Search results for: thermodynamic functions

Authors: Basma Hamdi, Lakdar Kairouani, Ezzedine Nahdi

Abstract:

The objective of this work is to present a thermodynamic analysis of low temperature solar Rankine cycle with ejector for power generation using zeotropic mixtures. Based on theoretical calculation, effects of zeotropic mixtures compositions on the performance of solar Rankine cycle with ejector are discussed and compared with corresponding pure fluids. Variations of net power output, thermal efficiency were calculating with changing evaporation temperature. The ejector coefficient had analyzed as independent variable. The result show that (R245fa/R152a) has a higher thermal efficiency than using pure fluids.

Keywords: zeotropic mixture, thermodynamic analysis, ejector, low-temperature solar rankine cycle

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Authors: Tulin Coskun

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We investigate the approximation of analytic functions of several variables in polydisc by the sequences of linear k-positive operators in Gadjiev sence. The approximation of analytic functions of complex variable by linear k-positive operators was tackled, and k-positive operators and formulated theorems of Korovkin's type for these operators in the space of analytic functions on the unit disc were introduced in the past. Recently, very general results on convergence of the sequences of linear k-positive operators on a simply connected bounded domain within the space of analytic functions were proved. In this presentation, we extend some of these results to the approximation of analytic functions of several complex variables by sequences of linear k-positive operators.

Keywords: analytic functions, approximation of analytic functions, Linear k-positive operators, Korovkin type theorems

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Authors: Seok Hong Min, Tae Kwon Ha

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With the increasing interest on Ti alloys, the extraction process of Ti from its typical ore, TiO₂, has long been and will be important issue. As an intermediate product for the production of pigment or titanium metal sponge, tetrachloride (TiCl₄) is produced by fluidized bed using high TiO₂ feedstock. The purity of TiCl₄ after chlorination is subjected to the quality of the titanium feedstock. Since the impurities in the TiCl₄ product are reported to final products, the purification process of the crude TiCl₄ is required. The purification process includes fractional distillation and chemical treatment, which depends on the nature of the impurities present and the required quality of the final product. In this study, thermodynamic analysis on the impurity effect in the chlorination process, which is the first step of extraction of Ti from TiO₂, has been conducted. All thermodynamic calculations were performed using the FactSage thermodynamical software.

Keywords: rutile, titanium, chlorination process, impurities, thermodynamic calculation, FactSage

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Authors: Carlos A. Domínguez Torres, Antonio Domínguez Delgado

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In this work we study the thermodynamic behavior of some ventilated facades under summer operating conditions in Southern Spain. Under these climatic conditions, indoor comfort implies a high energetic demand due to high temperatures that usually are reached in this season in the considered geographical area. The aim of this work is to determine if during summer operating conditions in Southern Spain, ventilated façades provide some energy saving compared to the non-ventilated façades and to deduce their behavior patterns in terms of energy efficiency. The modeling of the air flow in the channel has been performed by using Navier-Stokes equations for thermodynamic flows. Numerical simulations have been carried out with a 2D Finite Element approach. This way, we analyze the behavior of ventilated façades under different weather conditions as variable wind, variable temperature and different levels of solar irradiation. CFD computations show that the combined effect of the shading of the external wall and the ventilation by the natural convection into the air gap achieve a reduction of the heat load during the summer period. This reduction has been evaluated by comparing the thermodynamic performances of two ventilated and two unventilated façades with the same geometry and thermophysical characteristics.

