Modelling of Thermodynamic Pressure – Composition – Temperature Relationships in the Systems of Metallic Hydride Forming Materials with Gaseous Hydrogen Using C++ Software

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Mapula Lucey Moropeng ◽  
Andrei Kolesnikov ◽  
Mykhaylo Lototskyy ◽  
Avhafunani Mavhungu
Keyword(s):  
Nonlinear Equation ◽  
Hydrogen Storage ◽  
Numerical Method ◽  
Metal Hydride ◽  
Metal Hydrides ◽  
Gaseous Hydrogen ◽  
Newton Raphson ◽  
Thermodynamic Pressure ◽  
The Relationship ◽  
Raphson Method

Abstract In this paper, the solution of the Lacher model describing the relationship between the Pressure – Composition, and Temperature (PCT diagrams) of AB5 type metal-hydrides (LaNi4.8Sn0.2, LmNi4.91Sn0.15, LaNi4.5Al0.5) for hydrogen storage using C ++ platform, with the help of a numerical method of nonlinear equation, Newton-Raphson method is presented. This study focuses on the development of a C ++ code to describe the iteration of Newton-Raphson for application in Hydrogen to Metal-Hydride systems.

ASYMPTOTIC NUMERICAL METHOD FOR THE DYNAMIC STUDY OF NONLINEAR VIBRATION ABSORBERS

2014 ◽  
Vol 06 (05) ◽  
pp. 1450053 ◽  
Author(s):  
FATHI DJEMAL ◽  
FAKHER CHAARI ◽  
JEAN LUC DION ◽  
FRANCK RENAUD ◽  
IMAD TAWFIQ ◽  
...  
Keyword(s):  
Nonlinear Equation ◽  
Vibration Control ◽  
Numerical Method ◽  
Nonlinear Vibration ◽  
Degrees Of Freedom ◽  
Equation Of Motion ◽  
Vibration Absorbers ◽  
Asymptotic Numerical Method ◽  
Dynamic Absorber ◽  
Newton Raphson

Vibrations are usually undesired phenomena as they may cause discomfort, disturbance, damage, and sometimes destruction of machines and structures. It must be reduced or controlled or eliminated. One of the most common methods of vibration control is the use of the dynamic absorber. The paper is interested in the study of a nonlinear two degrees of freedom (DOF) model. To solve nonlinear equation of motion a high order implicit algorithm is proposed. It is based on the introduction of a homotopy, an implicit scheme of Newmark and the use of techniques of Asymptotic Numerical method (ANM). We propose also a regularization of the contact force to overcome the difficulty of the singularity in this model. A comparison will be presented between the results obtained by the proposed algorithm and those using the classical Newton–Raphson and Newmark time scheme.

scholarly journals Hydrogen storage in complex metal hydrides

2009 ◽  
Vol 74 (2) ◽  
pp. 183-196 ◽  
Author(s):  
Borislav Bogdanovic ◽  
Michael Felderhoff ◽  
Guido Streukens
Keyword(s):  
Fuel Cells ◽  
Solid State ◽  
Thermodynamic Properties ◽  
Hydrogen Storage ◽  
Sodium Borohydride ◽  
Metal Hydride ◽  
Metal Hydrides ◽  
Hydrogen Storage Materials ◽  
High Hydrogen ◽  
Complex Metal

Complex metal hydrides such as sodium aluminohydride (NaAlH4) and sodium borohydride (NaBH4) are solid-state hydrogen-storage materials with high hydrogen capacities. They can be used in combination with fuel cells as a hydrogen source thus enabling longer operation times compared with classical metal hydrides. The most important point for a wide application of these materials is the reversibility under moderate technical conditions. At present, only NaAlH4 has favorable thermodynamic properties and can be employed as a thermally reversible means of hydrogen storage. By contrast, NaBH4 is a typical non-reversible complex metal hydride; it reacts with water to produce hydrogen.

scholarly journals Numerical Solution of Nonlinear Equations in Maple

2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Qani Yalda
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Secant Method ◽  
Bisection Method ◽  
Real Roots ◽  
Newton Raphson ◽  
Root Analysis ◽  
Raphson Method

The main purpose of this paper is to obtain the real roots of an expression using the Numerical method, bisection method, Newton's method and secant method. Root analysis is calculated using specific, precise starting points and numerical methods and is represented by Maple. In this research, we used Maple software to analyze the roots of nonlinear equations by special methods, and by showing geometric diagrams, we examined the relevant examples. In this process, the Newton-Raphson method, the algorithm for root access, is fully illustrated by Maple. Also, the secant method and the bisection method were demonstrated by Maple by solving examples and drawing graphs related to each method.

