with the data measured by scaled reverberation chamber and impedance tubes for a prototype. If the method is used instead of experimental tuning in the development of car interior material, the time and money can be saved, and then, the development effort can be reduced because it can be optimized by simulation.

Keywords: Multi-layer nonwoven, sound absorption coefficient, scaled reverberation chamber, impedance tubes.

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Authors: Mansour Al Qubeissi, Sergei S. Sazhin, Cyril Crua, Morgan R. Heikal

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This paper presents the application of the Discrete Component Model for heating and evaporation to multi-component biodiesel fuel droplets in direct injection internal combustion engines. This model takes into account the effects of temperature gradient, recirculation and species diffusion inside droplets. A distinctive feature of the model used in the analysis is that it is based on the analytical solutions to the temperature and species diffusion equations inside the droplets. Nineteen types of biodiesel fuels are considered. It is shown that a simplistic model, based on the approximation of biodiesel fuel by a single component or ignoring the diffusion of components of biodiesel fuel, leads to noticeable errors in predicted droplet evaporation time and time evolution of droplet surface temperature and radius.

Keywords: Heat/Mass Transfer, Biodiesel, Multi-component Fuel, Droplet, Evaporation.

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Authors: Arash Mir Abdolah Lavasani, Meghdad Ebrahimi Sabet

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In this paper, the 2-D unsteady viscous flow around two cam shaped cylinders in tandem arrangement is numerically simulated in order to study the characteristics of the flow in turbulent regimes. The investigation covers the effects of high subcritical and supercritical Reynolds numbers and L/D ratio on total drag coefficient. The equivalent diameter of cylinders is 27.6 mm The space between center to center of two cam shaped cylinders is define as longitudinal pitch ratio and it varies in range of 1.5< L/D<6. Reynolds number base on equivalent circular cylinder varies in range of 27×103< Re <166×103 Results show that drag coefficient of both cylinders depends on pitch ratio. However, drag coefficient of downstream cylinder is more dependent on the pitch ratio.

Keywords: Cam shaped, tandem, numerical, drag coefficient, turbulent.

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Authors: Mefleh S. Hamideen

Abstract:

In this investigation, activity concentration of 226Ra, 232Th, and 40K, of some ceramic tile materials used in the local market of Jordan for interior decoration were determined by making use of High Purity Germanium (HPGe) detector. Twenty samples of different country of origin and sizes used in Jordan were analyzed. The concentration values of the last-mentioned radionuclides ranged from 30 Bq.kg-1 (Sample from Jordan) to 98 Bq.kg-1 (Sample from China) for 226Ra, 31 Bq.kg-1 (Sample from Italy) to 98 Bq.kg-1 (Sample from China) for 232Th, and 129 Bq.kg-1 (Sample from Spain) to 679 Bq.kg-1 (Sample from Italy) for 40K. Based on the calculated activity concentrations, some radiological parameters have been calculated to test the radiation hazards in the ceramic tiles. In this work, the following parameters: Total absorbed dose rate (DR), Annual effective dose rate (HR), Radium equivalent activity (Raeq), Radon emanation coefficient F (%) and Radon mass exhalation rate (Em) were calculated for all ceramic tiles and listed in the body of the work. Fortunately, the average calculated values of all parameters are less than the recommended values for each parameter. Consequently, almost all the examined ceramic materials appear to have low radon emanation coefficients. As a result of that investigation, no problems on people can appear by using those ceramic tiles in Jordan.

Keywords: radon emanation coefficient, radon mass exhalation rate, total annual effective dose, radon level

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Authors: C. C. Wong, P. L. Hiew

Abstract:

This research aims to examine the key success factors for the diffusion of mobile entertainment services in Malaysia. The drivers and barriers observed in this research include perceived benefit; concerns pertaining to pricing, product and technological standardization, privacy and security; as well as influences from peers and community. An analysis of a Malaysian survey of 384 respondents between 18 to 25 years shows that subscribers placed greater importance on perceived benefit of mobile entertainment services compared to other factors. Results of the survey also show that there are strong positive correlations between all the factors, with pricing issue–perceived benefit showing the strongest relationship. This paper aims to provide an extensive study on the drivers and barriers that could be used to derive architecture for entertainment service provision to serve as a guide for telcos to outline suitable approaches in order to encourage mass market adoption of mobile entertainment services in Malaysia.

Keywords: Barriers, Correlations, Diffusion, Drivers, Mobile Entertainment.

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

Abstract:

In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results is in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes.

Keywords: Semi-Lagrangian method, Iteration free method, Nonlinear advection-diffusion equation.

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Authors: Meriem Bahij, Ahmed Nafidi, Boujemâa Achchab, Sílvio M. A. Gama, José A. O. Matos

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Stochastic modeling concerns the use of probability to model real-world situations in which uncertainty is present. Therefore, the purpose of stochastic modeling is to estimate the probability of outcomes within a forecast, i.e. to be able to predict what conditions or decisions might happen under different situations. In the present study, we present a model of a stochastic diffusion process based on the bi-Weibull distribution function (its trend is proportional to the bi-Weibull probability density function). In general, the Weibull distribution has the ability to assume the characteristics of many different types of distributions. This has made it very popular among engineers and quality practitioners, who have considered it the most commonly used distribution for studying problems such as modeling reliability data, accelerated life testing, and maintainability modeling and analysis. In this work, we start by obtaining the probabilistic characteristics of this model, as the explicit expression of the process, its trends, and its distribution by transforming the diffusion process in a Wiener process as shown in the Ricciaardi theorem. Then, we develop the statistical inference of this model using the maximum likelihood methodology. Finally, we analyse with simulated data the computational problems associated with the parameters, an issue of great importance in its application to real data with the use of the convergence analysis methods. Overall, the use of a stochastic model reflects only a pragmatic decision on the part of the modeler. According to the data that is available and the universe of models known to the modeler, this model represents the best currently available description of the phenomenon under consideration.

Keywords: Diffusion process, discrete sampling, likelihood estimation method, simulation, stochastic diffusion equation, trends functions, bi-parameters Weibull density function.

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