Keywords: passive cooling, ventilated façades, energy-efficient building, CFD, FEM

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Authors: M. Madigoe, R. Modiba

Abstract:

High alloyed beta (β) phase-stabilized titanium alloys are known to have a low elastic modulus comparable to that of the human bone (≈30 GPa). The β phase in titanium alloys exhibits an elastic Young’s modulus of about 60-80 GPa, which is nearly half that of α-phase (100-120 GPa). In this work, a theoretical investigation of structural stability and thermodynamic stability, as well as the elastic properties of a quaternary Ti-Nb-Ta-Zr alloy, will be presented with an attempt to lower Young’s modulus. The structural stability and elastic properties of the alloy were evaluated using the first-principles approach within the density functional theory (DFT) framework implemented in the CASTEP code. The elastic properties include bulk modulus B, elastic Young’s modulus E, shear modulus cʹ and Poisson’s ratio v. Thermodynamic stability, as well as the fraction of β phase in the alloy, was evaluated using the Thermo-Calc software package. Thermodynamic properties such as Gibbs free energy (Δ?⁰?) and enthalpy of formation will be presented in addition to phase proportion diagrams. The stoichiometric compositions of the alloy is Ti-Nbx-Ta5-Zr5 (x = 5, 10, 20, 30, 40 at.%). An optimum alloy composition must satisfy the Born stability criteria and also possess low elastic Young’s modulus. In addition, the alloy must be thermodynamically stable, i.e., Δ?⁰? < 0.

Keywords: elastic modulus, phase proportion diagram, thermo-calc, titanium alloys

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Authors: Chahid K. Ghaddar

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The spreadsheet engine is exploited via a non-conventional mechanism to enable novel worksheet solver functions for computational calculus. The solver functions bypass inherent restrictions on built-in math and user defined functions by taking variable formulas as a new type of argument while retaining purity and recursion properties. The enabling mechanism permits integration of numerical algorithms into worksheet functions for solving virtually any computational problem that can be modelled by formulas and variables. Several examples are presented for computing integrals, derivatives, and systems of deferential-algebraic equations. Incorporation of the worksheet solver functions with the ubiquitous spreadsheet extend the utility of the latter as a powerful tool for computational mathematics.

Keywords: calculus, differential algebraic equations, solvers, spreadsheet

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Authors: Sanjay Tushar Choudhary

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This paper focuses on the thermodynamic analysis of Solid Oxide Fuel Cell (SOFC). In the present work the SOFC has been modeled to work with internal reforming of fuel which takes place at high temperature and direct energy conversion from chemical energy to electrical energy takes place. The fuel-cell effluent is a high-temperature steam which can be used for co-generation purposes. Syn-gas has been used here as fuel which is essentially produced by steam reforming of methane in the internal reformer of the SOFC. A thermodynamic model of SOFC has been developed for planar cell configuration to evaluate various losses in the energy conversion process within the fuel cell. Cycle parameters like fuel utilization ratio and the air-recirculation ratio have been varied to evaluate the thermodynamic performance of the fuel cell. Output performance parameters like terminal voltage, cell-efficiency and power output have been evaluated for various values of current densities. It has been observed that a combination of a lower value of air-circulation ratio and higher values of fuel utilization efficiency gives a better overall thermodynamic performance.

Keywords: current density, SOFC, suel utilization factor, recirculation ratio

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Authors: Mohamad Saab, Florent Real, Francois Virot, Laurent Cantrel, Valerie Vallet