THERMODYNAMIC CALCULATION OF n-COMPONENT EUTECTIC MIXTURES

2004 ◽  
Vol 15 (05) ◽  
pp. 675-687 ◽  
Author(s):  
L. BRUNET ◽  
J. CAILLARD ◽  
P. ANDRÉ
Keyword(s):  
Organic Compound ◽  
Numerical Method ◽  
Melting Temperature ◽  
Nonlinear Problem ◽  
Thermodynamic Calculation ◽  
Eutectic Mixture ◽  
Organic Mixtures ◽  
Eutectic Mixtures ◽  
Newton Raphson ◽  
Raphson Method

This paper presents a simple numerical method to calculate the eutectic mixture composition and melting temperature. Using a Newton–Raphson method to solve the nonlinear problem, the calculation is possible for n-component eutectic. We tested this algorithm on inorganic and organic mixtures. A better correlation between experimental and numerical results has been found for organic compound.

Numerical Simulation of Dynamically Loaded Flexible Short Journal Bearings

1985 ◽  
Vol 107 (3) ◽  
pp. 396-401 ◽  
Author(s):  
L. van der Tempel ◽  
H. Moes ◽  
R. Bosma
Keyword(s):  
Numerical Simulation ◽  
Differential Equations ◽  
Numerical Method ◽  
Dynamic Load ◽  
High Speed ◽  
Journal Bearings ◽  
Combustion Engines ◽  
Dynamically Loaded ◽  
Newton Raphson ◽  
Raphson Method

A numerical method is proposed for calculating film thicknesses in flexible short journal bearings under dynamic load. The system of elastohydrodynamic integro-differential equations is discretized directly and solved by a 2-step Newton-Raphson method. The cavitation boundaries are located by a special discretization of the pressure. This type of condition puts practically no restrictions on the boundary alterations. The results for the con rod bearings of medium- and high-speed combustion engines are compared.

scholarly journals Perbandingan Metode Newton-Raphson & Metode Secant Untuk Mencari Akar Persamaan Dalam Sistem Persamaan Non-Linier

Petir ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 72-79
Author(s):  
Endang Sunandar ◽  
Indrianto Indrianto
Keyword(s):  
Linear Equation ◽  
Numerical Method ◽  
Equation System ◽  
Elimination Method ◽  
Non Linear Equation ◽  
Linear Equation System ◽  
Non Linear ◽  
Mathematical Problems ◽  
Newton Raphson ◽  
Raphson Method

The numerical method is a technique used to formulate mathematical problems so that it can be solved using ordinary arithmetic operations. In general, numerical methods are used to solve mathematical problems that cannot be solved by ordinary analytic methods. In the Numerical Method, we recognize two types of systems of equations, namely the Linear Equation System and the Non-Linear Equation System. Each system of equations has several methods. In the Linear Equation System between methods is the Gauss Elimination method, the Gauss-Jordan Elimination method, the LU (Lower-Upper) Decomposition method. And for Non-Linear Equation Systems between the methods are the Bisection method, the Regula Falsi method, the Newton Raphson method, the Secant method, and the Fix Iteration method. In this study, researchers are interested in analyzing 2 methods in the Non-Linear Equation System, the Newton-Raphson method and the Secant method. And this analysis process uses the Java programming language tools, this is to facilitate the analysis of method completion algorithm, and monitoring in terms of execution time and analysis of output results. So we can clearly know the difference between what happens between the two methods.

Transient Plane Source Method for Thermal Property Measurements of Metal Hydrides

2008 ◽  
Author(s):  
Scott Flueckiger ◽  
Yuan Zheng ◽  
Timothe´e Pourpoint
Keyword(s):  
Thermal Conductivity ◽  
Stainless Steel ◽  
Thermal Diffusivity ◽  
Hydrogen Storage ◽  
Thermal Property ◽  
Metal Hydride ◽  
Metal Hydrides ◽  
Flash Method ◽  
Plane Source ◽  
Transient Plane Source

Metal hydrides are promising hydrogen storage materials with potential for practical use in a passenger car. To be a viable hydrogen storage option, metal hydride heat transfer behavior must be well understood and accounted for. As such, the thermal properties of the metal hydride are measured and compiled to assess this behavior. These properties include thermal conductivity, specific heat, and thermal diffusivity. The transient plane source (TPS) method was selected primarily due to a high level of versatility, including customization for high pressure hydrogen environments. To perform this measurement, a TPS 2500 S thermal property analyzer by the Hot Disk Company was employed. To understand the measurement and analysis process of the TPS method, two different sample materials were evaluated at ambient conditions. These samples included a stainless steel pellet and an inactivated (non-pyrophoric) metal hydride pellet. Thermal conductivity and thermal diffusivity of these samples were measured using the TPS method. The thermal property measurements are compared to the data available in the literature (stainless steel) and the data obtained using laser flash method (metal hydride). The improvements needed to successfully implement the TPS method are discussed in detail.