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All spent nuclear fuel reprocessing plants use the PUREX process (Plutonium Uranium Refining by Extraction), which is a liquid-liquid extraction method. The organic extracting solvent is a mixture of tri-n-butyl phosphate (TBP) and hydrocarbon solvent such as hydrogenated tetra-propylene (TPH). By chemical complexation, uranium and plutonium (from spent fuel dissolved in nitric acid solution), are separated from fission products and minor actinides. During a normal extraction operation, uranium is extracted in the organic phase as the UO₂(NO₃)₂(TBP)₂ complex. The TBP solvent can form an explosive mixture called red oil when it comes in contact with nitric acid. The formation of this unstable organic phase originates from the reaction between TBP and its degradation products on the one hand, and nitric acid, its derivatives and heavy metal nitrate complexes on the other hand. The decomposition of the red oil can lead to violent explosive thermal runaway. These hazards are at the origin of several accidents such as the two in the United States in 1953 and 1975 (Savannah River) and, more recently, the one in Russia in 1993 (Tomsk). This raises the question of the exothermicity of reactions that involve TBP and all other degradation products, and calls for a better knowledge of the underlying chemical phenomena. A simulation tool (Alambic) is currently being developed at IRSN that integrates thermal and kinetic functions related to the deterioration of uranyl nitrates in organic and aqueous phases, but not of the n-butyl phosphate. To include them in the modeling scheme, there is an urgent need to obtain the thermodynamic and kinetic functions governing the deterioration processes in liquid phase. However, little is known about the thermodynamic properties, like standard enthalpies of formation, of the n-butyl phosphate molecules and of the UO₂(NO₃)₂(TBP)₂ UO₂(NO₃)₂(HDBP)(TBP) and UO₂(NO₃)₂(HDBP)₂ complexes. In this work, we propose to estimate the thermodynamic properties with Quantum Methods (QM). Thus, in the first part of our project, we focused on the mono, di, and tri-butyl complexes. Quantum chemical calculations have been performed to study several reactions leading to the formation of mono-(H₂MBP), di-(HDBP), and TBP in gas and liquid phases. In the gas phase, the optimal structures of all species were optimized using the B3LYP density functional. Triple-ζ def2-TZVP basis sets were used for all atoms. All geometries were optimized in the gas-phase, and the corresponding harmonic frequencies were used without scaling to compute the vibrational partition functions at 298.15 K and 0.1 Mpa. Accurate single point energies were calculated using the efficient localized LCCSD(T) method to the complete basis set limit. Whenever species in the liquid phase are considered, solvent effects are included with the COSMO-RS continuum model. The standard enthalpies of formation of TBP, HDBP, and H2MBP are finally predicted with an uncertainty of about 15 kJ mol⁻¹. In the second part of this project, we have investigated the fundamental properties of three organic species that mostly contribute to the thermal runaway: UO₂(NO₃)₂(TBP)₂, UO₂(NO₃)₂(HDBP)(TBP), and UO₂(NO₃)₂(HDBP)₂ using the same quantum chemical methods that were used for TBP and its derivatives in both the gas and the liquid phase. We will discuss the structures and thermodynamic properties of all these species.

Keywords: PUREX process, red oils, quantum chemical methods, hydrolysis

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Authors: Heba Ahmed Nawafleh

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In this study, two commercial resins were evaluated to concentrate uranium from real solutions that were produced from analkaline leaching process of carbonate deposits. The adsorption was examined using a batch process. Different parameters were evaluated, including initial pH, contact time, temperature, adsorbent dose, and finally, uranium initial concentration. Both resins were effective and selective for uranium ions from the tested leaching solution. The adsorption isotherms data were well fitted for both resins using the Langmuir model. Thermodynamic functions (Gibbs free energy change ΔG, enthalpy change ΔH, and entropy change ΔS) were calculated for the adsorption of uranium. The result shows that the adsorption process is endothermic, spontaneous, and chemisorption processes took place for both resins. The kinetic studies showed that the equilibrium time for uranium ions is about two hours, where the maximum uptake levels were achieved. The kinetics studies were carried out for the adsorption of U ions, and the data was found to follow pseudo-second-order kinetics, which indicates that the adsorption of U ions was chemically controlled. In addition, the reusability (adsorption/ desorption) process was tested for both resins for five cycles, these adsorbents maintained removal efficiency close to first cycle efficiency of about 91% and 80%.

Keywords: uranium, adsorption, ion exchange, thermodynamic and kinetic studies

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Authors: M. Zemouli, K. Amara, M. Elkeurti, Y. Benallou

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We present the molecular dynamic simulations results of the structural and dynamical properties of the zinc-blende GaBi over a wide range of temperature (300-1000) K. Our simulation where performed in the framework of the three-body Tersoff potential, which accurately reproduces the lattice constants and elastic constants of the GaBi. A good agreement was found between our calculated results and the available theoretical data of the lattice constant, the bulk modulus and the cohesive energy. Our study allows us to predict the thermodynamic properties such as the specific heat and the lattice thermal expansion. In addition, this method allows us to check its ability to predict the phase transition of this compound. In particular, the transition pressure to the rock-salt phase is calculated and the results are compared with other available works.

Keywords: Gallium compounds, molecular dynamics simulations, interatomic potential thermodynamic properties, structural phase transition

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Authors: Joe Hachem, Marianne Cuif-Sjostrand, Thierry Schuhler, Dominique Orhon, Assaad Zoughaib

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The exhaust gas recirculation, EGR, implementation on gas turbines is increasingly gaining the attention of many researchers. This emerging technology presents many advantages, such as lowering the NOx emissions and facilitating post-combustion carbon capture as the carbon dioxide concentration in the cycle increases. As interesting as this technology may seem, the gas turbine, or its thermodynamic equivalent, the Brayton cycle, shows an intrinsic efficiency decrease with increasing EGR rate. In this paper, a thermodynamic model is presented to show the cycle efficiency decrease with EGR, alternative values of design parameters of both the pressure ratio (PR) and the turbine inlet temperature (TIT) are then proposed to optimize the cycle efficiency with different EGR rates. Results show that depending on the given EGR rate, both the design PR & TIT should be increased to compensate for the deficit in efficiency.

Keywords: gas turbines, exhaust gas recirculation, design parameters optimization, thermodynamic approach

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Authors: Luiz F. J. Maia

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This paper presents an approach to fuzzy control, with the use of new pertinence functions, applied in the case of an inverted pendulum. Appropriate definitions of pertinence functions to fuzzy sets make possible the implementation of the controller with only one control rule, resulting in a smooth control surface. The fuzzy control system can be implemented with analog devices, affording a true real-time performance.

Keywords: control surface, fuzzy control, Inverted pendulum, pertinence functions

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Authors: Mohammad Mehdi Mazarei, Ali Asghar Behroozpoor

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In this paper, we define an optimization problem corresponding to smooth and nonsmooth functions which its optimal solution is the first derivative of these functions in a domain. For this purpose, a linear programming problem corresponding to optimization problem is obtained. The optimal solution of this linear programming problem is the approximate generalized first derivative. In fact, we approximate generalized first derivative of nonsmooth functions as tailor series. We show the efficiency of our approach by some smooth and nonsmooth functions in some examples.

Keywords: general derivative, linear programming, optimization problem, smooth and nonsmooth functions

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Authors: Mihir Mouchum Hazarika, Maddali Ramgopal, Souvik Bhattacharyya

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The thermodynamic analysis shows that the performance of the R744 based transcritical refrigeration cycle drops drastically for higher ambient temperatures. This is due to the peculiar s-shape of the isotherm in the supercritical region. However, subcooling of the refrigerant at the gas cooler exit enhances the performance of the R744 based system. The present study is carried out to analyze the R744 based transcritical system with dedicated mechanical subcooling cycle. Based on this proposed cycle, the thermodynamic analysis is performed, and optimum operating parameters are determined. The amount of subcooling and the pressure ratio in the subcooling cycle are the parameters which are needed to be optimized to extract the maximum COP from this proposed cycle. It is expected that this study will be helpful in implementing the dedicated subcooling cycle with R744 based transcritical system to improve the performance.

Keywords: optimization, R744, subcooling, transcritical

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Authors: N. Alhazmi

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Knowing the thermodynamics properties of hydrocarbons is vital when it comes to analyzing the related chemical reaction outcomes and understanding the reaction process, especially in terms of petrochemical industrial applications, combustions, and catalytic reactions. However, measuring the thermodynamics properties experimentally is time-consuming and costly. In this paper, Gaussian process regression (GPR) has been used to directly predict the main thermodynamic properties - standard enthalpy of formation, standard entropy, and heat capacity -for more than 360 cyclic and non-cyclic alkanes, alkenes, and alkynes. A simple workflow has been proposed that can be applied to directly predict the main properties of any hydrocarbon by knowing its descriptors and chemical structure and can be generalized to predict the main properties of any material. The model was evaluated by calculating the statistical error R², which was more than 0.9794 for all the predicted properties.