scholarly journals An experimental high temperature thermal battery coupled to a low temperature metal hydride for solar thermal energy storage

2020 ◽  
Vol 4 (1) ◽  
pp. 285-292 ◽  
Author(s):  
Lucas Poupin ◽  
Terry D. Humphries ◽  
Mark Paskevicius ◽  
Craig E. Buckley
Keyword(s):  
High Temperature ◽  
Energy Storage ◽  
Low Temperature ◽  
Thermal Energy ◽  
Thermal Energy Storage ◽  
Metal Hydride ◽  
Metal Hydrides ◽  
Gaseous Hydrogen ◽  
Solar Thermal Energy ◽  
Thermal Battery

Cycling of a high temperature thermal battery using a pair of metal hydrides to store thermal energy and the associated evolved gaseous hydrogen.

scholarly journals Quadratic Convergence Iterative Algorithms of Taylor Series for Solving Non-linear Equations

2020 ◽  
Vol 18 (02) ◽  
pp. 150-156
Author(s):  
Umair Khalid Qureshi ◽  
Zubair Ahmed Kalhoro ◽  
Rajab Ali Malookani ◽  
Sanaullah Dehraj ◽  
Shahid Hussain Siyal ◽  
...  
Keyword(s):  
Nonlinear Equation ◽  
Quadratic Convergence ◽  
Linear Equations ◽  
Classical Problem ◽  
Iterative Algorithms ◽  
Initial Guess ◽  
Single Root ◽  
Newton Raphson ◽  
Steffensen Method ◽  
Raphson Method

Solving the root of algebraic and transcendental nonlinear equation f' (x) = 0 is a classical problem which has many interesting applications in computational mathematics and various branches of science and engineering. This paper examines the quadratic convergence iterative algorithms for solving a single root nonlinear equation which depends on the Taylor’s series and backward difference method. It is shown that the proposed iterative algorithms converge quadratically. In order to justify the results and graphs of quadratic convergence iterative algorithms, C++/MATLAB and EXCELL are used. The efficiency of the proposed iterative algorithms in comparison with Newton Raphson method and Steffensen method is illustrated via examples. Newton Raphson method fails if f' (x) = 0, whereas Steffensen method fails if the initial guess is not close enough to the actual solution. Furthermore, there are several other numerical methods which contain drawbacks and possess large number of evolution; however, the developed iterated algorithms are good in these conditions. It is found out that the quadratic convergence iterative algorithms are good achievement in the field of research for computing a single root of nonlinear equations.

scholarly journals On the Modification of Newton-Secant Method in Solving Nonlinear Equations for Multiple Zeros of Trigonometric Function

CAUCHY ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 84-96
Author(s):  
Juhari Juhari
Keyword(s):  
Mathematical Model ◽  
Nonlinear Equation ◽  
Nonlinear Equations ◽  
Trigonometric Function ◽  
Secant Method ◽  
Second Step ◽  
Initial Values ◽  
Newton Raphson ◽  
Modified Formula ◽  
Raphson Method

This study discusses the analysis of the modification of Newton-Secant method and solving nonlinear equations having a multiplicity of  by using a modified Newton-Secant method. A nonlinear equation that has a multiplicity   is an equation that has more than one root. The first step is to analyze the modification of the Newton-Secant method, namely to construct a mathematical model of the Newton-Secant method using the concept of the Newton method and the concept of the Secant method. The second step is to construct a modified mathematical model of the Newton-Secant method by adding the parameter . After obtaining the modified formula for the Newton-Secant method, then applying the method to solve a nonlinear equations that have a multiplicity . In this case, it is applied to the nonlinear equation which has a multiplicity of . The solution is done by selecting two different initial values, namely  and . Furthermore, to determine the effectivity of this method, the researcher compared the result with the Newton-Raphson method, the Secant method, and the Newton-Secant method that has not been modified. The obtained results from the analysis of modification of Newton-Secant method is an iteration formula of the modified Newton-Secant method. And for the result of  using a modified Newton-Secant method with two different initial values, the root of  is obtained approximately, namely  with less than iterations. whereas when using the Newton-Raphson method, the Secant method, and the Newton-Secant method, the root  is also approximated, namely  with more than  iterations. Based on the problem to find the root of the nonlinear equation  it can be concluded that the modified Newton-Secant method is more effective than the Newton-Raphson method, the Secant method, and the Newton-Secant method that has not been modified

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