Keywords: thermodynamic, Gaussian process regression, hydrocarbons, regression, supervised learning, entropy, enthalpy, heat capacity

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Authors: Sujin Hong, Seokyoon Moon, Heejoong Kim, Yunseok Lee, Youngjune Park

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Gas hydrate is an inclusion compound in which a low-molecular-weight gas or organic molecule is trapped inside a three-dimensional lattice structure created by water-molecule via intermolecular hydrogen bonding. It is generally formed at low temperature and high pressure, and exists as crystal structures of cubic systems − structure I, structure II, and hexagonal system − structure H. Many efforts have been made to apply them to various energy and environmental fields such as gas transportation and storage, CO₂ capture and separation, and desalination of seawater. Particularly, studies on the behavior of gas hydrates by new organic materials for CO₂ storage and various applications are underway. In this study, thermodynamic and spectroscopic analyses of the gas hydrate system were performed focusing on cyclopentanol, an organic molecule that forms gas hydrate at relatively low pressure. The thermodynamic equilibria of CH₄ and CO₂ hydrate systems including cyclopentanol were measured and spectroscopic analyses of XRD and Raman were performed. The differences in thermodynamic systems and formation kinetics of CO₂ added cyclopentane, cyclopentanol and cyclopentanone hydrate systems were compared. From the thermodynamic point of view, cyclopentanol was found to be a hydrate promotor. Spectroscopic analyses showed that cyclopentanol formed a hydrate crystal structure of cubic structure II in the presence of CH₄ and CO₂. It was found that the differences in the functional groups among the organic guest molecules significantly affected the rate of hydrate formation and the total amounts of CO₂ stored in the hydrate systems. The total amount of CO₂ stored in the cyclopentanone hydrate was found to be twice that of the amount of CO₂ stored in the cyclopentane and the cyclopentanol hydrates. The findings are expected to open up new opportunity to develop the gas hydrate based wastewater desalination technology.

Keywords: gas hydrate, CO₂, separation, desalination, formation kinetics, thermodynamic equilibria

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Authors: Seok Hong Min, Tae Kwon Ha

Abstract:

With increasing demands for high performance materials, intensive interest on the Ti has been focused. Especially, low cost production process of Ti has been extremely necessitated from wide parts and various industries. Tetrachloride (TiCl₄) is produced by fluidized bed using high TiO₂ feedstock and used as an intermediate product for the production of metal titanium sponge. Reduction of TiCl₄ is usually conducted by Kroll process using magnesium as a reduction reagent, producing metallic Ti in the shape of sponge. The process is batch type and takes very long time including post processes treating sponge. As an alternative reduction reagent, hydrogen in the state of plasma has long been strongly recommended. Experimental confirmation has not been completely reported yet and more strict analysis is required. In the present study, hydrogen plasma reduction process has been thermodynamically analyzed focusing the effects of temperature, pressure and concentration. All thermodynamic calculations were performed using the FactSage® thermodynamical software.

Keywords: TiCl₄, titanium, hydrogen, plasma, reduction, thermodynamic calculation

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Authors: Jeni A. Popescu, Ionut Porumbel, Valeriu A. Vilag, Cleopatra F. Cuciumita

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The paper presents a thermodynamic cycle analysis for three turboshaft engines. The first is the cycle is a Brayton cycle, describing the evolution of a classical turboshaft, based on the Klimov TV2 engine. The other two cycles aim at approaching an Ericsson cycle, by replacing the Brayton cycle adiabatic expansion in the turbine by quasi-isothermal expansion. The maximum quasi-Ericsson cycles temperature is set to a lower value than the maximum Brayton cycle temperature, equal to the Brayton cycle power turbine inlet temperature, in order to decrease the engine NOx emissions. Also, the power distribution over the stages of the gas generator turbine is maintained the same. In the first of the two considered quasi-Ericsson cycle, the efficiencies of the gas generator turbine stage. Also, the power distribution over the stages of the gas generator turbine is maintained the same. In the first of the two considered quasi-Ericsson cycle, the efficiencies of the gas generator turbine stages are maintained the same as for the reference case, while for the second, the efficiencies are increased in order to obtain the same shaft power as in the reference case. It is found that in the first case, both the shaft power and the thermodynamic efficiency of the engine decrease, while in the second, the power is maintained, and even a slight increase in efficiency can be noted.

Keywords: combustion, Ericsson, thermodynamic analysis, turbine

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Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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The Bessel function J₀(x) is very important in Electrodynamics and Physics, as well as its zeros. In this work, a method to obtain high accuracy approximation is presented through an application to that function. In most of the applications of this function, the values of the zeros are very important. In this work, analytic approximations for this function have been obtained valid for all positive values of the variable x, which have high accuracy for the function as well as for the zeros. The approximation is determined by the simultaneous used of the power series and asymptotic expansion. The structure of the approximation is a combination of two rational functions with elementary functions as trigonometric and fractional powers. Here us in Pade method, rational functions are used, but now there combined with elementary functions us fractional powers hyperbolic or trigonometric functions, and others. The reason of this is that now power series of the exact function are used, but together with the asymptotic expansion, which usually includes fractional powers trigonometric functions and other type of elementary functions. The approximation must be a bridge between both expansions, and this can not be accomplished using only with rational functions. In the simplest approximation using 4 parameters the maximum absolute error is less than 0.006 at x ∼ 4.9. In this case also the maximum relative error for the zeros is less than 0.003 which is for the second zero, but that value decreases rapidly for the other zeros. The same kind of behaviour happens for the relative error of the maximum and minimum of the functions. Approximations with higher accuracy and more parameters will be also shown. All the approximations are valid for any positive value of x, and they can be calculated easily.

Keywords: analytic approximations, asymptotic approximations, Bessel functions, quasirational approximations

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Authors: Priestly Malambo, Sonja Van Putten, Hanlie Botha, Gerrit Stols

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The relevance of what is content is taught in tertiary teacher training has long been in question. This study attempts to understand how advanced mathematics courses equip student teachers to teach functions at secondary school level. This paper reports on an investigation that was conducted in an African university, where preservice teachers were purposefully selected for participation in individual semi-structured interviews after completing a test on functions as taught at secondary school. They were asked to justify their reasoning in the test and to explain functions in a way that might bring about understanding of the topic in someone who did not know how functions work. These were final year preservice mathematics teachers who had studied advanced mathematics courses for three years. More than 50% of the students were not able to explain concepts or to justify their reasoning about secondary school functions in a coherent way. The results of this study suggest that the study of advanced mathematics does not automatically enable students to teach secondary school functions, and that, although these students were able to do advanced mathematics, they were unable to explain the working of functions in a way that would allow them to teach this topic successfully.

Keywords: secondary school, mathematical reasoning, student-teachers, functions

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Authors: Thulane Paepae, Tumisang Seodigeng

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This paper demonstrates the use of a method of synthesizing process flowsheets using a graphical tool called the GH-plot and in particular, to look at how it can be used to compare the reactions of a combined simultaneous process with regard to their thermodynamics. The technique uses fundamental thermodynamic principles to allow the mass, energy and work balances locate the attainable region for chemical processes in a reactor. This provides guidance on what design decisions would be best suited to developing new processes that are more effective and make lower demands on raw material and energy usage.

Keywords: attainable regions, dimethyl ether, optimal reaction network, GH Space

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Authors: Yilmaz Simsek

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In this paper, we study the Bernstein-type basis functions with their generating functions. We give various properties of these polynomials with the aid of their generating functions. These polynomials and generating functions have many valuable applications in mathematics, in probability, in statistics and also in mathematical physics. By using the Bernstein-Galerkin and the Bernstein-Petrov-Galerkin methods, we give some applications of the Bernstein-type polynomials for solving high even-order differential equations with their numerical computations. We also give Bezier-type curves related to the Bernstein-type basis functions. We investigate fundamental properties of these curves. These curves have many applications in mathematics, in computer geometric design and other related areas. Moreover, we simulate these polynomials with their plots for some selected numerical values.

Keywords: generating functions, Bernstein basis functions, Bernstein polynomials, Bezier curves, differential equations

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Authors: Paola Utreras, Yazmina Olmos, Loreto Sanhueza

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This work shows how the learning of physics is enriched with scientific inquiry practices, achieving learning that results in the use of higher-level cognitive skills. The activities, which were carried out with students of the 3rd semester of the courses of the Faculty of Sciences of the Engineering of the Austral University of Chile, focused on the understanding of the nature of the thermodynamic variables and how they relate to each other. This, through the analysis of atmospheric data obtained in the meteorological station Miraflores, located on the campus. The proposed activities consisted of the elaboration of time series, linear analysis of variables, as well as the analysis of frequencies and periods. From their results, the students reached conclusions associated with the nature of the thermodynamic variables studied and the relationships between them, to finally make public their results in a report using scientific writing standards. It is observed that introducing topics that are close to them, interesting and which affect their daily lives allows a better understanding of the subjects, which is reflected in higher levels of approval and motivation for the subject.

Keywords: basic sciences, inquiry-based learning, scientific inquiry, thermodynamics

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Authors: Hai Hoang, Thanh Xuan Nguyen Thi, Guillaume Galliero

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Coarse-Grained (CG) molecular simulations have shown to be an efficient way to estimate thermophysical (static and dynamic) properties of fluids. Several strategies have been developed and reported in the literature for defining CG molecular models. Among them, those based on a top-down strategy (i.e. CG molecular models related to macroscopic observables), despite being heuristic, have increasingly gained attention. This is probably due to its simplicity in implementation and its ability to provide reasonable results for not only simple but also complex systems. Regarding simple Force-Fields associated with these CG molecular models, it has been found that the four parameters Mie chain model is one of the best compromises to describe thermophysical static properties (e.g. phase diagram, saturation pressure). However, parameterization procedures of these Mie-chain GC molecular models given in literature are generally insufficient to simultaneously provide static and dynamic (e.g. viscosity) properties. To deal with such situations, we have extended the corresponding states by using a quantity associated with the liquid viscosity. Results obtained from molecular simulations have shown that our approach is able to yield good estimates for both static and dynamic thermophysical properties for various real non-associating fluids. In addition, we will show that on simple (e.g. phase diagram, saturation pressure) and complex (e.g. thermodynamic response functions, thermodynamic energy potentials) static properties, results of our scheme generally provides improved results compared to existing approaches.

Keywords: coarse-grained model, mie potential, molecular simulations, thermophysical properties, phase equilibria

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

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Authors: Haoshu Li, Shaolong Wan

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The recent focus has been on directional signal amplification of a signal input at one end of a one-dimensional chain and measured at the other end. The amplification rate is given by the end-to-end Green’s functions of the system. In this work, we derive the exact formulas for the end-to-end Green's functions of non-Hermitian single-band systems. While in the bulk region, it is found that the Green's functions are displaced from the prior established integral formula by O(e⁻ᵇᴸ). The results confirm the correspondence between the signal amplification and the non-Hermitian skin effect.

Keywords: non-Hermitian, Green's function, non-Hermitian skin effect, signal amplification

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Authors: Kassim A. Jassim

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In the present paper, we introduce and discuss a new class Kp(λ,α) of meromorphic multivalent functions in the punctured unit disk U*={z∈¢:0<|z|<1} defined by Ruscheweyh derivative. We obtain some sufficient conditions for the functions belonging to the class Kp(λ,α).

Keywords: meromorphic multivalent function, Ruscheweyh derivative, hadamard product

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Authors: Sabrina Ladjama, Aicha Rizi, Azzedine Abbaci

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In this work, we use the crossover model to formulate a comprehensive fundamental equation of state for the thermodynamic properties for several n-alkanes in the critical region that extends to the classical region. This equation of state is constructed on the basis of comparison of selected measurements of pressure-density-temperature data, isochoric and isobaric heat capacity. The model can be applied in a wide range of temperatures and densities around the critical point for n-heptane. It is found that the developed model represents most of the reliable experimental data accurately.

Keywords: crossover model, critical region, fundamental equation, n-heptane

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

Abstract:

Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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